9"""Z3 is a high performance theorem prover developed at Microsoft Research.
11Z3 is used in many applications such as: software/hardware verification and testing,
12constraint solving, analysis of hybrid systems, security, biology (in silico analysis),
13and geometrical problems.
16Please send feedback, comments and/or corrections on the Issue tracker for
17https://github.com/Z3prover/z3.git. Your comments are very valuable.
38... x = BitVec('x', 32)
40... # the expression x + y is type incorrect
42... except Z3Exception as ex:
43... print("failed: %s" % ex)
49from .z3consts
import *
50from .z3printer
import *
51from fractions
import Fraction
56if sys.version_info.major >= 3:
57 from typing
import Iterable
67if sys.version_info.major < 3:
69 return isinstance(v, (int, long))
72 return isinstance(v, int)
84 major = ctypes.c_uint(0)
85 minor = ctypes.c_uint(0)
86 build = ctypes.c_uint(0)
87 rev = ctypes.c_uint(0)
89 return "%s.%s.%s" % (major.value, minor.value, build.value)
93 major = ctypes.c_uint(0)
94 minor = ctypes.c_uint(0)
95 build = ctypes.c_uint(0)
96 rev = ctypes.c_uint(0)
98 return (major.value, minor.value, build.value, rev.value)
107 raise Z3Exception(msg)
111 _z3_assert(ctypes.c_int(n).value == n, name +
" is too large")
115 """Log interaction to a file. This function must be invoked immediately after init(). """
120 """Append user-defined string to interaction log. """
125 """Convert an integer or string into a Z3 symbol."""
133 """Convert a Z3 symbol back into a Python object. """
146 if len(args) == 1
and (isinstance(args[0], tuple)
or isinstance(args[0], list)):
148 elif len(args) == 1
and (isinstance(args[0], set)
or isinstance(args[0], AstVector)):
149 return [arg
for arg
in args[0]]
160 if isinstance(args, (set, AstVector, tuple)):
161 return [arg
for arg
in args]
169 if isinstance(val, bool):
170 return "true" if val
else "false"
181 """A Context manages all other Z3 objects, global configuration options, etc.
183 Z3Py uses a default global context. For most applications this is sufficient.
184 An application may use multiple Z3 contexts. Objects created in one context
185 cannot be used in another one. However, several objects may be "translated" from
186 one context to another. It is not safe to access Z3 objects from multiple threads.
187 The only exception is the method `interrupt()` that can be used to interrupt() a long
189 The initialization method receives global configuration options for the new context.
194 _z3_assert(len(args) % 2 == 0,
"Argument list must have an even number of elements.")
213 if Z3_del_context
is not None and self.
owner:
219 """Return a reference to the actual C pointer to the Z3 context."""
223 """Interrupt a solver performing a satisfiability test, a tactic processing a goal, or simplify functions.
225 This method can be invoked from a thread different from the one executing the
226 interruptible procedure.
231 """Return the global parameter description set."""
240 """Return a reference to the global Z3 context.
243 >>> x.ctx == main_ctx()
248 >>> x2 = Real('x', c)
255 if _main_ctx
is None:
272 """Set Z3 global (or module) parameters.
274 >>> set_param(precision=10)
277 _z3_assert(len(args) % 2 == 0,
"Argument list must have an even number of elements.")
281 if not set_pp_option(k, v):
296 """Reset all global (or module) parameters.
302 """Alias for 'set_param' for backward compatibility.
308 """Return the value of a Z3 global (or module) parameter
310 >>> get_param('nlsat.reorder')
313 ptr = (ctypes.c_char_p * 1)()
315 r = z3core._to_pystr(ptr[0])
317 raise Z3Exception(
"failed to retrieve value for '%s'" % name)
329 """Superclass for all Z3 objects that have support for pretty printing."""
335 in_html = in_html_mode()
338 set_html_mode(in_html)
343 """AST are Direct Acyclic Graphs (DAGs) used to represent sorts, declarations and expressions."""
351 if self.
ctx.ref()
is not None and self.
ast is not None and Z3_dec_ref
is not None:
359 return obj_to_string(self)
362 return obj_to_string(self)
365 return self.
eq(other)
378 elif is_eq(self)
and self.num_args() == 2:
379 return self.arg(0).
eq(self.arg(1))
381 raise Z3Exception(
"Symbolic expressions cannot be cast to concrete Boolean values.")
384 """Return a string representing the AST node in s-expression notation.
387 >>> ((x + 1)*x).sexpr()
393 """Return a pointer to the corresponding C Z3_ast object."""
397 """Return unique identifier for object. It can be used for hash-tables and maps."""
401 """Return a reference to the C context where this AST node is stored."""
402 return self.
ctx.ref()
405 """Return `True` if `self` and `other` are structurally identical.
412 >>> n1 = simplify(n1)
413 >>> n2 = simplify(n2)
422 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
428 >>> # Nodes in different contexts can't be mixed.
429 >>> # However, we can translate nodes from one context to another.
430 >>> x.translate(c2) + y
434 _z3_assert(isinstance(target, Context),
"argument must be a Z3 context")
441 """Return a hashcode for the `self`.
443 >>> n1 = simplify(Int('x') + 1)
444 >>> n2 = simplify(2 + Int('x') - 1)
445 >>> n1.hash() == n2.hash()
452 """Return `True` if `a` is an AST node.
456 >>> is_ast(IntVal(10))
460 >>> is_ast(BoolSort())
462 >>> is_ast(Function('f', IntSort(), IntSort()))
469 return isinstance(a, AstRef)
473 """Return `True` if `a` and `b` are structurally identical AST nodes.
483 >>> eq(simplify(x + 1), simplify(1 + x))
517 _args = (FuncDecl * sz)()
519 _args[i] = args[i].as_func_decl()
527 _args[i] = args[i].as_ast()
535 _args[i] = args[i].as_ast()
543 elif k == Z3_FUNC_DECL_AST:
560 """A Sort is essentially a type. Every Z3 expression has a sort. A sort is an AST node."""
569 """Return the Z3 internal kind of a sort.
570 This method can be used to test if `self` is one of the Z3 builtin sorts.
573 >>> b.kind() == Z3_BOOL_SORT
575 >>> b.kind() == Z3_INT_SORT
577 >>> A = ArraySort(IntSort(), IntSort())
578 >>> A.kind() == Z3_ARRAY_SORT
580 >>> A.kind() == Z3_INT_SORT
586 """Return `True` if `self` is a subsort of `other`.
588 >>> IntSort().subsort(RealSort())
594 """Try to cast `val` as an element of sort `self`.
596 This method is used in Z3Py to convert Python objects such as integers,
597 floats, longs and strings into Z3 expressions.
600 >>> RealSort().cast(x)
609 """Return the name (string) of sort `self`.
611 >>> BoolSort().name()
613 >>> ArraySort(IntSort(), IntSort()).name()
619 """Return `True` if `self` and `other` are the same Z3 sort.
622 >>> p.sort() == BoolSort()
624 >>> p.sort() == IntSort()
632 """Return `True` if `self` and `other` are not the same Z3 sort.
635 >>> p.sort() != BoolSort()
637 >>> p.sort() != IntSort()
644 return AstRef.__hash__(self)
648 """Return `True` if `s` is a Z3 sort.
650 >>> is_sort(IntSort())
652 >>> is_sort(Int('x'))
654 >>> is_expr(Int('x'))
657 return isinstance(s, SortRef)
662 _z3_assert(isinstance(s, Sort),
"Z3 Sort expected")
664 if k == Z3_BOOL_SORT:
666 elif k == Z3_INT_SORT
or k == Z3_REAL_SORT:
668 elif k == Z3_BV_SORT:
670 elif k == Z3_ARRAY_SORT:
672 elif k == Z3_DATATYPE_SORT:
674 elif k == Z3_FINITE_DOMAIN_SORT:
676 elif k == Z3_FLOATING_POINT_SORT:
678 elif k == Z3_ROUNDING_MODE_SORT:
680 elif k == Z3_RE_SORT:
682 elif k == Z3_SEQ_SORT:
684 elif k == Z3_CHAR_SORT:
694 """Create a new uninterpreted sort named `name`.
696 If `ctx=None`, then the new sort is declared in the global Z3Py context.
698 >>> A = DeclareSort('A')
699 >>> a = Const('a', A)
700 >>> b = Const('b', A)
719 """Function declaration. Every constant and function have an associated declaration.
721 The declaration assigns a name, a sort (i.e., type), and for function
722 the sort (i.e., type) of each of its arguments. Note that, in Z3,
723 a constant is a function with 0 arguments.
736 """Return the name of the function declaration `self`.
738 >>> f = Function('f', IntSort(), IntSort())
741 >>> isinstance(f.name(), str)
747 """Return the number of arguments of a function declaration.
748 If `self` is a constant, then `self.arity()` is 0.
750 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
757 """Return the sort of the argument `i` of a function declaration.
758 This method assumes that `0 <= i < self.arity()`.
760 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
769 """Return the sort of the range of a function declaration.
770 For constants, this is the sort of the constant.
772 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
779 """Return the internal kind of a function declaration.
780 It can be used to identify Z3 built-in functions such as addition, multiplication, etc.
783 >>> d = (x + 1).decl()
784 >>> d.kind() == Z3_OP_ADD
786 >>> d.kind() == Z3_OP_MUL
794 result = [
None for i
in range(n)]
797 if k == Z3_PARAMETER_INT:
799 elif k == Z3_PARAMETER_DOUBLE:
801 elif k == Z3_PARAMETER_RATIONAL:
803 elif k == Z3_PARAMETER_SYMBOL:
805 elif k == Z3_PARAMETER_SORT:
807 elif k == Z3_PARAMETER_AST:
809 elif k == Z3_PARAMETER_FUNC_DECL:
816 """Create a Z3 application expression using the function `self`, and the given arguments.
818 The arguments must be Z3 expressions. This method assumes that
819 the sorts of the elements in `args` match the sorts of the
820 domain. Limited coercion is supported. For example, if
821 args[0] is a Python integer, and the function expects a Z3
822 integer, then the argument is automatically converted into a
825 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
835 _args = (Ast * num)()
840 tmp = self.
domain(i).cast(args[i])
842 _args[i] = tmp.as_ast()
847 """Return `True` if `a` is a Z3 function declaration.
849 >>> f = Function('f', IntSort(), IntSort())
856 return isinstance(a, FuncDeclRef)
860 """Create a new Z3 uninterpreted function with the given sorts.
862 >>> f = Function('f', IntSort(), IntSort())
868 _z3_assert(len(sig) > 0,
"At least two arguments expected")
873 dom = (Sort * arity)()
874 for i
in range(arity):
883 """Create a new fresh Z3 uninterpreted function with the given sorts.
887 _z3_assert(len(sig) > 0,
"At least two arguments expected")
892 dom = (z3.Sort * arity)()
893 for i
in range(arity):
906 """Create a new Z3 recursive with the given sorts."""
909 _z3_assert(len(sig) > 0,
"At least two arguments expected")
914 dom = (Sort * arity)()
915 for i
in range(arity):
924 """Set the body of a recursive function.
925 Recursive definitions can be simplified if they are applied to ground
928 >>> fac = RecFunction('fac', IntSort(ctx), IntSort(ctx))
929 >>> n = Int('n', ctx)
930 >>> RecAddDefinition(fac, n, If(n == 0, 1, n*fac(n-1)))
933 >>> s = Solver(ctx=ctx)
934 >>> s.add(fac(n) < 3)
937 >>> s.model().eval(fac(5))
947 _args[i] = args[i].ast
958 """Constraints, formulas and terms are expressions in Z3.
960 Expressions are ASTs. Every expression has a sort.
961 There are three main kinds of expressions:
962 function applications, quantifiers and bounded variables.
963 A constant is a function application with 0 arguments.
964 For quantifier free problems, all expressions are
965 function applications.
975 """Return the sort of expression `self`.
987 """Shorthand for `self.sort().kind()`.
989 >>> a = Array('a', IntSort(), IntSort())
990 >>> a.sort_kind() == Z3_ARRAY_SORT
992 >>> a.sort_kind() == Z3_INT_SORT
995 return self.
sort().kind()
998 """Return a Z3 expression that represents the constraint `self == other`.
1000 If `other` is `None`, then this method simply returns `False`.
1016 return AstRef.__hash__(self)
1019 """Return a Z3 expression that represents the constraint `self != other`.
1021 If `other` is `None`, then this method simply returns `True`.
1040 """Return the Z3 function declaration associated with a Z3 application.
1042 >>> f = Function('f', IntSort(), IntSort())
1055 """Return the number of arguments of a Z3 application.
1059 >>> (a + b).num_args()
1061 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1071 """Return argument `idx` of the application `self`.
1073 This method assumes that `self` is a function application with at least `idx+1` arguments.
1077 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1092 """Return a list containing the children of the given expression
1096 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1102 return [self.
arg(i)
for i
in range(self.
num_args())]
1116 """inverse function to the serialize method on ExprRef.
1117 It is made available to make it easier for users to serialize expressions back and forth between
1118 strings. Solvers can be serialized using the 'sexpr()' method.
1122 if len(s.assertions()) != 1:
1123 raise Z3Exception(
"single assertion expected")
1124 fml = s.assertions()[0]
1125 if fml.num_args() != 1:
1126 raise Z3Exception(
"dummy function 'F' expected")
1130 if isinstance(a, Pattern):
1134 if k == Z3_QUANTIFIER_AST:
1137 if sk == Z3_BOOL_SORT:
1139 if sk == Z3_INT_SORT:
1140 if k == Z3_NUMERAL_AST:
1143 if sk == Z3_REAL_SORT:
1144 if k == Z3_NUMERAL_AST:
1149 if sk == Z3_BV_SORT:
1150 if k == Z3_NUMERAL_AST:
1154 if sk == Z3_ARRAY_SORT:
1156 if sk == Z3_DATATYPE_SORT:
1158 if sk == Z3_FLOATING_POINT_SORT:
1162 return FPRef(a, ctx)
1163 if sk == Z3_FINITE_DOMAIN_SORT:
1164 if k == Z3_NUMERAL_AST:
1168 if sk == Z3_ROUNDING_MODE_SORT:
1170 if sk == Z3_SEQ_SORT:
1172 if sk == Z3_CHAR_SORT:
1174 if sk == Z3_RE_SORT:
1175 return ReRef(a, ctx)
1192 _z3_assert(s1.ctx == s.ctx,
"context mismatch")
1202 if isinstance(a, str)
and isinstance(b, SeqRef):
1204 if isinstance(b, str)
and isinstance(a, SeqRef):
1206 if isinstance(a, float)
and isinstance(b, ArithRef):
1208 if isinstance(b, float)
and isinstance(a, ArithRef):
1221 for element
in sequence:
1222 result = func(result, element)
1233 alist = [
_py2expr(a, ctx)
for a
in alist]
1234 s =
_reduce(_coerce_expr_merge, alist,
None)
1235 return [s.cast(a)
for a
in alist]
1239 """Return `True` if `a` is a Z3 expression.
1246 >>> is_expr(IntSort())
1250 >>> is_expr(IntVal(1))
1253 >>> is_expr(ForAll(x, x >= 0))
1255 >>> is_expr(FPVal(1.0))
1258 return isinstance(a, ExprRef)
1262 """Return `True` if `a` is a Z3 function application.
1264 Note that, constants are function applications with 0 arguments.
1271 >>> is_app(IntSort())
1275 >>> is_app(IntVal(1))
1278 >>> is_app(ForAll(x, x >= 0))
1281 if not isinstance(a, ExprRef):
1284 return k == Z3_NUMERAL_AST
or k == Z3_APP_AST
1288 """Return `True` if `a` is Z3 constant/variable expression.
1297 >>> is_const(IntVal(1))
1300 >>> is_const(ForAll(x, x >= 0))
1303 return is_app(a)
and a.num_args() == 0
1307 """Return `True` if `a` is variable.
1309 Z3 uses de-Bruijn indices for representing bound variables in
1317 >>> f = Function('f', IntSort(), IntSort())
1318 >>> # Z3 replaces x with bound variables when ForAll is executed.
1319 >>> q = ForAll(x, f(x) == x)
1325 >>> is_var(b.arg(1))
1332 """Return the de-Bruijn index of the Z3 bounded variable `a`.
1340 >>> f = Function('f', IntSort(), IntSort(), IntSort())
1341 >>> # Z3 replaces x and y with bound variables when ForAll is executed.
1342 >>> q = ForAll([x, y], f(x, y) == x + y)
1344 f(Var(1), Var(0)) == Var(1) + Var(0)
1348 >>> v1 = b.arg(0).arg(0)
1349 >>> v2 = b.arg(0).arg(1)
1354 >>> get_var_index(v1)
1356 >>> get_var_index(v2)
1365 """Return `True` if `a` is an application of the given kind `k`.
1369 >>> is_app_of(n, Z3_OP_ADD)
1371 >>> is_app_of(n, Z3_OP_MUL)
1374 return is_app(a)
and a.decl().kind() == k
1377def If(a, b, c, ctx=None):
1378 """Create a Z3 if-then-else expression.
1382 >>> max = If(x > y, x, y)
1388 if isinstance(a, Probe)
or isinstance(b, Tactic)
or isinstance(c, Tactic):
1389 return Cond(a, b, c, ctx)
1396 _z3_assert(a.ctx == b.ctx,
"Context mismatch")
1401 """Create a Z3 distinct expression.
1408 >>> Distinct(x, y, z)
1410 >>> simplify(Distinct(x, y, z))
1412 >>> simplify(Distinct(x, y, z), blast_distinct=True)
1413 And(Not(x == y), Not(x == z), Not(y == z))
1418 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression")
1427 _z3_assert(a.ctx == b.ctx,
"Context mismatch")
1428 args[0] = a.as_ast()
1429 args[1] = b.as_ast()
1430 return f(a.ctx.ref(), 2, args)
1434 """Create a constant of the given sort.
1436 >>> Const('x', IntSort())
1440 _z3_assert(isinstance(sort, SortRef),
"Z3 sort expected")
1446 """Create several constants of the given sort.
1448 `names` is a string containing the names of all constants to be created.
1449 Blank spaces separate the names of different constants.
1451 >>> x, y, z = Consts('x y z', IntSort())
1455 if isinstance(names, str):
1456 names = names.split(
" ")
1457 return [
Const(name, sort)
for name
in names]
1461 """Create a fresh constant of a specified sort"""
1467 """Create a Z3 free variable. Free variables are used to create quantified formulas.
1468 A free variable with index n is bound when it occurs within the scope of n+1 quantified
1471 >>> Var(0, IntSort())
1473 >>> eq(Var(0, IntSort()), Var(0, BoolSort()))
1483 Create a real free variable. Free variables are used to create quantified formulas.
1484 They are also used to create polynomials.
1494 Create a list of Real free variables.
1495 The variables have ids: 0, 1, ..., n-1
1497 >>> x0, x1, x2, x3 = RealVarVector(4)
1501 return [
RealVar(i, ctx)
for i
in range(n)]
1514 """Try to cast `val` as a Boolean.
1516 >>> x = BoolSort().cast(True)
1526 if isinstance(val, bool):
1530 msg =
"True, False or Z3 Boolean expression expected. Received %s of type %s"
1532 if not self.
eq(val.sort()):
1533 _z3_assert(self.
eq(val.sort()),
"Value cannot be converted into a Z3 Boolean value")
1537 return isinstance(other, ArithSortRef)
1547 """All Boolean expressions are instances of this class."""
1556 """Create the Z3 expression `self * other`.
1558 if isinstance(other, int)
and other == 1:
1559 return If(self, 1, 0)
1560 if isinstance(other, int)
and other == 0:
1562 if isinstance(other, BoolRef):
1563 other =
If(other, 1, 0)
1564 return If(self, other, 0)
1568 """Return `True` if `a` is a Z3 Boolean expression.
1574 >>> is_bool(And(p, q))
1582 return isinstance(a, BoolRef)
1586 """Return `True` if `a` is the Z3 true expression.
1591 >>> is_true(simplify(p == p))
1596 >>> # True is a Python Boolean expression
1604 """Return `True` if `a` is the Z3 false expression.
1611 >>> is_false(BoolVal(False))
1618 """Return `True` if `a` is a Z3 and expression.
1620 >>> p, q = Bools('p q')
1621 >>> is_and(And(p, q))
1623 >>> is_and(Or(p, q))
1630 """Return `True` if `a` is a Z3 or expression.
1632 >>> p, q = Bools('p q')
1635 >>> is_or(And(p, q))
1642 """Return `True` if `a` is a Z3 implication expression.
1644 >>> p, q = Bools('p q')
1645 >>> is_implies(Implies(p, q))
1647 >>> is_implies(And(p, q))
1654 """Return `True` if `a` is a Z3 not expression.
1666 """Return `True` if `a` is a Z3 equality expression.
1668 >>> x, y = Ints('x y')
1676 """Return `True` if `a` is a Z3 distinct expression.
1678 >>> x, y, z = Ints('x y z')
1679 >>> is_distinct(x == y)
1681 >>> is_distinct(Distinct(x, y, z))
1688 """Return the Boolean Z3 sort. If `ctx=None`, then the global context is used.
1692 >>> p = Const('p', BoolSort())
1695 >>> r = Function('r', IntSort(), IntSort(), BoolSort())
1698 >>> is_bool(r(0, 1))
1706 """Return the Boolean value `True` or `False`. If `ctx=None`, then the global context is used.
1710 >>> is_true(BoolVal(True))
1714 >>> is_false(BoolVal(False))
1725 """Return a Boolean constant named `name`. If `ctx=None`, then the global context is used.
1737 """Return a tuple of Boolean constants.
1739 `names` is a single string containing all names separated by blank spaces.
1740 If `ctx=None`, then the global context is used.
1742 >>> p, q, r = Bools('p q r')
1743 >>> And(p, Or(q, r))
1747 if isinstance(names, str):
1748 names = names.split(
" ")
1749 return [
Bool(name, ctx)
for name
in names]
1753 """Return a list of Boolean constants of size `sz`.
1755 The constants are named using the given prefix.
1756 If `ctx=None`, then the global context is used.
1758 >>> P = BoolVector('p', 3)
1762 And(p__0, p__1, p__2)
1764 return [
Bool(
"%s__%s" % (prefix, i))
for i
in range(sz)]
1768 """Return a fresh Boolean constant in the given context using the given prefix.
1770 If `ctx=None`, then the global context is used.
1772 >>> b1 = FreshBool()
1773 >>> b2 = FreshBool()
1782 """Create a Z3 implies expression.
1784 >>> p, q = Bools('p q')
1796 """Create a Z3 Xor expression.
1798 >>> p, q = Bools('p q')
1801 >>> simplify(Xor(p, q))
1812 """Create a Z3 not expression or probe.
1817 >>> simplify(Not(Not(p)))
1838 """Return `True` if one of the elements of the given collection is a Z3 probe."""
1846 """Create a Z3 and-expression or and-probe.
1848 >>> p, q, r = Bools('p q r')
1851 >>> P = BoolVector('p', 5)
1853 And(p__0, p__1, p__2, p__3, p__4)
1857 last_arg = args[len(args) - 1]
1858 if isinstance(last_arg, Context):
1859 ctx = args[len(args) - 1]
1860 args = args[:len(args) - 1]
1861 elif len(args) == 1
and isinstance(args[0], AstVector):
1863 args = [a
for a
in args[0]]
1869 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression or probe")
1879 """Create a Z3 or-expression or or-probe.
1881 >>> p, q, r = Bools('p q r')
1884 >>> P = BoolVector('p', 5)
1886 Or(p__0, p__1, p__2, p__3, p__4)
1890 last_arg = args[len(args) - 1]
1891 if isinstance(last_arg, Context):
1892 ctx = args[len(args) - 1]
1893 args = args[:len(args) - 1]
1894 elif len(args) == 1
and isinstance(args[0], AstVector):
1896 args = [a
for a
in args[0]]
1902 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression or probe")
1918 """Patterns are hints for quantifier instantiation.
1930 """Return `True` if `a` is a Z3 pattern (hint for quantifier instantiation.
1932 >>> f = Function('f', IntSort(), IntSort())
1934 >>> q = ForAll(x, f(x) == 0, patterns = [ f(x) ])
1936 ForAll(x, f(x) == 0)
1937 >>> q.num_patterns()
1939 >>> is_pattern(q.pattern(0))
1944 return isinstance(a, PatternRef)
1948 """Create a Z3 multi-pattern using the given expressions `*args`
1950 >>> f = Function('f', IntSort(), IntSort())
1951 >>> g = Function('g', IntSort(), IntSort())
1953 >>> q = ForAll(x, f(x) != g(x), patterns = [ MultiPattern(f(x), g(x)) ])
1955 ForAll(x, f(x) != g(x))
1956 >>> q.num_patterns()
1958 >>> is_pattern(q.pattern(0))
1961 MultiPattern(f(Var(0)), g(Var(0)))
1964 _z3_assert(len(args) > 0,
"At least one argument expected")
1985 """Universally and Existentially quantified formulas."""
1994 """Return the Boolean sort or sort of Lambda."""
2000 """Return `True` if `self` is a universal quantifier.
2002 >>> f = Function('f', IntSort(), IntSort())
2004 >>> q = ForAll(x, f(x) == 0)
2007 >>> q = Exists(x, f(x) != 0)
2014 """Return `True` if `self` is an existential quantifier.
2016 >>> f = Function('f', IntSort(), IntSort())
2018 >>> q = ForAll(x, f(x) == 0)
2021 >>> q = Exists(x, f(x) != 0)
2028 """Return `True` if `self` is a lambda expression.
2030 >>> f = Function('f', IntSort(), IntSort())
2032 >>> q = Lambda(x, f(x))
2035 >>> q = Exists(x, f(x) != 0)
2042 """Return the Z3 expression `self[arg]`.
2049 """Return the weight annotation of `self`.
2051 >>> f = Function('f', IntSort(), IntSort())
2053 >>> q = ForAll(x, f(x) == 0)
2056 >>> q = ForAll(x, f(x) == 0, weight=10)
2063 """Return the number of patterns (i.e., quantifier instantiation hints) in `self`.
2065 >>> f = Function('f', IntSort(), IntSort())
2066 >>> g = Function('g', IntSort(), IntSort())
2068 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2069 >>> q.num_patterns()
2075 """Return a pattern (i.e., quantifier instantiation hints) in `self`.
2077 >>> f = Function('f', IntSort(), IntSort())
2078 >>> g = Function('g', IntSort(), IntSort())
2080 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2081 >>> q.num_patterns()
2093 """Return the number of no-patterns."""
2097 """Return a no-pattern."""
2103 """Return the expression being quantified.
2105 >>> f = Function('f', IntSort(), IntSort())
2107 >>> q = ForAll(x, f(x) == 0)
2114 """Return the number of variables bounded by this quantifier.
2116 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2119 >>> q = ForAll([x, y], f(x, y) >= x)
2126 """Return a string representing a name used when displaying the quantifier.
2128 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2131 >>> q = ForAll([x, y], f(x, y) >= x)
2142 """Return the sort of a bound variable.
2144 >>> f = Function('f', IntSort(), RealSort(), IntSort())
2147 >>> q = ForAll([x, y], f(x, y) >= x)
2158 """Return a list containing a single element self.body()
2160 >>> f = Function('f', IntSort(), IntSort())
2162 >>> q = ForAll(x, f(x) == 0)
2166 return [self.
body()]
2170 """Return `True` if `a` is a Z3 quantifier.
2172 >>> f = Function('f', IntSort(), IntSort())
2174 >>> q = ForAll(x, f(x) == 0)
2175 >>> is_quantifier(q)
2177 >>> is_quantifier(f(x))
2180 return isinstance(a, QuantifierRef)
2183def _mk_quantifier(is_forall, vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2188 _z3_assert(all([
is_expr(p)
for p
in no_patterns]),
"no patterns are Z3 expressions")
2199 _vs = (Ast * num_vars)()
2200 for i
in range(num_vars):
2202 _vs[i] = vs[i].as_ast()
2204 num_pats = len(patterns)
2205 _pats = (Pattern * num_pats)()
2206 for i
in range(num_pats):
2207 _pats[i] = patterns[i].ast
2214 num_no_pats, _no_pats,
2215 body.as_ast()), ctx)
2218def ForAll(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2219 """Create a Z3 forall formula.
2221 The parameters `weight`, `qid`, `skid`, `patterns` and `no_patterns` are optional annotations.
2223 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2226 >>> ForAll([x, y], f(x, y) >= x)
2227 ForAll([x, y], f(x, y) >= x)
2228 >>> ForAll([x, y], f(x, y) >= x, patterns=[ f(x, y) ])
2229 ForAll([x, y], f(x, y) >= x)
2230 >>> ForAll([x, y], f(x, y) >= x, weight=10)
2231 ForAll([x, y], f(x, y) >= x)
2233 return _mk_quantifier(
True, vs, body, weight, qid, skid, patterns, no_patterns)
2236def Exists(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2237 """Create a Z3 exists formula.
2239 The parameters `weight`, `qif`, `skid`, `patterns` and `no_patterns` are optional annotations.
2242 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2245 >>> q = Exists([x, y], f(x, y) >= x, skid="foo")
2247 Exists([x, y], f(x, y) >= x)
2248 >>> is_quantifier(q)
2250 >>> r = Tactic('nnf')(q).as_expr()
2251 >>> is_quantifier(r)
2254 return _mk_quantifier(
False, vs, body, weight, qid, skid, patterns, no_patterns)
2258 """Create a Z3 lambda expression.
2260 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2261 >>> mem0 = Array('mem0', IntSort(), IntSort())
2262 >>> lo, hi, e, i = Ints('lo hi e i')
2263 >>> mem1 = Lambda([i], If(And(lo <= i, i <= hi), e, mem0[i]))
2265 Lambda(i, If(And(lo <= i, i <= hi), e, mem0[i]))
2271 _vs = (Ast * num_vars)()
2272 for i
in range(num_vars):
2274 _vs[i] = vs[i].as_ast()
2285 """Real and Integer sorts."""
2288 """Return `True` if `self` is of the sort Real.
2293 >>> (x + 1).is_real()
2299 return self.
kind() == Z3_REAL_SORT
2302 """Return `True` if `self` is of the sort Integer.
2307 >>> (x + 1).is_int()
2313 return self.
kind() == Z3_INT_SORT
2319 """Return `True` if `self` is a subsort of `other`."""
2323 """Try to cast `val` as an Integer or Real.
2325 >>> IntSort().cast(10)
2327 >>> is_int(IntSort().cast(10))
2331 >>> RealSort().cast(10)
2333 >>> is_real(RealSort().cast(10))
2342 if val_s.is_int()
and self.
is_real():
2344 if val_s.is_bool()
and self.
is_int():
2345 return If(val, 1, 0)
2346 if val_s.is_bool()
and self.
is_real():
2349 _z3_assert(
False,
"Z3 Integer/Real expression expected")
2356 msg =
"int, long, float, string (numeral), or Z3 Integer/Real expression expected. Got %s"
2361 """Return `True` if s is an arithmetical sort (type).
2363 >>> is_arith_sort(IntSort())
2365 >>> is_arith_sort(RealSort())
2367 >>> is_arith_sort(BoolSort())
2369 >>> n = Int('x') + 1
2370 >>> is_arith_sort(n.sort())
2373 return isinstance(s, ArithSortRef)
2377 """Integer and Real expressions."""
2380 """Return the sort (type) of the arithmetical expression `self`.
2384 >>> (Real('x') + 1).sort()
2390 """Return `True` if `self` is an integer expression.
2395 >>> (x + 1).is_int()
2398 >>> (x + y).is_int()
2404 """Return `True` if `self` is an real expression.
2409 >>> (x + 1).is_real()
2415 """Create the Z3 expression `self + other`.
2428 """Create the Z3 expression `other + self`.
2438 """Create the Z3 expression `self * other`.
2447 if isinstance(other, BoolRef):
2448 return If(other, self, 0)
2453 """Create the Z3 expression `other * self`.
2463 """Create the Z3 expression `self - other`.
2476 """Create the Z3 expression `other - self`.
2486 """Create the Z3 expression `self**other` (** is the power operator).
2493 >>> simplify(IntVal(2)**8)
2500 """Create the Z3 expression `other**self` (** is the power operator).
2507 >>> simplify(2**IntVal(8))
2514 """Create the Z3 expression `other/self`.
2537 """Create the Z3 expression `other/self`."""
2541 """Create the Z3 expression `other/self`.
2558 """Create the Z3 expression `other/self`."""
2562 """Create the Z3 expression `other%self`.
2568 >>> simplify(IntVal(10) % IntVal(3))
2573 _z3_assert(a.is_int(),
"Z3 integer expression expected")
2577 """Create the Z3 expression `other%self`.
2585 _z3_assert(a.is_int(),
"Z3 integer expression expected")
2589 """Return an expression representing `-self`.
2609 """Create the Z3 expression `other <= self`.
2611 >>> x, y = Ints('x y')
2622 """Create the Z3 expression `other < self`.
2624 >>> x, y = Ints('x y')
2635 """Create the Z3 expression `other > self`.
2637 >>> x, y = Ints('x y')
2648 """Create the Z3 expression `other >= self`.
2650 >>> x, y = Ints('x y')
2662 """Return `True` if `a` is an arithmetical expression.
2671 >>> is_arith(IntVal(1))
2679 return isinstance(a, ArithRef)
2683 """Return `True` if `a` is an integer expression.
2690 >>> is_int(IntVal(1))
2702 """Return `True` if `a` is a real expression.
2714 >>> is_real(RealVal(1))
2729 """Return `True` if `a` is an integer value of sort Int.
2731 >>> is_int_value(IntVal(1))
2735 >>> is_int_value(Int('x'))
2737 >>> n = Int('x') + 1
2742 >>> is_int_value(n.arg(1))
2744 >>> is_int_value(RealVal("1/3"))
2746 >>> is_int_value(RealVal(1))
2753 """Return `True` if `a` is rational value of sort Real.
2755 >>> is_rational_value(RealVal(1))
2757 >>> is_rational_value(RealVal("3/5"))
2759 >>> is_rational_value(IntVal(1))
2761 >>> is_rational_value(1)
2763 >>> n = Real('x') + 1
2766 >>> is_rational_value(n.arg(1))
2768 >>> is_rational_value(Real('x'))
2775 """Return `True` if `a` is an algebraic value of sort Real.
2777 >>> is_algebraic_value(RealVal("3/5"))
2779 >>> n = simplify(Sqrt(2))
2782 >>> is_algebraic_value(n)
2789 """Return `True` if `a` is an expression of the form b + c.
2791 >>> x, y = Ints('x y')
2801 """Return `True` if `a` is an expression of the form b * c.
2803 >>> x, y = Ints('x y')
2813 """Return `True` if `a` is an expression of the form b - c.
2815 >>> x, y = Ints('x y')
2825 """Return `True` if `a` is an expression of the form b / c.
2827 >>> x, y = Reals('x y')
2832 >>> x, y = Ints('x y')
2842 """Return `True` if `a` is an expression of the form b div c.
2844 >>> x, y = Ints('x y')
2854 """Return `True` if `a` is an expression of the form b % c.
2856 >>> x, y = Ints('x y')
2866 """Return `True` if `a` is an expression of the form b <= c.
2868 >>> x, y = Ints('x y')
2878 """Return `True` if `a` is an expression of the form b < c.
2880 >>> x, y = Ints('x y')
2890 """Return `True` if `a` is an expression of the form b >= c.
2892 >>> x, y = Ints('x y')
2902 """Return `True` if `a` is an expression of the form b > c.
2904 >>> x, y = Ints('x y')
2914 """Return `True` if `a` is an expression of the form IsInt(b).
2917 >>> is_is_int(IsInt(x))
2926 """Return `True` if `a` is an expression of the form ToReal(b).
2941 """Return `True` if `a` is an expression of the form ToInt(b).
2956 """Integer values."""
2959 """Return a Z3 integer numeral as a Python long (bignum) numeral.
2972 """Return a Z3 integer numeral as a Python string.
2980 """Return a Z3 integer numeral as a Python binary string.
2982 >>> v.as_binary_string()
2989 """Rational values."""
2992 """ Return the numerator of a Z3 rational numeral.
2994 >>> is_rational_value(RealVal("3/5"))
2996 >>> n = RealVal("3/5")
2999 >>> is_rational_value(Q(3,5))
3001 >>> Q(3,5).numerator()
3007 """ Return the denominator of a Z3 rational numeral.
3009 >>> is_rational_value(Q(3,5))
3018 """ Return the numerator as a Python long.
3020 >>> v = RealVal(10000000000)
3025 >>> v.numerator_as_long() + 1 == 10000000001
3031 """ Return the denominator as a Python long.
3033 >>> v = RealVal("1/3")
3036 >>> v.denominator_as_long()
3055 """ Return a Z3 rational value as a string in decimal notation using at most `prec` decimal places.
3057 >>> v = RealVal("1/5")
3060 >>> v = RealVal("1/3")
3067 """Return a Z3 rational numeral as a Python string.
3076 """Return a Z3 rational as a Python Fraction object.
3078 >>> v = RealVal("1/5")
3086 """Algebraic irrational values."""
3089 """Return a Z3 rational number that approximates the algebraic number `self`.
3090 The result `r` is such that |r - self| <= 1/10^precision
3092 >>> x = simplify(Sqrt(2))
3094 6838717160008073720548335/4835703278458516698824704
3101 """Return a string representation of the algebraic number `self` in decimal notation
3102 using `prec` decimal places.
3104 >>> x = simplify(Sqrt(2))
3105 >>> x.as_decimal(10)
3107 >>> x.as_decimal(20)
3108 '1.41421356237309504880?'
3120 if isinstance(a, bool):
3124 if isinstance(a, float):
3126 if isinstance(a, str):
3131 _z3_assert(
False,
"Python bool, int, long or float expected")
3135 """Return the integer sort in the given context. If `ctx=None`, then the global context is used.
3139 >>> x = Const('x', IntSort())
3142 >>> x.sort() == IntSort()
3144 >>> x.sort() == BoolSort()
3152 """Return the real sort in the given context. If `ctx=None`, then the global context is used.
3156 >>> x = Const('x', RealSort())
3161 >>> x.sort() == RealSort()
3169 if isinstance(val, float):
3170 return str(int(val))
3171 elif isinstance(val, bool):
3181 """Return a Z3 integer value. If `ctx=None`, then the global context is used.
3193 """Return a Z3 real value.
3195 `val` may be a Python int, long, float or string representing a number in decimal or rational notation.
3196 If `ctx=None`, then the global context is used.
3200 >>> RealVal(1).sort()
3212 """Return a Z3 rational a/b.
3214 If `ctx=None`, then the global context is used.
3218 >>> RatVal(3,5).sort()
3222 _z3_assert(
_is_int(a)
or isinstance(a, str),
"First argument cannot be converted into an integer")
3223 _z3_assert(
_is_int(b)
or isinstance(b, str),
"Second argument cannot be converted into an integer")
3227def Q(a, b, ctx=None):
3228 """Return a Z3 rational a/b.
3230 If `ctx=None`, then the global context is used.
3241 """Return an integer constant named `name`. If `ctx=None`, then the global context is used.
3254 """Return a tuple of Integer constants.
3256 >>> x, y, z = Ints('x y z')
3261 if isinstance(names, str):
3262 names = names.split(
" ")
3263 return [
Int(name, ctx)
for name
in names]
3267 """Return a list of integer constants of size `sz`.
3269 >>> X = IntVector('x', 3)
3276 return [
Int(
"%s__%s" % (prefix, i), ctx)
for i
in range(sz)]
3280 """Return a fresh integer constant in the given context using the given prefix.
3294 """Return a real constant named `name`. If `ctx=None`, then the global context is used.
3307 """Return a tuple of real constants.
3309 >>> x, y, z = Reals('x y z')
3312 >>> Sum(x, y, z).sort()
3316 if isinstance(names, str):
3317 names = names.split(
" ")
3318 return [
Real(name, ctx)
for name
in names]
3322 """Return a list of real constants of size `sz`.
3324 >>> X = RealVector('x', 3)
3333 return [
Real(
"%s__%s" % (prefix, i), ctx)
for i
in range(sz)]
3337 """Return a fresh real constant in the given context using the given prefix.
3351 """ Return the Z3 expression ToReal(a).
3363 _z3_assert(a.is_int(),
"Z3 integer expression expected.")
3369 """ Return the Z3 expression ToInt(a).
3381 _z3_assert(a.is_real(),
"Z3 real expression expected.")
3387 """ Return the Z3 predicate IsInt(a).
3390 >>> IsInt(x + "1/2")
3392 >>> solve(IsInt(x + "1/2"), x > 0, x < 1)
3394 >>> solve(IsInt(x + "1/2"), x > 0, x < 1, x != "1/2")
3398 _z3_assert(a.is_real(),
"Z3 real expression expected.")
3404 """ Return a Z3 expression which represents the square root of a.
3417 """ Return a Z3 expression which represents the cubic root of a.
3436 """Bit-vector sort."""
3439 """Return the size (number of bits) of the bit-vector sort `self`.
3441 >>> b = BitVecSort(32)
3451 """Try to cast `val` as a Bit-Vector.
3453 >>> b = BitVecSort(32)
3456 >>> b.cast(10).sexpr()
3469 """Return True if `s` is a Z3 bit-vector sort.
3471 >>> is_bv_sort(BitVecSort(32))
3473 >>> is_bv_sort(IntSort())
3476 return isinstance(s, BitVecSortRef)
3480 """Bit-vector expressions."""
3483 """Return the sort of the bit-vector expression `self`.
3485 >>> x = BitVec('x', 32)
3488 >>> x.sort() == BitVecSort(32)
3494 """Return the number of bits of the bit-vector expression `self`.
3496 >>> x = BitVec('x', 32)
3499 >>> Concat(x, x).size()
3505 """Create the Z3 expression `self + other`.
3507 >>> x = BitVec('x', 32)
3508 >>> y = BitVec('y', 32)
3518 """Create the Z3 expression `other + self`.
3520 >>> x = BitVec('x', 32)
3528 """Create the Z3 expression `self * other`.
3530 >>> x = BitVec('x', 32)
3531 >>> y = BitVec('y', 32)
3541 """Create the Z3 expression `other * self`.
3543 >>> x = BitVec('x', 32)
3551 """Create the Z3 expression `self - other`.
3553 >>> x = BitVec('x', 32)
3554 >>> y = BitVec('y', 32)
3564 """Create the Z3 expression `other - self`.
3566 >>> x = BitVec('x', 32)
3574 """Create the Z3 expression bitwise-or `self | other`.
3576 >>> x = BitVec('x', 32)
3577 >>> y = BitVec('y', 32)
3587 """Create the Z3 expression bitwise-or `other | self`.
3589 >>> x = BitVec('x', 32)
3597 """Create the Z3 expression bitwise-and `self & other`.
3599 >>> x = BitVec('x', 32)
3600 >>> y = BitVec('y', 32)
3610 """Create the Z3 expression bitwise-or `other & self`.
3612 >>> x = BitVec('x', 32)
3620 """Create the Z3 expression bitwise-xor `self ^ other`.
3622 >>> x = BitVec('x', 32)
3623 >>> y = BitVec('y', 32)
3633 """Create the Z3 expression bitwise-xor `other ^ self`.
3635 >>> x = BitVec('x', 32)
3645 >>> x = BitVec('x', 32)
3652 """Return an expression representing `-self`.
3654 >>> x = BitVec('x', 32)
3663 """Create the Z3 expression bitwise-not `~self`.
3665 >>> x = BitVec('x', 32)
3674 """Create the Z3 expression (signed) division `self / other`.
3676 Use the function UDiv() for unsigned division.
3678 >>> x = BitVec('x', 32)
3679 >>> y = BitVec('y', 32)
3686 >>> UDiv(x, y).sexpr()
3693 """Create the Z3 expression (signed) division `self / other`."""
3697 """Create the Z3 expression (signed) division `other / self`.
3699 Use the function UDiv() for unsigned division.
3701 >>> x = BitVec('x', 32)
3704 >>> (10 / x).sexpr()
3705 '(bvsdiv #x0000000a x)'
3706 >>> UDiv(10, x).sexpr()
3707 '(bvudiv #x0000000a x)'
3713 """Create the Z3 expression (signed) division `other / self`."""
3717 """Create the Z3 expression (signed) mod `self % other`.
3719 Use the function URem() for unsigned remainder, and SRem() for signed remainder.
3721 >>> x = BitVec('x', 32)
3722 >>> y = BitVec('y', 32)
3729 >>> URem(x, y).sexpr()
3731 >>> SRem(x, y).sexpr()
3738 """Create the Z3 expression (signed) mod `other % self`.
3740 Use the function URem() for unsigned remainder, and SRem() for signed remainder.
3742 >>> x = BitVec('x', 32)
3745 >>> (10 % x).sexpr()
3746 '(bvsmod #x0000000a x)'
3747 >>> URem(10, x).sexpr()
3748 '(bvurem #x0000000a x)'
3749 >>> SRem(10, x).sexpr()
3750 '(bvsrem #x0000000a x)'
3756 """Create the Z3 expression (signed) `other <= self`.
3758 Use the function ULE() for unsigned less than or equal to.
3760 >>> x, y = BitVecs('x y', 32)
3763 >>> (x <= y).sexpr()
3765 >>> ULE(x, y).sexpr()
3772 """Create the Z3 expression (signed) `other < self`.
3774 Use the function ULT() for unsigned less than.
3776 >>> x, y = BitVecs('x y', 32)
3781 >>> ULT(x, y).sexpr()
3788 """Create the Z3 expression (signed) `other > self`.
3790 Use the function UGT() for unsigned greater than.
3792 >>> x, y = BitVecs('x y', 32)
3797 >>> UGT(x, y).sexpr()
3804 """Create the Z3 expression (signed) `other >= self`.
3806 Use the function UGE() for unsigned greater than or equal to.
3808 >>> x, y = BitVecs('x y', 32)
3811 >>> (x >= y).sexpr()
3813 >>> UGE(x, y).sexpr()
3820 """Create the Z3 expression (arithmetical) right shift `self >> other`
3822 Use the function LShR() for the right logical shift
3824 >>> x, y = BitVecs('x y', 32)
3827 >>> (x >> y).sexpr()
3829 >>> LShR(x, y).sexpr()
3833 >>> BitVecVal(4, 3).as_signed_long()
3835 >>> simplify(BitVecVal(4, 3) >> 1).as_signed_long()
3837 >>> simplify(BitVecVal(4, 3) >> 1)
3839 >>> simplify(LShR(BitVecVal(4, 3), 1))
3841 >>> simplify(BitVecVal(2, 3) >> 1)
3843 >>> simplify(LShR(BitVecVal(2, 3), 1))
3850 """Create the Z3 expression left shift `self << other`
3852 >>> x, y = BitVecs('x y', 32)
3855 >>> (x << y).sexpr()
3857 >>> simplify(BitVecVal(2, 3) << 1)
3864 """Create the Z3 expression (arithmetical) right shift `other` >> `self`.
3866 Use the function LShR() for the right logical shift
3868 >>> x = BitVec('x', 32)
3871 >>> (10 >> x).sexpr()
3872 '(bvashr #x0000000a x)'
3878 """Create the Z3 expression left shift `other << self`.
3880 Use the function LShR() for the right logical shift
3882 >>> x = BitVec('x', 32)
3885 >>> (10 << x).sexpr()
3886 '(bvshl #x0000000a x)'
3893 """Bit-vector values."""
3896 """Return a Z3 bit-vector numeral as a Python long (bignum) numeral.
3898 >>> v = BitVecVal(0xbadc0de, 32)
3901 >>> print("0x%.8x" % v.as_long())
3907 """Return a Z3 bit-vector numeral as a Python long (bignum) numeral.
3908 The most significant bit is assumed to be the sign.
3910 >>> BitVecVal(4, 3).as_signed_long()
3912 >>> BitVecVal(7, 3).as_signed_long()
3914 >>> BitVecVal(3, 3).as_signed_long()
3916 >>> BitVecVal(2**32 - 1, 32).as_signed_long()
3918 >>> BitVecVal(2**64 - 1, 64).as_signed_long()
3923 if val >= 2**(sz - 1):
3925 if val < -2**(sz - 1):
3937 """Return `True` if `a` is a Z3 bit-vector expression.
3939 >>> b = BitVec('b', 32)
3947 return isinstance(a, BitVecRef)
3951 """Return `True` if `a` is a Z3 bit-vector numeral value.
3953 >>> b = BitVec('b', 32)
3956 >>> b = BitVecVal(10, 32)
3966 """Return the Z3 expression BV2Int(a).
3968 >>> b = BitVec('b', 3)
3969 >>> BV2Int(b).sort()
3974 >>> x > BV2Int(b, is_signed=False)
3976 >>> x > BV2Int(b, is_signed=True)
3977 x > If(b < 0, BV2Int(b) - 8, BV2Int(b))
3978 >>> solve(x > BV2Int(b), b == 1, x < 3)
3982 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
3989 """Return the z3 expression Int2BV(a, num_bits).
3990 It is a bit-vector of width num_bits and represents the
3991 modulo of a by 2^num_bits
3998 """Return a Z3 bit-vector sort of the given size. If `ctx=None`, then the global context is used.
4000 >>> Byte = BitVecSort(8)
4001 >>> Word = BitVecSort(16)
4004 >>> x = Const('x', Byte)
4005 >>> eq(x, BitVec('x', 8))
4013 """Return a bit-vector value with the given number of bits. If `ctx=None`, then the global context is used.
4015 >>> v = BitVecVal(10, 32)
4018 >>> print("0x%.8x" % v.as_long())
4030 """Return a bit-vector constant named `name`. `bv` may be the number of bits of a bit-vector sort.
4031 If `ctx=None`, then the global context is used.
4033 >>> x = BitVec('x', 16)
4040 >>> word = BitVecSort(16)
4041 >>> x2 = BitVec('x', word)
4045 if isinstance(bv, BitVecSortRef):
4054 """Return a tuple of bit-vector constants of size bv.
4056 >>> x, y, z = BitVecs('x y z', 16)
4063 >>> Product(x, y, z)
4065 >>> simplify(Product(x, y, z))
4069 if isinstance(names, str):
4070 names = names.split(
" ")
4071 return [
BitVec(name, bv, ctx)
for name
in names]
4075 """Create a Z3 bit-vector concatenation expression.
4077 >>> v = BitVecVal(1, 4)
4078 >>> Concat(v, v+1, v)
4079 Concat(Concat(1, 1 + 1), 1)
4080 >>> simplify(Concat(v, v+1, v))
4082 >>> print("%.3x" % simplify(Concat(v, v+1, v)).as_long())
4088 _z3_assert(sz >= 2,
"At least two arguments expected.")
4095 if is_seq(args[0])
or isinstance(args[0], str):
4098 _z3_assert(all([
is_seq(a)
for a
in args]),
"All arguments must be sequence expressions.")
4101 v[i] = args[i].as_ast()
4106 _z3_assert(all([
is_re(a)
for a
in args]),
"All arguments must be regular expressions.")
4109 v[i] = args[i].as_ast()
4113 _z3_assert(all([
is_bv(a)
for a
in args]),
"All arguments must be Z3 bit-vector expressions.")
4115 for i
in range(sz - 1):
4121 """Create a Z3 bit-vector extraction expression.
4122 Extract is overloaded to also work on sequence extraction.
4123 The functions SubString and SubSeq are redirected to Extract.
4124 For this case, the arguments are reinterpreted as:
4125 high - is a sequence (string)
4127 a - is the length to be extracted
4129 >>> x = BitVec('x', 8)
4130 >>> Extract(6, 2, x)
4132 >>> Extract(6, 2, x).sort()
4134 >>> simplify(Extract(StringVal("abcd"),2,1))
4137 if isinstance(high, str):
4144 _z3_assert(low <= high,
"First argument must be greater than or equal to second argument")
4146 "First and second arguments must be non negative integers")
4147 _z3_assert(
is_bv(a),
"Third argument must be a Z3 bit-vector expression")
4153 _z3_assert(
is_bv(a)
or is_bv(b),
"First or second argument must be a Z3 bit-vector expression")
4157 """Create the Z3 expression (unsigned) `other <= self`.
4159 Use the operator <= for signed less than or equal to.
4161 >>> x, y = BitVecs('x y', 32)
4164 >>> (x <= y).sexpr()
4166 >>> ULE(x, y).sexpr()
4175 """Create the Z3 expression (unsigned) `other < self`.
4177 Use the operator < for signed less than.
4179 >>> x, y = BitVecs('x y', 32)
4184 >>> ULT(x, y).sexpr()
4193 """Create the Z3 expression (unsigned) `other >= self`.
4195 Use the operator >= for signed greater than or equal to.
4197 >>> x, y = BitVecs('x y', 32)
4200 >>> (x >= y).sexpr()
4202 >>> UGE(x, y).sexpr()
4211 """Create the Z3 expression (unsigned) `other > self`.
4213 Use the operator > for signed greater than.
4215 >>> x, y = BitVecs('x y', 32)
4220 >>> UGT(x, y).sexpr()
4229 """Create the Z3 expression (unsigned) division `self / other`.
4231 Use the operator / for signed division.
4233 >>> x = BitVec('x', 32)
4234 >>> y = BitVec('y', 32)
4237 >>> UDiv(x, y).sort()
4241 >>> UDiv(x, y).sexpr()
4250 """Create the Z3 expression (unsigned) remainder `self % other`.
4252 Use the operator % for signed modulus, and SRem() for signed remainder.
4254 >>> x = BitVec('x', 32)
4255 >>> y = BitVec('y', 32)
4258 >>> URem(x, y).sort()
4262 >>> URem(x, y).sexpr()
4271 """Create the Z3 expression signed remainder.
4273 Use the operator % for signed modulus, and URem() for unsigned remainder.
4275 >>> x = BitVec('x', 32)
4276 >>> y = BitVec('y', 32)
4279 >>> SRem(x, y).sort()
4283 >>> SRem(x, y).sexpr()
4292 """Create the Z3 expression logical right shift.
4294 Use the operator >> for the arithmetical right shift.
4296 >>> x, y = BitVecs('x y', 32)
4299 >>> (x >> y).sexpr()
4301 >>> LShR(x, y).sexpr()
4305 >>> BitVecVal(4, 3).as_signed_long()
4307 >>> simplify(BitVecVal(4, 3) >> 1).as_signed_long()
4309 >>> simplify(BitVecVal(4, 3) >> 1)
4311 >>> simplify(LShR(BitVecVal(4, 3), 1))
4313 >>> simplify(BitVecVal(2, 3) >> 1)
4315 >>> simplify(LShR(BitVecVal(2, 3), 1))
4324 """Return an expression representing `a` rotated to the left `b` times.
4326 >>> a, b = BitVecs('a b', 16)
4327 >>> RotateLeft(a, b)
4329 >>> simplify(RotateLeft(a, 0))
4331 >>> simplify(RotateLeft(a, 16))
4340 """Return an expression representing `a` rotated to the right `b` times.
4342 >>> a, b = BitVecs('a b', 16)
4343 >>> RotateRight(a, b)
4345 >>> simplify(RotateRight(a, 0))
4347 >>> simplify(RotateRight(a, 16))
4356 """Return a bit-vector expression with `n` extra sign-bits.
4358 >>> x = BitVec('x', 16)
4359 >>> n = SignExt(8, x)
4366 >>> v0 = BitVecVal(2, 2)
4371 >>> v = simplify(SignExt(6, v0))
4376 >>> print("%.x" % v.as_long())
4381 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4386 """Return a bit-vector expression with `n` extra zero-bits.
4388 >>> x = BitVec('x', 16)
4389 >>> n = ZeroExt(8, x)
4396 >>> v0 = BitVecVal(2, 2)
4401 >>> v = simplify(ZeroExt(6, v0))
4409 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4414 """Return an expression representing `n` copies of `a`.
4416 >>> x = BitVec('x', 8)
4417 >>> n = RepeatBitVec(4, x)
4422 >>> v0 = BitVecVal(10, 4)
4423 >>> print("%.x" % v0.as_long())
4425 >>> v = simplify(RepeatBitVec(4, v0))
4428 >>> print("%.x" % v.as_long())
4433 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4438 """Return the reduction-and expression of `a`."""
4440 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4445 """Return the reduction-or expression of `a`."""
4447 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4452 """A predicate the determines that bit-vector addition does not overflow"""
4459 """A predicate the determines that signed bit-vector addition does not underflow"""
4466 """A predicate the determines that bit-vector subtraction does not overflow"""
4473 """A predicate the determines that bit-vector subtraction does not underflow"""
4480 """A predicate the determines that bit-vector signed division does not overflow"""
4487 """A predicate the determines that bit-vector unary negation does not overflow"""
4489 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4494 """A predicate the determines that bit-vector multiplication does not overflow"""
4501 """A predicate the determines that bit-vector signed multiplication does not underflow"""
4517 """Return the domain of the array sort `self`.
4519 >>> A = ArraySort(IntSort(), BoolSort())
4526 """Return the domain of the array sort `self`.
4531 """Return the range of the array sort `self`.
4533 >>> A = ArraySort(IntSort(), BoolSort())
4541 """Array expressions. """
4544 """Return the array sort of the array expression `self`.
4546 >>> a = Array('a', IntSort(), BoolSort())
4553 """Shorthand for `self.sort().domain()`.
4555 >>> a = Array('a', IntSort(), BoolSort())
4562 """Shorthand for self.sort().domain_n(i)`."""
4566 """Shorthand for `self.sort().range()`.
4568 >>> a = Array('a', IntSort(), BoolSort())
4575 """Return the Z3 expression `self[arg]`.
4577 >>> a = Array('a', IntSort(), BoolSort())
4591 if isinstance(arg, tuple):
4592 args = [ar.sort().domain_n(i).cast(arg[i])
for i
in range(len(arg))]
4595 arg = ar.sort().domain().cast(arg)
4604 """Return `True` if `a` is a Z3 array expression.
4606 >>> a = Array('a', IntSort(), IntSort())
4609 >>> is_array(Store(a, 0, 1))
4614 return isinstance(a, ArrayRef)
4618 """Return `True` if `a` is a Z3 constant array.
4620 >>> a = K(IntSort(), 10)
4621 >>> is_const_array(a)
4623 >>> a = Array('a', IntSort(), IntSort())
4624 >>> is_const_array(a)
4631 """Return `True` if `a` is a Z3 constant array.
4633 >>> a = K(IntSort(), 10)
4636 >>> a = Array('a', IntSort(), IntSort())
4644 """Return `True` if `a` is a Z3 map array expression.
4646 >>> f = Function('f', IntSort(), IntSort())
4647 >>> b = Array('b', IntSort(), IntSort())
4660 """Return `True` if `a` is a Z3 default array expression.
4661 >>> d = Default(K(IntSort(), 10))
4665 return is_app_of(a, Z3_OP_ARRAY_DEFAULT)
4669 """Return the function declaration associated with a Z3 map array expression.
4671 >>> f = Function('f', IntSort(), IntSort())
4672 >>> b = Array('b', IntSort(), IntSort())
4674 >>> eq(f, get_map_func(a))
4678 >>> get_map_func(a)(0)
4693 """Return the Z3 array sort with the given domain and range sorts.
4695 >>> A = ArraySort(IntSort(), BoolSort())
4702 >>> AA = ArraySort(IntSort(), A)
4704 Array(Int, Array(Int, Bool))
4708 _z3_assert(len(sig) > 1,
"At least two arguments expected")
4709 arity = len(sig) - 1
4715 _z3_assert(s.ctx == r.ctx,
"Context mismatch")
4719 dom = (Sort * arity)()
4720 for i
in range(arity):
4726 """Return an array constant named `name` with the given domain and range sorts.
4728 >>> a = Array('a', IntSort(), IntSort())
4740 """Return a Z3 store array expression.
4742 >>> a = Array('a', IntSort(), IntSort())
4743 >>> i, v = Ints('i v')
4744 >>> s = Update(a, i, v)
4747 >>> prove(s[i] == v)
4750 >>> prove(Implies(i != j, s[j] == a[j]))
4758 raise Z3Exception(
"array update requires index and value arguments")
4762 i = a.sort().domain().cast(i)
4763 v = a.sort().range().cast(v)
4765 v = a.sort().range().cast(args[-1])
4766 idxs = [a.sort().domain_n(i).cast(args[i])
for i
in range(len(args)-1)]
4772 """ Return a default value for array expression.
4773 >>> b = K(IntSort(), 1)
4774 >>> prove(Default(b) == 1)
4783 """Return a Z3 store array expression.
4785 >>> a = Array('a', IntSort(), IntSort())
4786 >>> i, v = Ints('i v')
4787 >>> s = Store(a, i, v)
4790 >>> prove(s[i] == v)
4793 >>> prove(Implies(i != j, s[j] == a[j]))
4800 """Return a Z3 select array expression.
4802 >>> a = Array('a', IntSort(), IntSort())
4806 >>> eq(Select(a, i), a[i])
4816 """Return a Z3 map array expression.
4818 >>> f = Function('f', IntSort(), IntSort(), IntSort())
4819 >>> a1 = Array('a1', IntSort(), IntSort())
4820 >>> a2 = Array('a2', IntSort(), IntSort())
4821 >>> b = Map(f, a1, a2)
4824 >>> prove(b[0] == f(a1[0], a2[0]))
4829 _z3_assert(len(args) > 0,
"At least one Z3 array expression expected")
4832 _z3_assert(len(args) == f.arity(),
"Number of arguments mismatch")
4839 """Return a Z3 constant array expression.
4841 >>> a = K(IntSort(), 10)
4861 """Return extensionality index for one-dimensional arrays.
4862 >> a, b = Consts('a b', SetSort(IntSort()))
4879 """Return `True` if `a` is a Z3 array select application.
4881 >>> a = Array('a', IntSort(), IntSort())
4892 """Return `True` if `a` is a Z3 array store application.
4894 >>> a = Array('a', IntSort(), IntSort())
4897 >>> is_store(Store(a, 0, 1))
4910 """ Create a set sort over element sort s"""
4915 """Create the empty set
4916 >>> EmptySet(IntSort())
4924 """Create the full set
4925 >>> FullSet(IntSort())
4933 """ Take the union of sets
4934 >>> a = Const('a', SetSort(IntSort()))
4935 >>> b = Const('b', SetSort(IntSort()))
4946 """ Take the union of sets
4947 >>> a = Const('a', SetSort(IntSort()))
4948 >>> b = Const('b', SetSort(IntSort()))
4949 >>> SetIntersect(a, b)
4959 """ Add element e to set s
4960 >>> a = Const('a', SetSort(IntSort()))
4970 """ Remove element e to set s
4971 >>> a = Const('a', SetSort(IntSort()))
4981 """ The complement of set s
4982 >>> a = Const('a', SetSort(IntSort()))
4983 >>> SetComplement(a)
4991 """ The set difference of a and b
4992 >>> a = Const('a', SetSort(IntSort()))
4993 >>> b = Const('b', SetSort(IntSort()))
4994 >>> SetDifference(a, b)
5002 """ Check if e is a member of set s
5003 >>> a = Const('a', SetSort(IntSort()))
5013 """ Check if a is a subset of b
5014 >>> a = Const('a', SetSort(IntSort()))
5015 >>> b = Const('b', SetSort(IntSort()))
5030 """Return `True` if acc is pair of the form (String, Datatype or Sort). """
5031 if not isinstance(acc, tuple):
5035 return isinstance(acc[0], str)
and (isinstance(acc[1], Datatype)
or is_sort(acc[1]))
5039 """Helper class for declaring Z3 datatypes.
5041 >>> List = Datatype('List')
5042 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5043 >>> List.declare('nil')
5044 >>> List = List.create()
5045 >>> # List is now a Z3 declaration
5048 >>> List.cons(10, List.nil)
5050 >>> List.cons(10, List.nil).sort()
5052 >>> cons = List.cons
5056 >>> n = cons(1, cons(0, nil))
5058 cons(1, cons(0, nil))
5059 >>> simplify(cdr(n))
5061 >>> simplify(car(n))
5077 _z3_assert(isinstance(name, str),
"String expected")
5078 _z3_assert(isinstance(rec_name, str),
"String expected")
5081 "Valid list of accessors expected. An accessor is a pair of the form (String, Datatype|Sort)",
5086 """Declare constructor named `name` with the given accessors `args`.
5087 Each accessor is a pair `(name, sort)`, where `name` is a string and `sort` a Z3 sort
5088 or a reference to the datatypes being declared.
5090 In the following example `List.declare('cons', ('car', IntSort()), ('cdr', List))`
5091 declares the constructor named `cons` that builds a new List using an integer and a List.
5092 It also declares the accessors `car` and `cdr`. The accessor `car` extracts the integer
5093 of a `cons` cell, and `cdr` the list of a `cons` cell. After all constructors were declared,
5094 we use the method create() to create the actual datatype in Z3.
5096 >>> List = Datatype('List')
5097 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5098 >>> List.declare('nil')
5099 >>> List = List.create()
5102 _z3_assert(isinstance(name, str),
"String expected")
5103 _z3_assert(name !=
"",
"Constructor name cannot be empty")
5110 """Create a Z3 datatype based on the constructors declared using the method `declare()`.
5112 The function `CreateDatatypes()` must be used to define mutually recursive datatypes.
5114 >>> List = Datatype('List')
5115 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5116 >>> List.declare('nil')
5117 >>> List = List.create()
5120 >>> List.cons(10, List.nil)
5127 """Auxiliary object used to create Z3 datatypes."""
5134 if self.
ctx.ref()
is not None and Z3_del_constructor
is not None:
5139 """Auxiliary object used to create Z3 datatypes."""
5146 if self.
ctx.ref()
is not None and Z3_del_constructor_list
is not None:
5151 """Create mutually recursive Z3 datatypes using 1 or more Datatype helper objects.
5153 In the following example we define a Tree-List using two mutually recursive datatypes.
5155 >>> TreeList = Datatype('TreeList')
5156 >>> Tree = Datatype('Tree')
5157 >>> # Tree has two constructors: leaf and node
5158 >>> Tree.declare('leaf', ('val', IntSort()))
5159 >>> # a node contains a list of trees
5160 >>> Tree.declare('node', ('children', TreeList))
5161 >>> TreeList.declare('nil')
5162 >>> TreeList.declare('cons', ('car', Tree), ('cdr', TreeList))
5163 >>> Tree, TreeList = CreateDatatypes(Tree, TreeList)
5164 >>> Tree.val(Tree.leaf(10))
5166 >>> simplify(Tree.val(Tree.leaf(10)))
5168 >>> n1 = Tree.node(TreeList.cons(Tree.leaf(10), TreeList.cons(Tree.leaf(20), TreeList.nil)))
5170 node(cons(leaf(10), cons(leaf(20), nil)))
5171 >>> n2 = Tree.node(TreeList.cons(n1, TreeList.nil))
5172 >>> simplify(n2 == n1)
5174 >>> simplify(TreeList.car(Tree.children(n2)) == n1)
5179 _z3_assert(len(ds) > 0,
"At least one Datatype must be specified")
5180 _z3_assert(all([isinstance(d, Datatype)
for d
in ds]),
"Arguments must be Datatypes")
5181 _z3_assert(all([d.ctx == ds[0].ctx
for d
in ds]),
"Context mismatch")
5182 _z3_assert(all([d.constructors != []
for d
in ds]),
"Non-empty Datatypes expected")
5185 names = (Symbol * num)()
5186 out = (Sort * num)()
5187 clists = (ConstructorList * num)()
5189 for i
in range(num):
5192 num_cs = len(d.constructors)
5193 cs = (Constructor * num_cs)()
5194 for j
in range(num_cs):
5195 c = d.constructors[j]
5200 fnames = (Symbol * num_fs)()
5201 sorts = (Sort * num_fs)()
5202 refs = (ctypes.c_uint * num_fs)()
5203 for k
in range(num_fs):
5207 if isinstance(ftype, Datatype):
5210 ds.count(ftype) == 1,
5211 "One and only one occurrence of each datatype is expected",
5214 refs[k] = ds.index(ftype)
5218 sorts[k] = ftype.ast
5227 for i
in range(num):
5229 num_cs = dref.num_constructors()
5230 for j
in range(num_cs):
5231 cref = dref.constructor(j)
5232 cref_name = cref.name()
5233 cref_arity = cref.arity()
5234 if cref.arity() == 0:
5236 setattr(dref, cref_name, cref)
5237 rref = dref.recognizer(j)
5238 setattr(dref,
"is_" + cref_name, rref)
5239 for k
in range(cref_arity):
5240 aref = dref.accessor(j, k)
5241 setattr(dref, aref.name(), aref)
5243 return tuple(result)
5247 """Datatype sorts."""
5250 """Return the number of constructors in the given Z3 datatype.
5252 >>> List = Datatype('List')
5253 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5254 >>> List.declare('nil')
5255 >>> List = List.create()
5256 >>> # List is now a Z3 declaration
5257 >>> List.num_constructors()
5263 """Return a constructor of the datatype `self`.
5265 >>> List = Datatype('List')
5266 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5267 >>> List.declare('nil')
5268 >>> List = List.create()
5269 >>> # List is now a Z3 declaration
5270 >>> List.num_constructors()
5272 >>> List.constructor(0)
5274 >>> List.constructor(1)
5282 """In Z3, each constructor has an associated recognizer predicate.
5284 If the constructor is named `name`, then the recognizer `is_name`.
5286 >>> List = Datatype('List')
5287 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5288 >>> List.declare('nil')
5289 >>> List = List.create()
5290 >>> # List is now a Z3 declaration
5291 >>> List.num_constructors()
5293 >>> List.recognizer(0)
5295 >>> List.recognizer(1)
5297 >>> simplify(List.is_nil(List.cons(10, List.nil)))
5299 >>> simplify(List.is_cons(List.cons(10, List.nil)))
5301 >>> l = Const('l', List)
5302 >>> simplify(List.is_cons(l))
5310 """In Z3, each constructor has 0 or more accessor.
5311 The number of accessors is equal to the arity of the constructor.
5313 >>> List = Datatype('List')
5314 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5315 >>> List.declare('nil')
5316 >>> List = List.create()
5317 >>> List.num_constructors()
5319 >>> List.constructor(0)
5321 >>> num_accs = List.constructor(0).arity()
5324 >>> List.accessor(0, 0)
5326 >>> List.accessor(0, 1)
5328 >>> List.constructor(1)
5330 >>> num_accs = List.constructor(1).arity()
5344 """Datatype expressions."""
5347 """Return the datatype sort of the datatype expression `self`."""
5351 """Create a reference to a sort that was declared, or will be declared, as a recursive datatype"""
5356 """Create a named tuple sort base on a set of underlying sorts
5358 >>> pair, mk_pair, (first, second) = TupleSort("pair", [IntSort(), StringSort()])
5361 projects = [(
"project%d" % i, sorts[i])
for i
in range(len(sorts))]
5362 tuple.declare(name, *projects)
5363 tuple = tuple.create()
5364 return tuple, tuple.constructor(0), [tuple.accessor(0, i)
for i
in range(len(sorts))]
5368 """Create a named tagged union sort base on a set of underlying sorts
5370 >>> sum, ((inject0, extract0), (inject1, extract1)) = DisjointSum("+", [IntSort(), StringSort()])
5373 for i
in range(len(sorts)):
5374 sum.declare(
"inject%d" % i, (
"project%d" % i, sorts[i]))
5376 return sum, [(sum.constructor(i), sum.accessor(i, 0))
for i
in range(len(sorts))]
5380 """Return a new enumeration sort named `name` containing the given values.
5382 The result is a pair (sort, list of constants).
5384 >>> Color, (red, green, blue) = EnumSort('Color', ['red', 'green', 'blue'])
5387 _z3_assert(isinstance(name, str),
"Name must be a string")
5388 _z3_assert(all([isinstance(v, str)
for v
in values]),
"Eumeration sort values must be strings")
5389 _z3_assert(len(values) > 0,
"At least one value expected")
5392 _val_names = (Symbol * num)()
5393 for i
in range(num):
5395 _values = (FuncDecl * num)()
5396 _testers = (FuncDecl * num)()
5400 for i
in range(num):
5402 V = [a()
for a
in V]
5413 """Set of parameters used to configure Solvers, Tactics and Simplifiers in Z3.
5415 Consider using the function `args2params` to create instances of this object.
5430 if self.
ctx.ref()
is not None and Z3_params_dec_ref
is not None:
5434 """Set parameter name with value val."""
5436 _z3_assert(isinstance(name, str),
"parameter name must be a string")
5438 if isinstance(val, bool):
5442 elif isinstance(val, float):
5444 elif isinstance(val, str):
5454 _z3_assert(isinstance(ds, ParamDescrsRef),
"parameter description set expected")
5459 """Convert python arguments into a Z3_params object.
5460 A ':' is added to the keywords, and '_' is replaced with '-'
5462 >>> args2params(['model', True, 'relevancy', 2], {'elim_and' : True})
5463 (params model true relevancy 2 elim_and true)
5466 _z3_assert(len(arguments) % 2 == 0,
"Argument list must have an even number of elements.")
5482 """Set of parameter descriptions for Solvers, Tactics and Simplifiers in Z3.
5486 _z3_assert(isinstance(descr, ParamDescrs),
"parameter description object expected")
5492 return ParamsDescrsRef(self.
descr, self.
ctx)
5495 if self.
ctx.ref()
is not None and Z3_param_descrs_dec_ref
is not None:
5499 """Return the size of in the parameter description `self`.
5504 """Return the size of in the parameter description `self`.
5509 """Return the i-th parameter name in the parameter description `self`.
5514 """Return the kind of the parameter named `n`.
5519 """Return the documentation string of the parameter named `n`.
5540 """Goal is a collection of constraints we want to find a solution or show to be unsatisfiable (infeasible).
5542 Goals are processed using Tactics. A Tactic transforms a goal into a set of subgoals.
5543 A goal has a solution if one of its subgoals has a solution.
5544 A goal is unsatisfiable if all subgoals are unsatisfiable.
5547 def __init__(self, models=True, unsat_cores=False, proofs=False, ctx=None, goal=None):
5550 "If goal is different from None, then ctx must be also different from None")
5553 if self.
goal is None:
5558 if self.
goal is not None and self.
ctx.ref()
is not None and Z3_goal_dec_ref
is not None:
5562 """Return the depth of the goal `self`.
5563 The depth corresponds to the number of tactics applied to `self`.
5565 >>> x, y = Ints('x y')
5567 >>> g.add(x == 0, y >= x + 1)
5570 >>> r = Then('simplify', 'solve-eqs')(g)
5571 >>> # r has 1 subgoal
5580 """Return `True` if `self` contains the `False` constraints.
5582 >>> x, y = Ints('x y')
5584 >>> g.inconsistent()
5586 >>> g.add(x == 0, x == 1)
5589 >>> g.inconsistent()
5591 >>> g2 = Tactic('propagate-values')(g)[0]
5592 >>> g2.inconsistent()
5598 """Return the precision (under-approximation, over-approximation, or precise) of the goal `self`.
5601 >>> g.prec() == Z3_GOAL_PRECISE
5603 >>> x, y = Ints('x y')
5604 >>> g.add(x == y + 1)
5605 >>> g.prec() == Z3_GOAL_PRECISE
5607 >>> t = With(Tactic('add-bounds'), add_bound_lower=0, add_bound_upper=10)
5610 [x == y + 1, x <= 10, x >= 0, y <= 10, y >= 0]
5611 >>> g2.prec() == Z3_GOAL_PRECISE
5613 >>> g2.prec() == Z3_GOAL_UNDER
5619 """Alias for `prec()`.
5622 >>> g.precision() == Z3_GOAL_PRECISE
5628 """Return the number of constraints in the goal `self`.
5633 >>> x, y = Ints('x y')
5634 >>> g.add(x == 0, y > x)
5641 """Return the number of constraints in the goal `self`.
5646 >>> x, y = Ints('x y')
5647 >>> g.add(x == 0, y > x)
5654 """Return a constraint in the goal `self`.
5657 >>> x, y = Ints('x y')
5658 >>> g.add(x == 0, y > x)
5667 """Return a constraint in the goal `self`.
5670 >>> x, y = Ints('x y')
5671 >>> g.add(x == 0, y > x)
5677 if arg >= len(self):
5679 return self.
get(arg)
5682 """Assert constraints into the goal.
5686 >>> g.assert_exprs(x > 0, x < 2)
5701 >>> g.append(x > 0, x < 2)
5712 >>> g.insert(x > 0, x < 2)
5723 >>> g.add(x > 0, x < 2)
5730 """Retrieve model from a satisfiable goal
5731 >>> a, b = Ints('a b')
5733 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
5734 >>> t = Then(Tactic('split-clause'), Tactic('solve-eqs'))
5737 [Or(b == 0, b == 1), Not(0 <= b)]
5739 [Or(b == 0, b == 1), Not(1 <= b)]
5740 >>> # Remark: the subgoal r[0] is unsatisfiable
5741 >>> # Creating a solver for solving the second subgoal
5748 >>> # Model s.model() does not assign a value to `a`
5749 >>> # It is a model for subgoal `r[1]`, but not for goal `g`
5750 >>> # The method convert_model creates a model for `g` from a model for `r[1]`.
5751 >>> r[1].convert_model(s.model())
5755 _z3_assert(isinstance(model, ModelRef),
"Z3 Model expected")
5759 return obj_to_string(self)
5762 """Return a textual representation of the s-expression representing the goal."""
5766 """Return a textual representation of the goal in DIMACS format."""
5770 """Copy goal `self` to context `target`.
5778 >>> g2 = g.translate(c2)
5781 >>> g.ctx == main_ctx()
5785 >>> g2.ctx == main_ctx()
5789 _z3_assert(isinstance(target, Context),
"target must be a context")
5799 """Return a new simplified goal.
5801 This method is essentially invoking the simplify tactic.
5805 >>> g.add(x + 1 >= 2)
5808 >>> g2 = g.simplify()
5811 >>> # g was not modified
5816 return t.apply(self, *arguments, **keywords)[0]
5819 """Return goal `self` as a single Z3 expression.
5838 return And([self.
get(i)
for i
in range(len(self))], self.
ctx)
5848 """A collection (vector) of ASTs."""
5857 assert ctx
is not None
5862 if self.
vector is not None and self.
ctx.ref()
is not None and Z3_ast_vector_dec_ref
is not None:
5866 """Return the size of the vector `self`.
5871 >>> A.push(Int('x'))
5872 >>> A.push(Int('x'))
5879 """Return the AST at position `i`.
5882 >>> A.push(Int('x') + 1)
5883 >>> A.push(Int('y'))
5890 if isinstance(i, int):
5898 elif isinstance(i, slice):
5900 for ii
in range(*i.indices(self.
__len__())):
5908 """Update AST at position `i`.
5911 >>> A.push(Int('x') + 1)
5912 >>> A.push(Int('y'))
5924 """Add `v` in the end of the vector.
5929 >>> A.push(Int('x'))
5936 """Resize the vector to `sz` elements.
5942 >>> for i in range(10): A[i] = Int('x')
5949 """Return `True` if the vector contains `item`.
5972 """Copy vector `self` to context `other_ctx`.
5978 >>> B = A.translate(c2)
5994 return obj_to_string(self)
5997 """Return a textual representation of the s-expression representing the vector."""
6008 """A mapping from ASTs to ASTs."""
6017 assert ctx
is not None
6025 if self.
map is not None and self.
ctx.ref()
is not None and Z3_ast_map_dec_ref
is not None:
6029 """Return the size of the map.
6035 >>> M[x] = IntVal(1)
6042 """Return `True` if the map contains key `key`.
6055 """Retrieve the value associated with key `key`.
6066 """Add/Update key `k` with value `v`.
6075 >>> M[x] = IntVal(1)
6085 """Remove the entry associated with key `k`.
6099 """Remove all entries from the map.
6104 >>> M[x+x] = IntVal(1)
6114 """Return an AstVector containing all keys in the map.
6119 >>> M[x+x] = IntVal(1)
6133 """Store the value of the interpretation of a function in a particular point."""
6144 if self.
ctx.ref()
is not None and Z3_func_entry_dec_ref
is not None:
6148 """Return the number of arguments in the given entry.
6150 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6152 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6157 >>> f_i.num_entries()
6159 >>> e = f_i.entry(0)
6166 """Return the value of argument `idx`.
6168 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6170 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6175 >>> f_i.num_entries()
6177 >>> e = f_i.entry(0)
6188 ... except IndexError:
6189 ... print("index error")
6197 """Return the value of the function at point `self`.
6199 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6201 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6206 >>> f_i.num_entries()
6208 >>> e = f_i.entry(0)
6219 """Return entry `self` as a Python list.
6220 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6222 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6227 >>> f_i.num_entries()
6229 >>> e = f_i.entry(0)
6234 args.append(self.
value())
6242 """Stores the interpretation of a function in a Z3 model."""
6247 if self.
f is not None:
6251 if self.
f is not None and self.
ctx.ref()
is not None and Z3_func_interp_dec_ref
is not None:
6256 Return the `else` value for a function interpretation.
6257 Return None if Z3 did not specify the `else` value for
6260 >>> f = Function('f', IntSort(), IntSort())
6262 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6268 >>> m[f].else_value()
6278 """Return the number of entries/points in the function interpretation `self`.
6280 >>> f = Function('f', IntSort(), IntSort())
6282 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6288 >>> m[f].num_entries()
6294 """Return the number of arguments for each entry in the function interpretation `self`.
6296 >>> f = Function('f', IntSort(), IntSort())
6298 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6308 """Return an entry at position `idx < self.num_entries()` in the function interpretation `self`.
6310 >>> f = Function('f', IntSort(), IntSort())
6312 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6318 >>> m[f].num_entries()
6328 """Copy model 'self' to context 'other_ctx'.
6339 """Return the function interpretation as a Python list.
6340 >>> f = Function('f', IntSort(), IntSort())
6342 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6356 return obj_to_string(self)
6360 """Model/Solution of a satisfiability problem (aka system of constraints)."""
6363 assert ctx
is not None
6369 if self.
ctx.ref()
is not None and Z3_model_dec_ref
is not None:
6373 return obj_to_string(self)
6376 """Return a textual representation of the s-expression representing the model."""
6379 def eval(self, t, model_completion=False):
6380 """Evaluate the expression `t` in the model `self`.
6381 If `model_completion` is enabled, then a default interpretation is automatically added
6382 for symbols that do not have an interpretation in the model `self`.
6386 >>> s.add(x > 0, x < 2)
6399 >>> m.eval(y, model_completion=True)
6401 >>> # Now, m contains an interpretation for y
6408 raise Z3Exception(
"failed to evaluate expression in the model")
6411 """Alias for `eval`.
6415 >>> s.add(x > 0, x < 2)
6419 >>> m.evaluate(x + 1)
6421 >>> m.evaluate(x == 1)
6424 >>> m.evaluate(y + x)
6428 >>> m.evaluate(y, model_completion=True)
6430 >>> # Now, m contains an interpretation for y
6431 >>> m.evaluate(y + x)
6434 return self.
eval(t, model_completion)
6437 """Return the number of constant and function declarations in the model `self`.
6439 >>> f = Function('f', IntSort(), IntSort())
6442 >>> s.add(x > 0, f(x) != x)
6451 return num_consts + num_funcs
6454 """Return the interpretation for a given declaration or constant.
6456 >>> f = Function('f', IntSort(), IntSort())
6459 >>> s.add(x > 0, x < 2, f(x) == 0)
6469 _z3_assert(isinstance(decl, FuncDeclRef)
or is_const(decl),
"Z3 declaration expected")
6473 if decl.arity() == 0:
6475 if _r.value
is None:
6491 sz = fi.num_entries()
6495 e =
Store(e, fe.arg_value(0), fe.value())
6506 """Return the number of uninterpreted sorts that contain an interpretation in the model `self`.
6508 >>> A = DeclareSort('A')
6509 >>> a, b = Consts('a b', A)
6521 """Return the uninterpreted sort at position `idx` < self.num_sorts().
6523 >>> A = DeclareSort('A')
6524 >>> B = DeclareSort('B')
6525 >>> a1, a2 = Consts('a1 a2', A)
6526 >>> b1, b2 = Consts('b1 b2', B)
6528 >>> s.add(a1 != a2, b1 != b2)
6544 """Return all uninterpreted sorts that have an interpretation in the model `self`.
6546 >>> A = DeclareSort('A')
6547 >>> B = DeclareSort('B')
6548 >>> a1, a2 = Consts('a1 a2', A)
6549 >>> b1, b2 = Consts('b1 b2', B)
6551 >>> s.add(a1 != a2, b1 != b2)
6561 """Return the interpretation for the uninterpreted sort `s` in the model `self`.
6563 >>> A = DeclareSort('A')
6564 >>> a, b = Consts('a b', A)
6570 >>> m.get_universe(A)
6574 _z3_assert(isinstance(s, SortRef),
"Z3 sort expected")
6581 """If `idx` is an integer, then the declaration at position `idx` in the model `self` is returned.
6582 If `idx` is a declaration, then the actual interpretation is returned.
6584 The elements can be retrieved using position or the actual declaration.
6586 >>> f = Function('f', IntSort(), IntSort())
6589 >>> s.add(x > 0, x < 2, f(x) == 0)
6603 >>> for d in m: print("%s -> %s" % (d, m[d]))
6608 if idx >= len(self):
6611 if (idx < num_consts):
6615 if isinstance(idx, FuncDeclRef):
6619 if isinstance(idx, SortRef):
6622 _z3_assert(
False,
"Integer, Z3 declaration, or Z3 constant expected")
6626 """Return a list with all symbols that have an interpretation in the model `self`.
6627 >>> f = Function('f', IntSort(), IntSort())
6630 >>> s.add(x > 0, x < 2, f(x) == 0)
6645 """Update the interpretation of a constant"""
6648 if is_func_decl(x)
and x.arity() != 0
and isinstance(value, FuncInterp):
6652 for i
in range(value.num_entries()):
6657 v.push(e.arg_value(j))
6662 raise Z3Exception(
"Expecting 0-ary function or constant expression")
6667 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
6670 _z3_assert(isinstance(target, Context),
"argument must be a Z3 context")
6687 """Return true if n is a Z3 expression of the form (_ as-array f)."""
6688 return isinstance(n, ExprRef)
and Z3_is_as_array(n.ctx.ref(), n.as_ast())
6692 """Return the function declaration f associated with a Z3 expression of the form (_ as-array f)."""
6705 """Statistics for `Solver.check()`."""
6716 if self.
ctx.ref()
is not None and Z3_stats_dec_ref
is not None:
6723 out.write(u(
'<table border="1" cellpadding="2" cellspacing="0">'))
6726 out.write(u(
'<tr style="background-color:#CFCFCF">'))
6729 out.write(u(
"<tr>"))
6731 out.write(u(
"<td>%s</td><td>%s</td></tr>" % (k, v)))
6732 out.write(u(
"</table>"))
6733 return out.getvalue()
6738 """Return the number of statistical counters.
6741 >>> s = Then('simplify', 'nlsat').solver()
6745 >>> st = s.statistics()
6752 """Return the value of statistical counter at position `idx`. The result is a pair (key, value).
6755 >>> s = Then('simplify', 'nlsat').solver()
6759 >>> st = s.statistics()
6763 ('nlsat propagations', 2)
6767 if idx >= len(self):
6776 """Return the list of statistical counters.
6779 >>> s = Then('simplify', 'nlsat').solver()
6783 >>> st = s.statistics()
6788 """Return the value of a particular statistical counter.
6791 >>> s = Then('simplify', 'nlsat').solver()
6795 >>> st = s.statistics()
6796 >>> st.get_key_value('nlsat propagations')
6799 for idx
in range(len(self)):
6805 raise Z3Exception(
"unknown key")
6808 """Access the value of statistical using attributes.
6810 Remark: to access a counter containing blank spaces (e.g., 'nlsat propagations'),
6811 we should use '_' (e.g., 'nlsat_propagations').
6814 >>> s = Then('simplify', 'nlsat').solver()
6818 >>> st = s.statistics()
6819 >>> st.nlsat_propagations
6824 key = name.replace(
"_",
" ")
6828 raise AttributeError
6838 """Represents the result of a satisfiability check: sat, unsat, unknown.
6844 >>> isinstance(r, CheckSatResult)
6855 return isinstance(other, CheckSatResult)
and self.
r == other.r
6858 return not self.
__eq__(other)
6862 if self.
r == Z3_L_TRUE:
6864 elif self.
r == Z3_L_FALSE:
6865 return "<b>unsat</b>"
6867 return "<b>unknown</b>"
6869 if self.
r == Z3_L_TRUE:
6871 elif self.
r == Z3_L_FALSE:
6877 in_html = in_html_mode()
6880 set_html_mode(in_html)
6891 Solver API provides methods for implementing the main SMT 2.0 commands:
6892 push, pop, check, get-model, etc.
6895 def __init__(self, solver=None, ctx=None, logFile=None):
6896 assert solver
is None or ctx
is not None
6905 if logFile
is not None:
6906 self.
set(
"smtlib2_log", logFile)
6909 if self.
solver is not None and self.
ctx.ref()
is not None and Z3_solver_dec_ref
is not None:
6913 """Set a configuration option.
6914 The method `help()` return a string containing all available options.
6917 >>> # The option MBQI can be set using three different approaches.
6918 >>> s.set(mbqi=True)
6919 >>> s.set('MBQI', True)
6920 >>> s.set(':mbqi', True)
6926 """Create a backtracking point.
6948 """Backtrack \\c num backtracking points.
6970 """Return the current number of backtracking points.
6988 """Remove all asserted constraints and backtracking points created using `push()`.
7002 """Assert constraints into the solver.
7006 >>> s.assert_exprs(x > 0, x < 2)
7013 if isinstance(arg, Goal)
or isinstance(arg, AstVector):
7021 """Assert constraints into the solver.
7025 >>> s.add(x > 0, x < 2)
7036 """Assert constraints into the solver.
7040 >>> s.append(x > 0, x < 2)
7047 """Assert constraints into the solver.
7051 >>> s.insert(x > 0, x < 2)
7058 """Assert constraint `a` and track it in the unsat core using the Boolean constant `p`.
7060 If `p` is a string, it will be automatically converted into a Boolean constant.
7065 >>> s.set(unsat_core=True)
7066 >>> s.assert_and_track(x > 0, 'p1')
7067 >>> s.assert_and_track(x != 1, 'p2')
7068 >>> s.assert_and_track(x < 0, p3)
7069 >>> print(s.check())
7071 >>> c = s.unsat_core()
7081 if isinstance(p, str):
7083 _z3_assert(isinstance(a, BoolRef),
"Boolean expression expected")
7088 """Check whether the assertions in the given solver plus the optional assumptions are consistent or not.
7094 >>> s.add(x > 0, x < 2)
7097 >>> s.model().eval(x)
7103 >>> s.add(2**x == 4)
7109 num = len(assumptions)
7110 _assumptions = (Ast * num)()
7111 for i
in range(num):
7112 _assumptions[i] = s.cast(assumptions[i]).as_ast()
7117 """Return a model for the last `check()`.
7119 This function raises an exception if
7120 a model is not available (e.g., last `check()` returned unsat).
7124 >>> s.add(a + 2 == 0)
7133 raise Z3Exception(
"model is not available")
7136 """Import model converter from other into the current solver"""
7137 Z3_solver_import_model_converter(self.ctx.ref(), other.solver, self.solver)
7139 def unsat_core(self):
7140 """Return a subset (as an AST vector) of the assumptions provided to the last check().
7142 These are the assumptions Z3 used in the unsatisfiability proof.
7143 Assumptions are available in Z3. They are used to extract unsatisfiable cores.
7144 They may be also used to "retract" assumptions. Note that, assumptions are not really
7145 "soft constraints", but they can be used to implement them.
7147 >>> p1, p2, p3 = Bools('p1 p2 p3')
7148 >>> x, y = Ints('x y')
7150 >>> s.add(Implies(p1, x > 0))
7151 >>> s.add(Implies(p2, y > x))
7152 >>> s.add(Implies(p2, y < 1))
7153 >>> s.add(Implies(p3, y > -3))
7154 >>> s.check(p1, p2, p3)
7156 >>> core = s.unsat_core()
7165 >>> # "Retracting" p2
7169 return AstVector(Z3_solver_get_unsat_core(self.ctx.ref(), self.solver), self.ctx)
7171 def consequences(self, assumptions, variables):
7172 """Determine fixed values for the variables based on the solver state and assumptions.
7174 >>> a, b, c, d = Bools('a b c d')
7175 >>> s.add(Implies(a,b), Implies(b, c))
7176 >>> s.consequences([a],[b,c,d])
7177 (sat, [Implies(a, b), Implies(a, c)])
7178 >>> s.consequences([Not(c),d],[a,b,c,d])
7179 (sat, [Implies(d, d), Implies(Not(c), Not(c)), Implies(Not(c), Not(b)), Implies(Not(c), Not(a))])
7181 if isinstance(assumptions, list):
7182 _asms = AstVector(None, self.ctx)
7183 for a in assumptions:
7186 if isinstance(variables, list):
7187 _vars = AstVector(None, self.ctx)
7191 _z3_assert(isinstance(assumptions, AstVector), "ast vector expected")
7192 _z3_assert(isinstance(variables, AstVector), "ast vector expected")
7193 consequences = AstVector(None, self.ctx)
7194 r = Z3_solver_get_consequences(self.ctx.ref(), self.solver, assumptions.vector,
7195 variables.vector, consequences.vector)
7196 sz = len(consequences)
7197 consequences = [consequences[i] for i in range(sz)]
7198 return CheckSatResult(r), consequences
7200 def from_file(self, filename):
7201 """Parse assertions from a file"""
7202 Z3_solver_from_file(self.ctx.ref(), self.solver, filename)
7204 def from_string(self, s):
7205 """Parse assertions from a string"""
7206 Z3_solver_from_string(self.ctx.ref(), self.solver, s)
7208 def cube(self, vars=None):
7210 The method takes an optional set of variables that restrict which
7211 variables may be used as a starting point for cubing.
7212 If vars is not None, then the first case split is based on a variable in
7215 self.cube_vs = AstVector(None, self.ctx)
7216 if vars is not None:
7218 self.cube_vs.push(v)
7220 lvl = self.backtrack_level
7221 self.backtrack_level = 4000000000
7222 r = AstVector(Z3_solver_cube(self.ctx.ref(), self.solver, self.cube_vs.vector, lvl), self.ctx)
7223 if (len(r) == 1 and is_false(r[0])):
7229 def cube_vars(self):
7230 """Access the set of variables that were touched by the most recently generated cube.
7231 This set of variables can be used as a starting point for additional cubes.
7232 The idea is that variables that appear in clauses that are reduced by the most recent
7233 cube are likely more useful to cube on."""
7237 t = _py2expr(t, self.ctx)
7238 """Retrieve congruence closure root of the term t relative to the current search state
7239 The function primarily works for SimpleSolver. Terms and variables that are
7240 eliminated during pre-processing are not visible to the congruence closure.
7242 return _to_expr_ref(Z3_solver_congruence_root(self.ctx.ref(), self.solver, t.ast), self.ctx)
7245 t = _py2expr(t, self.ctx)
7246 """Retrieve congruence closure sibling of the term t relative to the current search state
7247 The function primarily works for SimpleSolver. Terms and variables that are
7248 eliminated during pre-processing are not visible to the congruence closure.
7250 return _to_expr_ref(Z3_solver_congruence_next(self.ctx.ref(), self.solver, t.ast), self.ctx)
7253 """Return a proof for the last `check()`. Proof construction must be enabled."""
7254 return _to_expr_ref(Z3_solver_get_proof(self.ctx.ref(), self.solver), self.ctx)
7256 def assertions(self):
7257 """Return an AST vector containing all added constraints.
7268 return AstVector(Z3_solver_get_assertions(self.ctx.ref(), self.solver), self.ctx)
7271 """Return an AST vector containing all currently inferred units.
7273 return AstVector(Z3_solver_get_units(self.ctx.ref(), self.solver), self.ctx)
7275 def non_units(self):
7276 """Return an AST vector containing all atomic formulas in solver state that are not units.
7278 return AstVector(Z3_solver_get_non_units(self.ctx.ref(), self.solver), self.ctx)
7280 def trail_levels(self):
7281 """Return trail and decision levels of the solver state after a check() call.
7283 trail = self.trail()
7284 levels = (ctypes.c_uint * len(trail))()
7285 Z3_solver_get_levels(self.ctx.ref(), self.solver, trail.vector, len(trail), levels)
7286 return trail, levels
7289 """Return trail of the solver state after a check() call.
7291 return AstVector(Z3_solver_get_trail(self.ctx.ref(), self.solver), self.ctx)
7293 def statistics(self):
7294 """Return statistics for the last `check()`.
7296 >>> s = SimpleSolver()
7301 >>> st = s.statistics()
7302 >>> st.get_key_value('final checks')
7309 return Statistics(Z3_solver_get_statistics(self.ctx.ref(), self.solver), self.ctx)
7311 def reason_unknown(self):
7312 """Return a string describing why the last `check()` returned `unknown`.
7315 >>> s = SimpleSolver()
7316 >>> s.add(2**x == 4)
7319 >>> s.reason_unknown()
7320 '(incomplete (theory arithmetic))'
7322 return Z3_solver_get_reason_unknown(self.ctx.ref(), self.solver)
7325 """Display a string describing all available options."""
7326 print(Z3_solver_get_help(self.ctx.ref(), self.solver))
7328 def param_descrs(self):
7329 """Return the parameter description set."""
7330 return ParamDescrsRef(Z3_solver_get_param_descrs(self.ctx.ref(), self.solver), self.ctx)
7333 """Return a formatted string with all added constraints."""
7334 return obj_to_string(self)
7336 def translate(self, target):
7337 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
7341 >>> s1 = Solver(ctx=c1)
7342 >>> s2 = s1.translate(c2)
7345 _z3_assert(isinstance(target, Context), "argument must be a Z3 context")
7346 solver = Z3_solver_translate(self.ctx.ref(), self.solver, target.ref())
7347 return Solver(solver, target)
7350 return self.translate(self.ctx)
7352 def __deepcopy__(self, memo={}):
7353 return self.translate(self.ctx)
7356 """Return a formatted string (in Lisp-like format) with all added constraints.
7357 We say the string is in s-expression format.
7365 return Z3_solver_to_string(self.ctx.ref(), self.solver)
7367 def dimacs(self, include_names=True):
7368 """Return a textual representation of the solver in DIMACS format."""
7369 return Z3_solver_to_dimacs_string(self.ctx.ref(), self.solver, include_names)
7372 """return SMTLIB2 formatted benchmark for solver's assertions"""
7373 es = self.assertions()
7379 for i in range(sz1):
7380 v[i] = es[i].as_ast()
7382 e = es[sz1].as_ast()
7384 e = BoolVal(True, self.ctx).as_ast()
7385 return Z3_benchmark_to_smtlib_string(
7386 self.ctx.ref(), "benchmark generated from python API", "", "unknown", "", sz1, v, e,
7390def SolverFor(logic, ctx=None, logFile=None):
7391 """Create a solver customized for the given logic.
7393 The parameter `logic` is a string. It should be contains
7394 the name of a SMT-LIB logic.
7395 See http://www.smtlib.org/ for the name of all available logics.
7397 >>> s = SolverFor("QF_LIA")
7407 logic = to_symbol(logic)
7408 return Solver(Z3_mk_solver_for_logic(ctx.ref(), logic), ctx, logFile)
7411def SimpleSolver(ctx=None, logFile=None):
7412 """Return a simple general purpose solver with limited amount of preprocessing.
7414 >>> s = SimpleSolver()
7421 return Solver(Z3_mk_simple_solver(ctx.ref()), ctx, logFile)
7423#########################################
7427#########################################
7430class Fixedpoint(Z3PPObject):
7431 """Fixedpoint API provides methods for solving with recursive predicates"""
7433 def __init__(self, fixedpoint=None, ctx=None):
7434 assert fixedpoint is None or ctx is not None
7435 self.ctx = _get_ctx(ctx)
7436 self.fixedpoint = None
7437 if fixedpoint is None:
7438 self.fixedpoint = Z3_mk_fixedpoint(self.ctx.ref())
7440 self.fixedpoint = fixedpoint
7441 Z3_fixedpoint_inc_ref(self.ctx.ref(), self.fixedpoint)
7444 def __deepcopy__(self, memo={}):
7445 return FixedPoint(self.fixedpoint, self.ctx)
7448 if self.fixedpoint is not None and self.ctx.ref() is not None and Z3_fixedpoint_dec_ref is not None:
7449 Z3_fixedpoint_dec_ref(self.ctx.ref(), self.fixedpoint)
7451 def set(self, *args, **keys):
7452 """Set a configuration option. The method `help()` return a string containing all available options.
7454 p = args2params(args, keys, self.ctx)
7455 Z3_fixedpoint_set_params(self.ctx.ref(), self.fixedpoint, p.params)
7458 """Display a string describing all available options."""
7459 print(Z3_fixedpoint_get_help(self.ctx.ref(), self.fixedpoint))
7461 def param_descrs(self):
7462 """Return the parameter description set."""
7463 return ParamDescrsRef(Z3_fixedpoint_get_param_descrs(self.ctx.ref(), self.fixedpoint), self.ctx)
7465 def assert_exprs(self, *args):
7466 """Assert constraints as background axioms for the fixedpoint solver."""
7467 args = _get_args(args)
7468 s = BoolSort(self.ctx)
7470 if isinstance(arg, Goal) or isinstance(arg, AstVector):
7472 f = self.abstract(f)
7473 Z3_fixedpoint_assert(self.ctx.ref(), self.fixedpoint, f.as_ast())
7476 arg = self.abstract(arg)
7477 Z3_fixedpoint_assert(self.ctx.ref(), self.fixedpoint, arg.as_ast())
7479 def add(self, *args):
7480 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7481 self.assert_exprs(*args)
7483 def __iadd__(self, fml):
7487 def append(self, *args):
7488 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7489 self.assert_exprs(*args)
7491 def insert(self, *args):
7492 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7493 self.assert_exprs(*args)
7495 def add_rule(self, head, body=None, name=None):
7496 """Assert rules defining recursive predicates to the fixedpoint solver.
7499 >>> s = Fixedpoint()
7500 >>> s.register_relation(a.decl())
7501 >>> s.register_relation(b.decl())
7509 name = to_symbol(name, self.ctx)
7511 head = self.abstract(head)
7512 Z3_fixedpoint_add_rule(self.ctx.ref(), self.fixedpoint, head.as_ast(), name)
7514 body = _get_args(body)
7515 f = self.abstract(Implies(And(body, self.ctx), head))
7516 Z3_fixedpoint_add_rule(self.ctx.ref(), self.fixedpoint, f.as_ast(), name)
7518 def rule(self, head, body=None, name=None):
7519 """Assert rules defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7520 self.add_rule(head, body, name)
7522 def fact(self, head, name=None):
7523 """Assert facts defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7524 self.add_rule(head, None, name)
7526 def query(self, *query):
7527 """Query the fixedpoint engine whether formula is derivable.
7528 You can also pass an tuple or list of recursive predicates.
7530 query = _get_args(query)
7532 if sz >= 1 and isinstance(query[0], FuncDeclRef):
7533 _decls = (FuncDecl * sz)()
7538 r = Z3_fixedpoint_query_relations(self.ctx.ref(), self.fixedpoint, sz, _decls)
7543 query = And(query, self.ctx)
7544 query = self.abstract(query, False)
7545 r = Z3_fixedpoint_query(self.ctx.ref(), self.fixedpoint, query.as_ast())
7546 return CheckSatResult(r)
7548 def query_from_lvl(self, lvl, *query):
7549 """Query the fixedpoint engine whether formula is derivable starting at the given query level.
7551 query = _get_args(query)
7553 if sz >= 1 and isinstance(query[0], FuncDecl):
7554 _z3_assert(False, "unsupported")
7560 query = self.abstract(query, False)
7561 r = Z3_fixedpoint_query_from_lvl(self.ctx.ref(), self.fixedpoint, query.as_ast(), lvl)
7562 return CheckSatResult(r)
7564 def update_rule(self, head, body, name):
7568 name = to_symbol(name, self.ctx)
7569 body = _get_args(body)
7570 f = self.abstract(Implies(And(body, self.ctx), head))
7571 Z3_fixedpoint_update_rule(self.ctx.ref(), self.fixedpoint, f.as_ast(), name)
7573 def get_answer(self):
7574 """Retrieve answer from last query call."""
7575 r = Z3_fixedpoint_get_answer(self.ctx.ref(), self.fixedpoint)
7576 return _to_expr_ref(r, self.ctx)
7578 def get_ground_sat_answer(self):
7579 """Retrieve a ground cex from last query call."""
7580 r = Z3_fixedpoint_get_ground_sat_answer(self.ctx.ref(), self.fixedpoint)
7581 return _to_expr_ref(r, self.ctx)
7583 def get_rules_along_trace(self):
7584 """retrieve rules along the counterexample trace"""
7585 return AstVector(Z3_fixedpoint_get_rules_along_trace(self.ctx.ref(), self.fixedpoint), self.ctx)
7587 def get_rule_names_along_trace(self):
7588 """retrieve rule names along the counterexample trace"""
7589 # this is a hack as I don't know how to return a list of symbols from C++;
7590 # obtain names as a single string separated by semicolons
7591 names = _symbol2py(self.ctx, Z3_fixedpoint_get_rule_names_along_trace(self.ctx.ref(), self.fixedpoint))
7592 # split into individual names
7593 return names.split(";")
7595 def get_num_levels(self, predicate):
7596 """Retrieve number of levels used for predicate in PDR engine"""
7597 return Z3_fixedpoint_get_num_levels(self.ctx.ref(), self.fixedpoint, predicate.ast)
7599 def get_cover_delta(self, level, predicate):
7600 """Retrieve properties known about predicate for the level'th unfolding.
7601 -1 is treated as the limit (infinity)
7603 r = Z3_fixedpoint_get_cover_delta(self.ctx.ref(), self.fixedpoint, level, predicate.ast)
7604 return _to_expr_ref(r, self.ctx)
7606 def add_cover(self, level, predicate, property):
7607 """Add property to predicate for the level'th unfolding.
7608 -1 is treated as infinity (infinity)
7610 Z3_fixedpoint_add_cover(self.ctx.ref(), self.fixedpoint, level, predicate.ast, property.ast)
7612 def register_relation(self, *relations):
7613 """Register relation as recursive"""
7614 relations = _get_args(relations)
7616 Z3_fixedpoint_register_relation(self.ctx.ref(), self.fixedpoint, f.ast)
7618 def set_predicate_representation(self, f, *representations):
7619 """Control how relation is represented"""
7620 representations = _get_args(representations)
7621 representations = [to_symbol(s) for s in representations]
7622 sz = len(representations)
7623 args = (Symbol * sz)()
7625 args[i] = representations[i]
7626 Z3_fixedpoint_set_predicate_representation(self.ctx.ref(), self.fixedpoint, f.ast, sz, args)
7628 def parse_string(self, s):
7629 """Parse rules and queries from a string"""
7630 return AstVector(Z3_fixedpoint_from_string(self.ctx.ref(), self.fixedpoint, s), self.ctx)
7632 def parse_file(self, f):
7633 """Parse rules and queries from a file"""
7634 return AstVector(Z3_fixedpoint_from_file(self.ctx.ref(), self.fixedpoint, f), self.ctx)
7636 def get_rules(self):
7637 """retrieve rules that have been added to fixedpoint context"""
7638 return AstVector(Z3_fixedpoint_get_rules(self.ctx.ref(), self.fixedpoint), self.ctx)
7640 def get_assertions(self):
7641 """retrieve assertions that have been added to fixedpoint context"""
7642 return AstVector(Z3_fixedpoint_get_assertions(self.ctx.ref(), self.fixedpoint), self.ctx)
7645 """Return a formatted string with all added rules and constraints."""
7649 """Return a formatted string (in Lisp-like format) with all added constraints.
7650 We say the string is in s-expression format.
7652 return Z3_fixedpoint_to_string(self.ctx.ref(), self.fixedpoint, 0, (Ast * 0)())
7654 def to_string(self, queries):
7655 """Return a formatted string (in Lisp-like format) with all added constraints.
7656 We say the string is in s-expression format.
7657 Include also queries.
7659 args, len = _to_ast_array(queries)
7660 return Z3_fixedpoint_to_string(self.ctx.ref(), self.fixedpoint, len, args)
7662 def statistics(self):
7663 """Return statistics for the last `query()`.
7665 return Statistics(Z3_fixedpoint_get_statistics(self.ctx.ref(), self.fixedpoint), self.ctx)
7667 def reason_unknown(self):
7668 """Return a string describing why the last `query()` returned `unknown`.
7670 return Z3_fixedpoint_get_reason_unknown(self.ctx.ref(), self.fixedpoint)
7672 def declare_var(self, *vars):
7673 """Add variable or several variables.
7674 The added variable or variables will be bound in the rules
7677 vars = _get_args(vars)
7681 def abstract(self, fml, is_forall=True):
7685 return ForAll(self.vars, fml)
7687 return Exists(self.vars, fml)
7690#########################################
7694#########################################
7696class FiniteDomainSortRef(SortRef):
7697 """Finite domain sort."""
7700 """Return the size of the finite domain sort"""
7701 r = (ctypes.c_ulonglong * 1)()
7702 if Z3_get_finite_domain_sort_size(self.ctx_ref(), self.ast, r):
7705 raise Z3Exception("Failed to retrieve finite domain sort size")
7708def FiniteDomainSort(name, sz, ctx=None):
7709 """Create a named finite domain sort of a given size sz"""
7710 if not isinstance(name, Symbol):
7711 name = to_symbol(name)
7713 return FiniteDomainSortRef(Z3_mk_finite_domain_sort(ctx.ref(), name, sz), ctx)
7716def is_finite_domain_sort(s):
7717 """Return True if `s` is a Z3 finite-domain sort.
7719 >>> is_finite_domain_sort(FiniteDomainSort('S', 100))
7721 >>> is_finite_domain_sort(IntSort())
7724 return isinstance(s, FiniteDomainSortRef)
7727class FiniteDomainRef(ExprRef):
7728 """Finite-domain expressions."""
7731 """Return the sort of the finite-domain expression `self`."""
7732 return FiniteDomainSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
7734 def as_string(self):
7735 """Return a Z3 floating point expression as a Python string."""
7736 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
7739def is_finite_domain(a):
7740 """Return `True` if `a` is a Z3 finite-domain expression.
7742 >>> s = FiniteDomainSort('S', 100)
7743 >>> b = Const('b', s)
7744 >>> is_finite_domain(b)
7746 >>> is_finite_domain(Int('x'))
7749 return isinstance(a, FiniteDomainRef)
7752class FiniteDomainNumRef(FiniteDomainRef):
7753 """Integer values."""
7756 """Return a Z3 finite-domain numeral as a Python long (bignum) numeral.
7758 >>> s = FiniteDomainSort('S', 100)
7759 >>> v = FiniteDomainVal(3, s)
7765 return int(self.as_string())
7767 def as_string(self):
7768 """Return a Z3 finite-domain numeral as a Python string.
7770 >>> s = FiniteDomainSort('S', 100)
7771 >>> v = FiniteDomainVal(42, s)
7775 return Z3_get_numeral_string(self.ctx_ref(), self.as_ast())
7778def FiniteDomainVal(val, sort, ctx=None):
7779 """Return a Z3 finite-domain value. If `ctx=None`, then the global context is used.
7781 >>> s = FiniteDomainSort('S', 256)
7782 >>> FiniteDomainVal(255, s)
7784 >>> FiniteDomainVal('100', s)
7788 _z3_assert(is_finite_domain_sort(sort), "Expected finite-domain sort")
7790 return FiniteDomainNumRef(Z3_mk_numeral(ctx.ref(), _to_int_str(val), sort.ast), ctx)
7793def is_finite_domain_value(a):
7794 """Return `True` if `a` is a Z3 finite-domain value.
7796 >>> s = FiniteDomainSort('S', 100)
7797 >>> b = Const('b', s)
7798 >>> is_finite_domain_value(b)
7800 >>> b = FiniteDomainVal(10, s)
7803 >>> is_finite_domain_value(b)
7806 return is_finite_domain(a) and _is_numeral(a.ctx, a.as_ast())
7809#########################################
7813#########################################
7815class OptimizeObjective:
7816 def __init__(self, opt, value, is_max):
7819 self._is_max = is_max
7823 return _to_expr_ref(Z3_optimize_get_lower(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
7827 return _to_expr_ref(Z3_optimize_get_upper(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
7829 def lower_values(self):
7831 return AstVector(Z3_optimize_get_lower_as_vector(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
7833 def upper_values(self):
7835 return AstVector(Z3_optimize_get_upper_as_vector(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
7844 return "%s:%s" % (self._value, self._is_max)
7850def _global_on_model(ctx):
7851 (fn, mdl) = _on_models[ctx]
7855_on_model_eh = on_model_eh_type(_global_on_model)
7858class Optimize(Z3PPObject):
7859 """Optimize API provides methods for solving using objective functions and weighted soft constraints"""
7861 def __init__(self, ctx=None):
7862 self.ctx = _get_ctx(ctx)
7863 self.optimize = Z3_mk_optimize(self.ctx.ref())
7864 self._on_models_id = None
7865 Z3_optimize_inc_ref(self.ctx.ref(), self.optimize)
7867 def __deepcopy__(self, memo={}):
7868 return Optimize(self.optimize, self.ctx)
7871 if self.optimize is not None and self.ctx.ref() is not None and Z3_optimize_dec_ref is not None:
7872 Z3_optimize_dec_ref(self.ctx.ref(), self.optimize)
7873 if self._on_models_id is not None:
7874 del _on_models[self._on_models_id]
7876 def set(self, *args, **keys):
7877 """Set a configuration option.
7878 The method `help()` return a string containing all available options.
7880 p = args2params(args, keys, self.ctx)
7881 Z3_optimize_set_params(self.ctx.ref(), self.optimize, p.params)
7884 """Display a string describing all available options."""
7885 print(Z3_optimize_get_help(self.ctx.ref(), self.optimize))
7887 def param_descrs(self):
7888 """Return the parameter description set."""
7889 return ParamDescrsRef(Z3_optimize_get_param_descrs(self.ctx.ref(), self.optimize), self.ctx)
7891 def assert_exprs(self, *args):
7892 """Assert constraints as background axioms for the optimize solver."""
7893 args = _get_args(args)
7894 s = BoolSort(self.ctx)
7896 if isinstance(arg, Goal) or isinstance(arg, AstVector):
7898 Z3_optimize_assert(self.ctx.ref(), self.optimize, f.as_ast())
7901 Z3_optimize_assert(self.ctx.ref(), self.optimize, arg.as_ast())
7903 def add(self, *args):
7904 """Assert constraints as background axioms for the optimize solver. Alias for assert_expr."""
7905 self.assert_exprs(*args)
7907 def __iadd__(self, fml):
7911 def assert_and_track(self, a, p):
7912 """Assert constraint `a` and track it in the unsat core using the Boolean constant `p`.
7914 If `p` is a string, it will be automatically converted into a Boolean constant.
7919 >>> s.assert_and_track(x > 0, 'p1')
7920 >>> s.assert_and_track(x != 1, 'p2')
7921 >>> s.assert_and_track(x < 0, p3)
7922 >>> print(s.check())
7924 >>> c = s.unsat_core()
7934 if isinstance(p, str):
7935 p = Bool(p, self.ctx)
7936 _z3_assert(isinstance(a, BoolRef), "Boolean expression expected")
7937 _z3_assert(isinstance(p, BoolRef) and is_const(p), "Boolean expression expected")
7938 Z3_optimize_assert_and_track(self.ctx.ref(), self.optimize, a.as_ast(), p.as_ast())
7940 def add_soft(self, arg, weight="1", id=None):
7941 """Add soft constraint with optional weight and optional identifier.
7942 If no weight is supplied, then the penalty for violating the soft constraint
7944 Soft constraints are grouped by identifiers. Soft constraints that are
7945 added without identifiers are grouped by default.
7948 weight = "%d" % weight
7949 elif isinstance(weight, float):
7950 weight = "%f" % weight
7951 if not isinstance(weight, str):
7952 raise Z3Exception("weight should be a string or an integer")
7955 id = to_symbol(id, self.ctx)
7958 v = Z3_optimize_assert_soft(self.ctx.ref(), self.optimize, a.as_ast(), weight, id)
7959 return OptimizeObjective(self, v, False)
7960 if sys.version_info.major >= 3 and isinstance(arg, Iterable):
7961 return [asoft(a) for a in arg]
7964 def maximize(self, arg):
7965 """Add objective function to maximize."""
7966 return OptimizeObjective(
7968 Z3_optimize_maximize(self.ctx.ref(), self.optimize, arg.as_ast()),
7972 def minimize(self, arg):
7973 """Add objective function to minimize."""
7974 return OptimizeObjective(
7976 Z3_optimize_minimize(self.ctx.ref(), self.optimize, arg.as_ast()),
7981 """create a backtracking point for added rules, facts and assertions"""
7982 Z3_optimize_push(self.ctx.ref(), self.optimize)
7985 """restore to previously created backtracking point"""
7986 Z3_optimize_pop(self.ctx.ref(), self.optimize)
7988 def check(self, *assumptions):
7989 """Check satisfiability while optimizing objective functions."""
7990 assumptions = _get_args(assumptions)
7991 num = len(assumptions)
7992 _assumptions = (Ast * num)()
7993 for i in range(num):
7994 _assumptions[i] = assumptions[i].as_ast()
7995 return CheckSatResult(Z3_optimize_check(self.ctx.ref(), self.optimize, num, _assumptions))
7997 def reason_unknown(self):
7998 """Return a string that describes why the last `check()` returned `unknown`."""
7999 return Z3_optimize_get_reason_unknown(self.ctx.ref(), self.optimize)
8002 """Return a model for the last check()."""
8004 return ModelRef(Z3_optimize_get_model(self.ctx.ref(), self.optimize), self.ctx)
8006 raise Z3Exception("model is not available")
8008 def unsat_core(self):
8009 return AstVector(Z3_optimize_get_unsat_core(self.ctx.ref(), self.optimize), self.ctx)
8011 def lower(self, obj):
8012 if not isinstance(obj, OptimizeObjective):
8013 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8016 def upper(self, obj):
8017 if not isinstance(obj, OptimizeObjective):
8018 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8021 def lower_values(self, obj):
8022 if not isinstance(obj, OptimizeObjective):
8023 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8024 return obj.lower_values()
8026 def upper_values(self, obj):
8027 if not isinstance(obj, OptimizeObjective):
8028 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8029 return obj.upper_values()
8031 def from_file(self, filename):
8032 """Parse assertions and objectives from a file"""
8033 Z3_optimize_from_file(self.ctx.ref(), self.optimize, filename)
8035 def from_string(self, s):
8036 """Parse assertions and objectives from a string"""
8037 Z3_optimize_from_string(self.ctx.ref(), self.optimize, s)
8039 def assertions(self):
8040 """Return an AST vector containing all added constraints."""
8041 return AstVector(Z3_optimize_get_assertions(self.ctx.ref(), self.optimize), self.ctx)
8043 def objectives(self):
8044 """returns set of objective functions"""
8045 return AstVector(Z3_optimize_get_objectives(self.ctx.ref(), self.optimize), self.ctx)
8048 """Return a formatted string with all added rules and constraints."""
8052 """Return a formatted string (in Lisp-like format) with all added constraints.
8053 We say the string is in s-expression format.
8055 return Z3_optimize_to_string(self.ctx.ref(), self.optimize)
8057 def statistics(self):
8058 """Return statistics for the last check`.
8060 return Statistics(Z3_optimize_get_statistics(self.ctx.ref(), self.optimize), self.ctx)
8062 def set_on_model(self, on_model):
8063 """Register a callback that is invoked with every incremental improvement to
8064 objective values. The callback takes a model as argument.
8065 The life-time of the model is limited to the callback so the
8066 model has to be (deep) copied if it is to be used after the callback
8068 id = len(_on_models) + 41
8069 mdl = Model(self.ctx)
8070 _on_models[id] = (on_model, mdl)
8071 self._on_models_id = id
8072 Z3_optimize_register_model_eh(
8073 self.ctx.ref(), self.optimize, mdl.model, ctypes.c_void_p(id), _on_model_eh,
8077#########################################
8081#########################################
8082class ApplyResult(Z3PPObject):
8083 """An ApplyResult object contains the subgoals produced by a tactic when applied to a goal.
8084 It also contains model and proof converters.
8087 def __init__(self, result, ctx):
8088 self.result = result
8090 Z3_apply_result_inc_ref(self.ctx.ref(), self.result)
8092 def __deepcopy__(self, memo={}):
8093 return ApplyResult(self.result, self.ctx)
8096 if self.ctx.ref() is not None and Z3_apply_result_dec_ref is not None:
8097 Z3_apply_result_dec_ref(self.ctx.ref(), self.result)
8100 """Return the number of subgoals in `self`.
8102 >>> a, b = Ints('a b')
8104 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
8105 >>> t = Tactic('split-clause')
8109 >>> t = Then(Tactic('split-clause'), Tactic('split-clause'))
8112 >>> t = Then(Tactic('split-clause'), Tactic('split-clause'), Tactic('propagate-values'))
8116 return int(Z3_apply_result_get_num_subgoals(self.ctx.ref(), self.result))
8118 def __getitem__(self, idx):
8119 """Return one of the subgoals stored in ApplyResult object `self`.
8121 >>> a, b = Ints('a b')
8123 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
8124 >>> t = Tactic('split-clause')
8127 [a == 0, Or(b == 0, b == 1), a > b]
8129 [a == 1, Or(b == 0, b == 1), a > b]
8131 if idx >= len(self):
8133 return Goal(goal=Z3_apply_result_get_subgoal(self.ctx.ref(), self.result, idx), ctx=self.ctx)
8136 return obj_to_string(self)
8139 """Return a textual representation of the s-expression representing the set of subgoals in `self`."""
8140 return Z3_apply_result_to_string(self.ctx.ref(), self.result)
8143 """Return a Z3 expression consisting of all subgoals.
8148 >>> g.add(Or(x == 2, x == 3))
8149 >>> r = Tactic('simplify')(g)
8151 [[Not(x <= 1), Or(x == 2, x == 3)]]
8153 And(Not(x <= 1), Or(x == 2, x == 3))
8154 >>> r = Tactic('split-clause')(g)
8156 [[x > 1, x == 2], [x > 1, x == 3]]
8158 Or(And(x > 1, x == 2), And(x > 1, x == 3))
8162 return BoolVal(False, self.ctx)
8164 return self[0].as_expr()
8166 return Or([self[i].as_expr() for i in range(len(self))])
8168#########################################
8172#########################################
8175 """Simplifiers act as pre-processing utilities for solvers.
8176 Build a custom simplifier and add it to a solve
r"""
8178 def __init__(self, simplifier, ctx=None):
8179 self.ctx = _get_ctx(ctx)
8180 self.simplifier = None
8181 if isinstance(simplifier, SimplifierObj):
8182 self.simplifier = simplifier
8183 elif isinstance(simplifier, list):
8184 simps = [Simplifier(s, ctx) for s in simplifier]
8185 self.simplifier = simps[0].simplifier
8186 for i in range(1, len(simps)):
8187 self.simplifier = Z3_simplifier_and_then(self.ctx.ref(), self.simplifier, simps[i].simplifier)
8188 Z3_simplifier_inc_ref(self.ctx.ref(), self.simplifier)
8192 _z3_assert(isinstance(simplifier, str), "simplifier name expected")
8194 self.simplifier = Z3_mk_simplifier(self.ctx.ref(), str(simplifier))
8196 raise Z3Exception("unknown simplifier '%s'" % simplifier)
8197 Z3_simplifier_inc_ref(self.ctx.ref(), self.simplifier)
8199 def __deepcopy__(self, memo={}):
8200 return Simplifier(self.simplifier, self.ctx)
8203 if self.simplifier is not None and self.ctx.ref() is not None and Z3_simplifier_dec_ref is not None:
8204 Z3_simplifier_dec_ref(self.ctx.ref(), self.simplifier)
8206 def using_params(self, *args, **keys):
8207 """Return a simplifier that uses the given configuration options"""
8208 p = args2params(args, keys, self.ctx)
8209 return Simplifier(Z3_simplifier_using_params(self.ctx.ref(), self.simplifier, p.params), self.ctx)
8211 def add(self, solver):
8212 """Return a solver that applies the simplification pre-processing specified by the simplifie
r"""
8213 return Solver(Z3_solver_add_simplifier(self.ctx.ref(), solver.solver, self.simplifier), self.ctx)
8216 """Display a string containing a description of the available options for the `self` simplifier."""
8217 print(Z3_simplifier_get_help(self.ctx.ref(), self.simplifier))
8219 def param_descrs(self):
8220 """Return the parameter description set."""
8221 return ParamDescrsRef(Z3_simplifier_get_param_descrs(self.ctx.ref(), self.simplifier), self.ctx)
8224#########################################
8228#########################################
8232 """Tactics transform, solver and/or simplify sets of constraints (Goal).
8233 A Tactic can be converted into a Solver using the method solver().
8235 Several combinators are available for creating new tactics using the built-in ones:
8236 Then(), OrElse(), FailIf(), Repeat(), When(), Cond().
8239 def __init__(self, tactic, ctx=None):
8240 self.ctx = _get_ctx(ctx)
8242 if isinstance(tactic, TacticObj):
8243 self.tactic = tactic
8246 _z3_assert(isinstance(tactic, str), "tactic name expected")
8248 self.tactic = Z3_mk_tactic(self.ctx.ref(), str(tactic))
8250 raise Z3Exception("unknown tactic '%s'" % tactic)
8251 Z3_tactic_inc_ref(self.ctx.ref(), self.tactic)
8253 def __deepcopy__(self, memo={}):
8254 return Tactic(self.tactic, self.ctx)
8257 if self.tactic is not None and self.ctx.ref() is not None and Z3_tactic_dec_ref is not None:
8258 Z3_tactic_dec_ref(self.ctx.ref(), self.tactic)
8260 def solver(self, logFile=None):
8261 """Create a solver using the tactic `self`.
8263 The solver supports the methods `push()` and `pop()`, but it
8264 will always solve each `check()` from scratch.
8266 >>> t = Then('simplify', 'nlsat')
8269 >>> s.add(x**2 == 2, x > 0)
8275 return Solver(Z3_mk_solver_from_tactic(self.ctx.ref(), self.tactic), self.ctx, logFile)
8277 def apply(self, goal, *arguments, **keywords):
8278 """Apply tactic `self` to the given goal or Z3 Boolean expression using the given options.
8280 >>> x, y = Ints('x y')
8281 >>> t = Tactic('solve-eqs')
8282 >>> t.apply(And(x == 0, y >= x + 1))
8286 _z3_assert(isinstance(goal, (Goal, BoolRef)), "Z3 Goal or Boolean expressions expected")
8287 goal = _to_goal(goal)
8288 if len(arguments) > 0 or len(keywords) > 0:
8289 p = args2params(arguments, keywords, self.ctx)
8290 return ApplyResult(Z3_tactic_apply_ex(self.ctx.ref(), self.tactic, goal.goal, p.params), self.ctx)
8292 return ApplyResult(Z3_tactic_apply(self.ctx.ref(), self.tactic, goal.goal), self.ctx)
8294 def __call__(self, goal, *arguments, **keywords):
8295 """Apply tactic `self` to the given goal or Z3 Boolean expression using the given options.
8297 >>> x, y = Ints('x y')
8298 >>> t = Tactic('solve-eqs')
8299 >>> t(And(x == 0, y >= x + 1))
8302 return self.apply(goal, *arguments, **keywords)
8305 """Display a string containing a description of the available options for the `self` tactic."""
8306 print(Z3_tactic_get_help(self.ctx.ref(), self.tactic))
8308 def param_descrs(self):
8309 """Return the parameter description set."""
8310 return ParamDescrsRef(Z3_tactic_get_param_descrs(self.ctx.ref(), self.tactic), self.ctx)
8314 if isinstance(a, BoolRef):
8315 goal = Goal(ctx=a.ctx)
8322def _to_tactic(t, ctx=None):
8323 if isinstance(t, Tactic):
8326 return Tactic(t, ctx)
8329def _and_then(t1, t2, ctx=None):
8330 t1 = _to_tactic(t1, ctx)
8331 t2 = _to_tactic(t2, ctx)
8333 _z3_assert(t1.ctx == t2.ctx, "Context mismatch")
8334 return Tactic(Z3_tactic_and_then(t1.ctx.ref(), t1.tactic, t2.tactic), t1.ctx)
8337def _or_else(t1, t2, ctx=None):
8338 t1 = _to_tactic(t1, ctx)
8339 t2 = _to_tactic(t2, ctx)
8341 _z3_assert(t1.ctx == t2.ctx, "Context mismatch")
8342 return Tactic(Z3_tactic_or_else(t1.ctx.ref(), t1.tactic, t2.tactic), t1.ctx)
8345def AndThen(*ts, **ks):
8346 """Return a tactic that applies the tactics in `*ts` in sequence.
8348 >>> x, y = Ints('x y')
8349 >>> t = AndThen(Tactic('simplify'), Tactic('solve-eqs'))
8350 >>> t(And(x == 0, y > x + 1))
8352 >>> t(And(x == 0, y > x + 1)).as_expr()
8356 _z3_assert(len(ts) >= 2, "At least two arguments expected")
8357 ctx = ks.get("ctx", None)
8360 for i in range(num - 1):
8361 r = _and_then(r, ts[i + 1], ctx)
8366 """Return a tactic that applies the tactics in `*ts` in sequence. Shorthand for AndThen(*ts, **ks).
8368 >>> x, y = Ints('x y')
8369 >>> t = Then(Tactic('simplify'), Tactic('solve-eqs'))
8370 >>> t(And(x == 0, y > x + 1))
8372 >>> t(And(x == 0, y > x + 1)).as_expr()
8375 return AndThen(*ts, **ks)
8378def OrElse(*ts, **ks):
8379 """Return a tactic that applies the tactics in `*ts` until one of them succeeds (it doesn't fail).
8382 >>> t = OrElse(Tactic('split-clause'), Tactic('skip'))
8383 >>> # Tactic split-clause fails if there is no clause in the given goal.
8386 >>> t(Or(x == 0, x == 1))
8387 [[x == 0], [x == 1]]
8390 _z3_assert(len(ts) >= 2, "At least two arguments expected")
8391 ctx = ks.get("ctx", None)
8394 for i in range(num - 1):
8395 r = _or_else(r, ts[i + 1], ctx)
8399def ParOr(*ts, **ks):
8400 """Return a tactic that applies the tactics in `*ts` in parallel until one of them succeeds (it doesn't fail).
8403 >>> t = ParOr(Tactic('simplify'), Tactic('fail'))
8408 _z3_assert(len(ts) >= 2, "At least two arguments expected")
8409 ctx = _get_ctx(ks.get("ctx", None))
8410 ts = [_to_tactic(t, ctx) for t in ts]
8412 _args = (TacticObj * sz)()
8414 _args[i] = ts[i].tactic
8415 return Tactic(Z3_tactic_par_or(ctx.ref(), sz, _args), ctx)
8418def ParThen(t1, t2, ctx=None):
8419 """Return a tactic that applies t1 and then t2 to every subgoal produced by t1.
8420 The subgoals are processed in parallel.
8422 >>> x, y = Ints('x y')
8423 >>> t = ParThen(Tactic('split-clause'), Tactic('propagate-values'))
8424 >>> t(And(Or(x == 1, x == 2), y == x + 1))
8425 [[x == 1, y == 2], [x == 2, y == 3]]
8427 t1 = _to_tactic(t1, ctx)
8428 t2 = _to_tactic(t2, ctx)
8430 _z3_assert(t1.ctx == t2.ctx, "Context mismatch")
8431 return Tactic(Z3_tactic_par_and_then(t1.ctx.ref(), t1.tactic, t2.tactic), t1.ctx)
8434def ParAndThen(t1, t2, ctx=None):
8435 """Alias for ParThen(t1, t2, ctx)."""
8436 return ParThen(t1, t2, ctx)
8439def With(t, *args, **keys):
8440 """Return a tactic that applies tactic `t` using the given configuration options.
8442 >>> x, y = Ints('x y')
8443 >>> t = With(Tactic('simplify'), som=True)
8444 >>> t((x + 1)*(y + 2) == 0)
8445 [[2*x + y + x*y == -2]]
8447 ctx = keys.pop("ctx", None)
8448 t = _to_tactic(t, ctx)
8449 p = args2params(args, keys, t.ctx)
8450 return Tactic(Z3_tactic_using_params(t.ctx.ref(), t.tactic, p.params), t.ctx)
8453def WithParams(t, p):
8454 """Return a tactic that applies tactic `t` using the given configuration options.
8456 >>> x, y = Ints('x y')
8458 >>> p.set("som", True)
8459 >>> t = WithParams(Tactic('simplify'), p)
8460 >>> t((x + 1)*(y + 2) == 0)
8461 [[2*x + y + x*y == -2]]
8463 t = _to_tactic(t, None)
8464 return Tactic(Z3_tactic_using_params(t.ctx.ref(), t.tactic, p.params), t.ctx)
8467def Repeat(t, max=4294967295, ctx=None):
8468 """Return a tactic that keeps applying `t` until the goal is not modified anymore
8469 or the maximum number of iterations `max` is reached.
8471 >>> x, y = Ints('x y')
8472 >>> c = And(Or(x == 0, x == 1), Or(y == 0, y == 1), x > y)
8473 >>> t = Repeat(OrElse(Tactic('split-clause'), Tactic('skip')))
8475 >>> for subgoal in r: print(subgoal)
8476 [x == 0, y == 0, x > y]
8477 [x == 0, y == 1, x > y]
8478 [x == 1, y == 0, x > y]
8479 [x == 1, y == 1, x > y]
8480 >>> t = Then(t, Tactic('propagate-values'))
8484 t = _to_tactic(t, ctx)
8485 return Tactic(Z3_tactic_repeat(t.ctx.ref(), t.tactic, max), t.ctx)
8488def TryFor(t, ms, ctx=None):
8489 """Return a tactic that applies `t` to a given goal for `ms` milliseconds.
8491 If `t` does not terminate in `ms` milliseconds, then it fails.
8493 t = _to_tactic(t, ctx)
8494 return Tactic(Z3_tactic_try_for(t.ctx.ref(), t.tactic, ms), t.ctx)
8497def tactics(ctx=None):
8498 """Return a list of all available tactics in Z3.
8501 >>> l.count('simplify') == 1
8505 return [Z3_get_tactic_name(ctx.ref(), i) for i in range(Z3_get_num_tactics(ctx.ref()))]
8508def tactic_description(name, ctx=None):
8509 """Return a short description for the tactic named `name`.
8511 >>> d = tactic_description('simplify')
8514 return Z3_tactic_get_descr(ctx.ref(), name)
8517def describe_tactics():
8518 """Display a (tabular) description of all available tactics in Z3."""
8521 print('<table border="1" cellpadding="2" cellspacing="0">')
8524 print('<tr style="background-color:#CFCFCF">')
8529 print("<td>%s</td><td>%s</td></tr>" % (t, insert_line_breaks(tactic_description(t), 40)))
8533 print("%s : %s" % (t, tactic_description(t)))
8537 """Probes are used to inspect a goal (aka problem) and collect information that may be used
8538 to decide which solver and/or preprocessing step will be used.
8541 def __init__(self, probe, ctx=None):
8542 self.ctx = _get_ctx(ctx)
8544 if isinstance(probe, ProbeObj):
8546 elif isinstance(probe, float):
8547 self.probe = Z3_probe_const(self.ctx.ref(), probe)
8548 elif _is_int(probe):
8549 self.probe = Z3_probe_const(self.ctx.ref(), float(probe))
8550 elif isinstance(probe, bool):
8552 self.probe = Z3_probe_const(self.ctx.ref(), 1.0)
8554 self.probe = Z3_probe_const(self.ctx.ref(), 0.0)
8557 _z3_assert(isinstance(probe, str), "probe name expected")
8559 self.probe = Z3_mk_probe(self.ctx.ref(), probe)
8561 raise Z3Exception("unknown probe '%s'" % probe)
8562 Z3_probe_inc_ref(self.ctx.ref(), self.probe)
8564 def __deepcopy__(self, memo={}):
8565 return Probe(self.probe, self.ctx)
8568 if self.probe is not None and self.ctx.ref() is not None and Z3_probe_dec_ref is not None:
8569 Z3_probe_dec_ref(self.ctx.ref(), self.probe)
8571 def __lt__(self, other):
8572 """Return a probe that evaluates to "true" when the value returned by `self`
8573 is less than the value returned by `other`.
8575 >>> p = Probe('size') < 10
8583 return Probe(Z3_probe_lt(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8585 def __gt__(self, other):
8586 """Return a probe that evaluates to "true" when the value returned by `self`
8587 is greater than the value returned by `other`.
8589 >>> p = Probe('size') > 10
8597 return Probe(Z3_probe_gt(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8599 def __le__(self, other):
8600 """Return a probe that evaluates to "true" when the value returned by `self`
8601 is less than or equal to the value returned by `other`.
8603 >>> p = Probe('size') <= 2
8611 return Probe(Z3_probe_le(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8613 def __ge__(self, other):
8614 """Return a probe that evaluates to "true" when the value returned by `self`
8615 is greater than or equal to the value returned by `other`.
8617 >>> p = Probe('size') >= 2
8625 return Probe(Z3_probe_ge(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8627 def __eq__(self, other):
8628 """Return a probe that evaluates to "true" when the value returned by `self`
8629 is equal to the value returned by `other`.
8631 >>> p = Probe('size') == 2
8639 return Probe(Z3_probe_eq(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8641 def __ne__(self, other):
8642 """Return a probe that evaluates to "true" when the value returned by `self`
8643 is not equal to the value returned by `other`.
8645 >>> p = Probe('size') != 2
8653 p = self.__eq__(other)
8654 return Probe(Z3_probe_not(self.ctx.ref(), p.probe), self.ctx)
8656 def __call__(self, goal):
8657 """Evaluate the probe `self` in the given goal.
8659 >>> p = Probe('size')
8669 >>> p = Probe('num-consts')
8672 >>> p = Probe('is-propositional')
8675 >>> p = Probe('is-qflia')
8680 _z3_assert(isinstance(goal, (Goal, BoolRef)), "Z3 Goal or Boolean expression expected")
8681 goal = _to_goal(goal)
8682 return Z3_probe_apply(self.ctx.ref(), self.probe, goal.goal)
8686 """Return `True` if `p` is a Z3 probe.
8688 >>> is_probe(Int('x'))
8690 >>> is_probe(Probe('memory'))
8693 return isinstance(p, Probe)
8696def _to_probe(p, ctx=None):
8700 return Probe(p, ctx)
8703def probes(ctx=None):
8704 """Return a list of all available probes in Z3.
8707 >>> l.count('memory') == 1
8711 return [Z3_get_probe_name(ctx.ref(), i) for i in range(Z3_get_num_probes(ctx.ref()))]
8714def probe_description(name, ctx=None):
8715 """Return a short description for the probe named `name`.
8717 >>> d = probe_description('memory')
8720 return Z3_probe_get_descr(ctx.ref(), name)
8723def describe_probes():
8724 """Display a (tabular) description of all available probes in Z3."""
8727 print('<table border="1" cellpadding="2" cellspacing="0">')
8730 print('<tr style="background-color:#CFCFCF">')
8735 print("<td>%s</td><td>%s</td></tr>" % (p, insert_line_breaks(probe_description(p), 40)))
8739 print("%s : %s" % (p, probe_description(p)))
8742def _probe_nary(f, args, ctx):
8744 _z3_assert(len(args) > 0, "At least one argument expected")
8746 r = _to_probe(args[0], ctx)
8747 for i in range(num - 1):
8748 r = Probe(f(ctx.ref(), r.probe, _to_probe(args[i + 1], ctx).probe), ctx)
8752def _probe_and(args, ctx):
8753 return _probe_nary(Z3_probe_and, args, ctx)
8756def _probe_or(args, ctx):
8757 return _probe_nary(Z3_probe_or, args, ctx)
8760def FailIf(p, ctx=None):
8761 """Return a tactic that fails if the probe `p` evaluates to true.
8762 Otherwise, it returns the input goal unmodified.
8764 In the following example, the tactic applies 'simplify' if and only if there are
8765 more than 2 constraints in the goal.
8767 >>> t = OrElse(FailIf(Probe('size') > 2), Tactic('simplify'))
8768 >>> x, y = Ints('x y')
8774 >>> g.add(x == y + 1)
8776 [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
8778 p = _to_probe(p, ctx)
8779 return Tactic(Z3_tactic_fail_if(p.ctx.ref(), p.probe), p.ctx)
8782def When(p, t, ctx=None):
8783 """Return a tactic that applies tactic `t` only if probe `p` evaluates to true.
8784 Otherwise, it returns the input goal unmodified.
8786 >>> t = When(Probe('size') > 2, Tactic('simplify'))
8787 >>> x, y = Ints('x y')
8793 >>> g.add(x == y + 1)
8795 [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
8797 p = _to_probe(p, ctx)
8798 t = _to_tactic(t, ctx)
8799 return Tactic(Z3_tactic_when(t.ctx.ref(), p.probe, t.tactic), t.ctx)
8802def Cond(p, t1, t2, ctx=None):
8803 """Return a tactic that applies tactic `t1` to a goal if probe `p` evaluates to true, and `t2` otherwise.
8805 >>> t = Cond(Probe('is-qfnra'), Tactic('qfnra'), Tactic('smt'))
8807 p = _to_probe(p, ctx)
8808 t1 = _to_tactic(t1, ctx)
8809 t2 = _to_tactic(t2, ctx)
8810 return Tactic(Z3_tactic_cond(t1.ctx.ref(), p.probe, t1.tactic, t2.tactic), t1.ctx)
8812#########################################
8816#########################################
8819def simplify(a, *arguments, **keywords):
8820 """Simplify the expression `a` using the given options.
8822 This function has many options. Use `help_simplify` to obtain the complete list.
8826 >>> simplify(x + 1 + y + x + 1)
8828 >>> simplify((x + 1)*(y + 1), som=True)
8830 >>> simplify(Distinct(x, y, 1), blast_distinct=True)
8831 And(Not(x == y), Not(x == 1), Not(y == 1))
8832 >>> simplify(And(x == 0, y == 1), elim_and=True)
8833 Not(Or(Not(x == 0), Not(y == 1)))
8836 _z3_assert(is_expr(a), "Z3 expression expected")
8837 if len(arguments) > 0 or len(keywords) > 0:
8838 p = args2params(arguments, keywords, a.ctx)
8839 return _to_expr_ref(Z3_simplify_ex(a.ctx_ref(), a.as_ast(), p.params), a.ctx)
8841 return _to_expr_ref(Z3_simplify(a.ctx_ref(), a.as_ast()), a.ctx)
8845 """Return a string describing all options available for Z3 `simplify` procedure."""
8846 print(Z3_simplify_get_help(main_ctx().ref()))
8849def simplify_param_descrs():
8850 """Return the set of parameter descriptions for Z3 `simplify` procedure."""
8851 return ParamDescrsRef(Z3_simplify_get_param_descrs(main_ctx().ref()), main_ctx())
8854def substitute(t, *m):
8855 """Apply substitution m on t, m is a list of pairs of the form (from, to).
8856 Every occurrence in t of from is replaced with to.
8860 >>> substitute(x + 1, (x, y + 1))
8862 >>> f = Function('f', IntSort(), IntSort())
8863 >>> substitute(f(x) + f(y), (f(x), IntVal(1)), (f(y), IntVal(1)))
8866 if isinstance(m, tuple):
8868 if isinstance(m1, list) and all(isinstance(p, tuple) for p in m1):
8871 _z3_assert(is_expr(t), "Z3 expression expected")
8873 all([isinstance(p, tuple) and is_expr(p[0]) and is_expr(p[1]) for p in m]),
8874 "Z3 invalid substitution, expression pairs expected.")
8876 all([p[0].sort().eq(p[1].sort()) for p in m]),
8877 'Z3 invalid substitution, mismatching "from" and "to" sorts.')
8879 _from = (Ast * num)()
8881 for i in range(num):
8882 _from[i] = m[i][0].as_ast()
8883 _to[i] = m[i][1].as_ast()
8884 return _to_expr_ref(Z3_substitute(t.ctx.ref(), t.as_ast(), num, _from, _to), t.ctx)
8887def substitute_vars(t, *m):
8888 """Substitute the free variables in t with the expression in m.
8890 >>> v0 = Var(0, IntSort())
8891 >>> v1 = Var(1, IntSort())
8893 >>> f = Function('f', IntSort(), IntSort(), IntSort())
8894 >>> # replace v0 with x+1 and v1 with x
8895 >>> substitute_vars(f(v0, v1), x + 1, x)
8899 _z3_assert(is_expr(t), "Z3 expression expected")
8900 _z3_assert(all([is_expr(n) for n in m]), "Z3 invalid substitution, list of expressions expected.")
8903 for i in range(num):
8904 _to[i] = m[i].as_ast()
8905 return _to_expr_ref(Z3_substitute_vars(t.ctx.ref(), t.as_ast(), num, _to), t.ctx)
8907def substitute_funs(t, *m):
8908 """Apply substitution m on t, m is a list of pairs of a function and expression (from, to)
8909 Every occurrence in to of the function from is replaced with the expression to.
8910 The expression to can have free variables, that refer to the arguments of from.
8913 if isinstance(m, tuple):
8915 if isinstance(m1, list) and all(isinstance(p, tuple) for p in m1):
8918 _z3_assert(is_expr(t), "Z3 expression expected")
8919 _z3_assert(all([isinstance(p, tuple) and is_func_decl(p[0]) and is_expr(p[1]) for p in m]), "Z3 invalid substitution, funcion pairs expected.")
8921 _from = (FuncDecl * num)()
8923 for i in range(num):
8924 _from[i] = m[i][0].as_func_decl()
8925 _to[i] = m[i][1].as_ast()
8926 return _to_expr_ref(Z3_substitute_funs(t.ctx.ref(), t.as_ast(), num, _from, _to), t.ctx)
8930 """Create the sum of the Z3 expressions.
8932 >>> a, b, c = Ints('a b c')
8937 >>> A = IntVector('a', 5)
8939 a__0 + a__1 + a__2 + a__3 + a__4
8941 args = _get_args(args)
8944 ctx = _ctx_from_ast_arg_list(args)
8946 return _reduce(lambda a, b: a + b, args, 0)
8947 args = _coerce_expr_list(args, ctx)
8949 return _reduce(lambda a, b: a + b, args, 0)
8951 _args, sz = _to_ast_array(args)
8952 return ArithRef(Z3_mk_add(ctx.ref(), sz, _args), ctx)
8956 """Create the product of the Z3 expressions.
8958 >>> a, b, c = Ints('a b c')
8959 >>> Product(a, b, c)
8961 >>> Product([a, b, c])
8963 >>> A = IntVector('a', 5)
8965 a__0*a__1*a__2*a__3*a__4
8967 args = _get_args(args)
8970 ctx = _ctx_from_ast_arg_list(args)
8972 return _reduce(lambda a, b: a * b, args, 1)
8973 args = _coerce_expr_list(args, ctx)
8975 return _reduce(lambda a, b: a * b, args, 1)
8977 _args, sz = _to_ast_array(args)
8978 return ArithRef(Z3_mk_mul(ctx.ref(), sz, _args), ctx)
8981 """Create the absolute value of an arithmetic expression"""
8982 return If(arg > 0, arg, -arg)
8986 """Create an at-most Pseudo-Boolean k constraint.
8988 >>> a, b, c = Bools('a b c')
8989 >>> f = AtMost(a, b, c, 2)
8991 args = _get_args(args)
8993 _z3_assert(len(args) > 1, "Non empty list of arguments expected")
8994 ctx = _ctx_from_ast_arg_list(args)
8996 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
8997 args1 = _coerce_expr_list(args[:-1], ctx)
8999 _args, sz = _to_ast_array(args1)
9000 return BoolRef(Z3_mk_atmost(ctx.ref(), sz, _args, k), ctx)
9004 """Create an at-most Pseudo-Boolean k constraint.
9006 >>> a, b, c = Bools('a b c')
9007 >>> f = AtLeast(a, b, c, 2)
9009 args = _get_args(args)
9011 _z3_assert(len(args) > 1, "Non empty list of arguments expected")
9012 ctx = _ctx_from_ast_arg_list(args)
9014 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
9015 args1 = _coerce_expr_list(args[:-1], ctx)
9017 _args, sz = _to_ast_array(args1)
9018 return BoolRef(Z3_mk_atleast(ctx.ref(), sz, _args, k), ctx)
9021def _reorder_pb_arg(arg):
9023 if not _is_int(b) and _is_int(a):
9028def _pb_args_coeffs(args, default_ctx=None):
9029 args = _get_args_ast_list(args)
9031 return _get_ctx(default_ctx), 0, (Ast * 0)(), (ctypes.c_int * 0)()
9032 args = [_reorder_pb_arg(arg) for arg in args]
9033 args, coeffs = zip(*args)
9035 _z3_assert(len(args) > 0, "Non empty list of arguments expected")
9036 ctx = _ctx_from_ast_arg_list(args)
9038 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
9039 args = _coerce_expr_list(args, ctx)
9040 _args, sz = _to_ast_array(args)
9041 _coeffs = (ctypes.c_int * len(coeffs))()
9042 for i in range(len(coeffs)):
9043 _z3_check_cint_overflow(coeffs[i], "coefficient")
9044 _coeffs[i] = coeffs[i]
9045 return ctx, sz, _args, _coeffs, args
9049 """Create a Pseudo-Boolean inequality k constraint.
9051 >>> a, b, c = Bools('a b c')
9052 >>> f = PbLe(((a,1),(b,3),(c,2)), 3)
9054 _z3_check_cint_overflow(k, "k")
9055 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9056 return BoolRef(Z3_mk_pble(ctx.ref(), sz, _args, _coeffs, k), ctx)
9060 """Create a Pseudo-Boolean inequality k constraint.
9062 >>> a, b, c = Bools('a b c')
9063 >>> f = PbGe(((a,1),(b,3),(c,2)), 3)
9065 _z3_check_cint_overflow(k, "k")
9066 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9067 return BoolRef(Z3_mk_pbge(ctx.ref(), sz, _args, _coeffs, k), ctx)
9070def PbEq(args, k, ctx=None):
9071 """Create a Pseudo-Boolean equality k constraint.
9073 >>> a, b, c = Bools('a b c')
9074 >>> f = PbEq(((a,1),(b,3),(c,2)), 3)
9076 _z3_check_cint_overflow(k, "k")
9077 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9078 return BoolRef(Z3_mk_pbeq(ctx.ref(), sz, _args, _coeffs, k), ctx)
9081def solve(*args, **keywords):
9082 """Solve the constraints `*args`.
9084 This is a simple function for creating demonstrations. It creates a solver,
9085 configure it using the options in `keywords`, adds the constraints
9086 in `args`, and invokes check.
9089 >>> solve(a > 0, a < 2)
9092 show = keywords.pop("show", False)
9100 print("no solution")
9102 print("failed to solve")
9111def solve_using(s, *args, **keywords):
9112 """Solve the constraints `*args` using solver `s`.
9114 This is a simple function for creating demonstrations. It is similar to `solve`,
9115 but it uses the given solver `s`.
9116 It configures solver `s` using the options in `keywords`, adds the constraints
9117 in `args`, and invokes check.
9119 show = keywords.pop("show", False)
9121 _z3_assert(isinstance(s, Solver), "Solver object expected")
9129 print("no solution")
9131 print("failed to solve")
9142def prove(claim, show=False, **keywords):
9143 """Try to prove the given claim.
9145 This is a simple function for creating demonstrations. It tries to prove
9146 `claim` by showing the negation is unsatisfiable.
9148 >>> p, q = Bools('p q')
9149 >>> prove(Not(And(p, q)) == Or(Not(p), Not(q)))
9153 _z3_assert(is_bool(claim), "Z3 Boolean expression expected")
9163 print("failed to prove")
9166 print("counterexample")
9170def _solve_html(*args, **keywords):
9171 """Version of function `solve` that renders HTML output."""
9172 show = keywords.pop("show", False)
9177 print("<b>Problem:</b>")
9181 print("<b>no solution</b>")
9183 print("<b>failed to solve</b>")
9190 print("<b>Solution:</b>")
9194def _solve_using_html(s, *args, **keywords):
9195 """Version of function `solve_using` that renders HTML."""
9196 show = keywords.pop("show", False)
9198 _z3_assert(isinstance(s, Solver), "Solver object expected")
9202 print("<b>Problem:</b>")
9206 print("<b>no solution</b>")
9208 print("<b>failed to solve</b>")
9215 print("<b>Solution:</b>")
9219def _prove_html(claim, show=False, **keywords):
9220 """Version of function `prove` that renders HTML."""
9222 _z3_assert(is_bool(claim), "Z3 Boolean expression expected")
9230 print("<b>proved</b>")
9232 print("<b>failed to prove</b>")
9235 print("<b>counterexample</b>")
9239def _dict2sarray(sorts, ctx):
9241 _names = (Symbol * sz)()
9242 _sorts = (Sort * sz)()
9247 _z3_assert(isinstance(k, str), "String expected")
9248 _z3_assert(is_sort(v), "Z3 sort expected")
9249 _names[i] = to_symbol(k, ctx)
9252 return sz, _names, _sorts
9255def _dict2darray(decls, ctx):
9257 _names = (Symbol * sz)()
9258 _decls = (FuncDecl * sz)()
9263 _z3_assert(isinstance(k, str), "String expected")
9264 _z3_assert(is_func_decl(v) or is_const(v), "Z3 declaration or constant expected")
9265 _names[i] = to_symbol(k, ctx)
9267 _decls[i] = v.decl().ast
9271 return sz, _names, _decls
9274 def __init__(self, ctx= None):
9275 self.ctx = _get_ctx(ctx)
9276 self.pctx = Z3_mk_parser_context(self.ctx.ref())
9277 Z3_parser_context_inc_ref(self.ctx.ref(), self.pctx)
9280 if self.ctx.ref() is not None and self.pctx is not None and Z3_parser_context_dec_ref is not None:
9281 Z3_parser_context_dec_ref(self.ctx.ref(), self.pctx)
9284 def add_sort(self, sort):
9285 Z3_parser_context_add_sort(self.ctx.ref(), self.pctx, sort.as_ast())
9287 def add_decl(self, decl):
9288 Z3_parser_context_add_decl(self.ctx.ref(), self.pctx, decl.as_ast())
9290 def from_string(self, s):
9291 return AstVector(Z3_parser_context_from_string(self.ctx.ref(), self.pctx, s), self.ctx)
9293def parse_smt2_string(s, sorts={}, decls={}, ctx=None):
9294 """Parse a string in SMT 2.0 format using the given sorts and decls.
9296 The arguments sorts and decls are Python dictionaries used to initialize
9297 the symbol table used for the SMT 2.0 parser.
9299 >>> parse_smt2_string('(declare-const x Int) (assert (> x 0)) (assert (< x 10))')
9301 >>> x, y = Ints('x y')
9302 >>> f = Function('f', IntSort(), IntSort())
9303 >>> parse_smt2_string('(assert (> (+ foo (g bar)) 0))', decls={ 'foo' : x, 'bar' : y, 'g' : f})
9305 >>> parse_smt2_string('(declare-const a U) (assert (> a 0))', sorts={ 'U' : IntSort() })
9309 ssz, snames, ssorts = _dict2sarray(sorts, ctx)
9310 dsz, dnames, ddecls = _dict2darray(decls, ctx)
9311 return AstVector(Z3_parse_smtlib2_string(ctx.ref(), s, ssz, snames, ssorts, dsz, dnames, ddecls), ctx)
9314def parse_smt2_file(f, sorts={}, decls={}, ctx=None):
9315 """Parse a file in SMT 2.0 format using the given sorts and decls.
9317 This function is similar to parse_smt2_string().
9320 ssz, snames, ssorts = _dict2sarray(sorts, ctx)
9321 dsz, dnames, ddecls = _dict2darray(decls, ctx)
9322 return AstVector(Z3_parse_smtlib2_file(ctx.ref(), f, ssz, snames, ssorts, dsz, dnames, ddecls), ctx)
9325#########################################
9327# Floating-Point Arithmetic
9329#########################################
9332# Global default rounding mode
9333_dflt_rounding_mode = Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN
9334_dflt_fpsort_ebits = 11
9335_dflt_fpsort_sbits = 53
9338def get_default_rounding_mode(ctx=None):
9339 """Retrieves the global default rounding mode."""
9340 global _dflt_rounding_mode
9341 if _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_ZERO:
9343 elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_NEGATIVE:
9345 elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_POSITIVE:
9347 elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN:
9349 elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_AWAY:
9353_ROUNDING_MODES = frozenset({
9354 Z3_OP_FPA_RM_TOWARD_ZERO,
9355 Z3_OP_FPA_RM_TOWARD_NEGATIVE,
9356 Z3_OP_FPA_RM_TOWARD_POSITIVE,
9357 Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN,
9358 Z3_OP_FPA_RM_NEAREST_TIES_TO_AWAY
9362def set_default_rounding_mode(rm, ctx=None):
9363 global _dflt_rounding_mode
9364 if is_fprm_value(rm):
9365 _dflt_rounding_mode = rm.decl().kind()
9367 _z3_assert(_dflt_rounding_mode in _ROUNDING_MODES, "illegal rounding mode")
9368 _dflt_rounding_mode = rm
9371def get_default_fp_sort(ctx=None):
9372 return FPSort(_dflt_fpsort_ebits, _dflt_fpsort_sbits, ctx)
9375def set_default_fp_sort(ebits, sbits, ctx=None):
9376 global _dflt_fpsort_ebits
9377 global _dflt_fpsort_sbits
9378 _dflt_fpsort_ebits = ebits
9379 _dflt_fpsort_sbits = sbits
9382def _dflt_rm(ctx=None):
9383 return get_default_rounding_mode(ctx)
9386def _dflt_fps(ctx=None):
9387 return get_default_fp_sort(ctx)
9390def _coerce_fp_expr_list(alist, ctx):
9391 first_fp_sort = None
9394 if first_fp_sort is None:
9395 first_fp_sort = a.sort()
9396 elif first_fp_sort == a.sort():
9397 pass # OK, same as before
9399 # we saw at least 2 different float sorts; something will
9400 # throw a sort mismatch later, for now assume None.
9401 first_fp_sort = None
9405 for i in range(len(alist)):
9407 is_repr = isinstance(a, str) and a.contains("2**(") and a.endswith(")")
9408 if is_repr or _is_int(a) or isinstance(a, (float, bool)):
9409 r.append(FPVal(a, None, first_fp_sort, ctx))
9412 return _coerce_expr_list(r, ctx)
9417class FPSortRef(SortRef):
9418 """Floating-point sort."""
9421 """Retrieves the number of bits reserved for the exponent in the FloatingPoint sort `self`.
9422 >>> b = FPSort(8, 24)
9426 return int(Z3_fpa_get_ebits(self.ctx_ref(), self.ast))
9429 """Retrieves the number of bits reserved for the significand in the FloatingPoint sort `self`.
9430 >>> b = FPSort(8, 24)
9434 return int(Z3_fpa_get_sbits(self.ctx_ref(), self.ast))
9436 def cast(self, val):
9437 """Try to cast `val` as a floating-point expression.
9438 >>> b = FPSort(8, 24)
9441 >>> b.cast(1.0).sexpr()
9442 '(fp #b0 #x7f #b00000000000000000000000)'
9446 _z3_assert(self.ctx == val.ctx, "Context mismatch")
9449 return FPVal(val, None, self, self.ctx)
9452def Float16(ctx=None):
9453 """Floating-point 16-bit (half) sort."""
9455 return FPSortRef(Z3_mk_fpa_sort_16(ctx.ref()), ctx)
9458def FloatHalf(ctx=None):
9459 """Floating-point 16-bit (half) sort."""
9461 return FPSortRef(Z3_mk_fpa_sort_half(ctx.ref()), ctx)
9464def Float32(ctx=None):
9465 """Floating-point 32-bit (single) sort."""
9467 return FPSortRef(Z3_mk_fpa_sort_32(ctx.ref()), ctx)
9470def FloatSingle(ctx=None):
9471 """Floating-point 32-bit (single) sort."""
9473 return FPSortRef(Z3_mk_fpa_sort_single(ctx.ref()), ctx)
9476def Float64(ctx=None):
9477 """Floating-point 64-bit (double) sort."""
9479 return FPSortRef(Z3_mk_fpa_sort_64(ctx.ref()), ctx)
9482def FloatDouble(ctx=None):
9483 """Floating-point 64-bit (double) sort."""
9485 return FPSortRef(Z3_mk_fpa_sort_double(ctx.ref()), ctx)
9488def Float128(ctx=None):
9489 """Floating-point 128-bit (quadruple) sort."""
9491 return FPSortRef(Z3_mk_fpa_sort_128(ctx.ref()), ctx)
9494def FloatQuadruple(ctx=None):
9495 """Floating-point 128-bit (quadruple) sort."""
9497 return FPSortRef(Z3_mk_fpa_sort_quadruple(ctx.ref()), ctx)
9500class FPRMSortRef(SortRef):
9501 """"Floating-point rounding mode sort."""
9505 """Return True if `s` is a Z3 floating-point sort.
9507 >>> is_fp_sort(FPSort(8, 24))
9509 >>> is_fp_sort(IntSort())
9512 return isinstance(s, FPSortRef)
9516 """Return True if `s` is a Z3 floating-point rounding mode sort.
9518 >>> is_fprm_sort(FPSort(8, 24))
9520 >>> is_fprm_sort(RNE().sort())
9523 return isinstance(s, FPRMSortRef)
9528class FPRef(ExprRef):
9529 """Floating-point expressions."""
9532 """Return the sort of the floating-point expression `self`.
9534 >>> x = FP('1.0', FPSort(8, 24))
9537 >>> x.sort() == FPSort(8, 24)
9540 return FPSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
9543 """Retrieves the number of bits reserved for the exponent in the FloatingPoint expression `self`.
9544 >>> b = FPSort(8, 24)
9548 return self.sort().ebits()
9551 """Retrieves the number of bits reserved for the exponent in the FloatingPoint expression `self`.
9552 >>> b = FPSort(8, 24)
9556 return self.sort().sbits()
9558 def as_string(self):
9559 """Return a Z3 floating point expression as a Python string."""
9560 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
9562 def __le__(self, other):
9563 return fpLEQ(self, other, self.ctx)
9565 def __lt__(self, other):
9566 return fpLT(self, other, self.ctx)
9568 def __ge__(self, other):
9569 return fpGEQ(self, other, self.ctx)
9571 def __gt__(self, other):
9572 return fpGT(self, other, self.ctx)
9574 def __add__(self, other):
9575 """Create the Z3 expression `self + other`.
9577 >>> x = FP('x', FPSort(8, 24))
9578 >>> y = FP('y', FPSort(8, 24))
9584 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9585 return fpAdd(_dflt_rm(), a, b, self.ctx)
9587 def __radd__(self, other):
9588 """Create the Z3 expression `other + self`.
9590 >>> x = FP('x', FPSort(8, 24))
9594 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9595 return fpAdd(_dflt_rm(), a, b, self.ctx)
9597 def __sub__(self, other):
9598 """Create the Z3 expression `self - other`.
9600 >>> x = FP('x', FPSort(8, 24))
9601 >>> y = FP('y', FPSort(8, 24))
9607 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9608 return fpSub(_dflt_rm(), a, b, self.ctx)
9610 def __rsub__(self, other):
9611 """Create the Z3 expression `other - self`.
9613 >>> x = FP('x', FPSort(8, 24))
9617 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9618 return fpSub(_dflt_rm(), a, b, self.ctx)
9620 def __mul__(self, other):
9621 """Create the Z3 expression `self * other`.
9623 >>> x = FP('x', FPSort(8, 24))
9624 >>> y = FP('y', FPSort(8, 24))
9632 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9633 return fpMul(_dflt_rm(), a, b, self.ctx)
9635 def __rmul__(self, other):
9636 """Create the Z3 expression `other * self`.
9638 >>> x = FP('x', FPSort(8, 24))
9639 >>> y = FP('y', FPSort(8, 24))
9645 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9646 return fpMul(_dflt_rm(), a, b, self.ctx)
9649 """Create the Z3 expression `+self`."""
9653 """Create the Z3 expression `-self`.
9655 >>> x = FP('x', Float32())
9661 def __div__(self, other):
9662 """Create the Z3 expression `self / other`.
9664 >>> x = FP('x', FPSort(8, 24))
9665 >>> y = FP('y', FPSort(8, 24))
9673 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9674 return fpDiv(_dflt_rm(), a, b, self.ctx)
9676 def __rdiv__(self, other):
9677 """Create the Z3 expression `other / self`.
9679 >>> x = FP('x', FPSort(8, 24))
9680 >>> y = FP('y', FPSort(8, 24))
9686 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9687 return fpDiv(_dflt_rm(), a, b, self.ctx)
9689 def __truediv__(self, other):
9690 """Create the Z3 expression division `self / other`."""
9691 return self.__div__(other)
9693 def __rtruediv__(self, other):
9694 """Create the Z3 expression division `other / self`."""
9695 return self.__rdiv__(other)
9697 def __mod__(self, other):
9698 """Create the Z3 expression mod `self % other`."""
9699 return fpRem(self, other)
9701 def __rmod__(self, other):
9702 """Create the Z3 expression mod `other % self`."""
9703 return fpRem(other, self)
9706class FPRMRef(ExprRef):
9707 """Floating-point rounding mode expressions"""
9709 def as_string(self):
9710 """Return a Z3 floating point expression as a Python string."""
9711 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
9714def RoundNearestTiesToEven(ctx=None):
9716 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_even(ctx.ref()), ctx)
9721 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_even(ctx.ref()), ctx)
9724def RoundNearestTiesToAway(ctx=None):
9726 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_away(ctx.ref()), ctx)
9731 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_away(ctx.ref()), ctx)
9734def RoundTowardPositive(ctx=None):
9736 return FPRMRef(Z3_mk_fpa_round_toward_positive(ctx.ref()), ctx)
9741 return FPRMRef(Z3_mk_fpa_round_toward_positive(ctx.ref()), ctx)
9744def RoundTowardNegative(ctx=None):
9746 return FPRMRef(Z3_mk_fpa_round_toward_negative(ctx.ref()), ctx)
9751 return FPRMRef(Z3_mk_fpa_round_toward_negative(ctx.ref()), ctx)
9754def RoundTowardZero(ctx=None):
9756 return FPRMRef(Z3_mk_fpa_round_toward_zero(ctx.ref()), ctx)
9761 return FPRMRef(Z3_mk_fpa_round_toward_zero(ctx.ref()), ctx)
9765 """Return `True` if `a` is a Z3 floating-point rounding mode expression.
9774 return isinstance(a, FPRMRef)
9777def is_fprm_value(a):
9778 """Return `True` if `a` is a Z3 floating-point rounding mode numeral value."""
9779 return is_fprm(a) and _is_numeral(a.ctx, a.ast)
9784class FPNumRef(FPRef):
9785 """The sign of the numeral.
9787 >>> x = FPVal(+1.0, FPSort(8, 24))
9790 >>> x = FPVal(-1.0, FPSort(8, 24))
9796 num = (ctypes.c_int)()
9797 nsign = Z3_fpa_get_numeral_sign(self.ctx.ref(), self.as_ast(), byref(num))
9799 raise Z3Exception("error retrieving the sign of a numeral.")
9800 return num.value != 0
9802 """The sign of a floating-point numeral as a bit-vector expression.
9804 Remark: NaN's are invalid arguments.
9807 def sign_as_bv(self):
9808 return BitVecNumRef(Z3_fpa_get_numeral_sign_bv(self.ctx.ref(), self.as_ast()), self.ctx)
9810 """The significand of the numeral.
9812 >>> x = FPVal(2.5, FPSort(8, 24))
9817 def significand(self):
9818 return Z3_fpa_get_numeral_significand_string(self.ctx.ref(), self.as_ast())
9820 """The significand of the numeral as a long.
9822 >>> x = FPVal(2.5, FPSort(8, 24))
9823 >>> x.significand_as_long()
9827 def significand_as_long(self):
9828 ptr = (ctypes.c_ulonglong * 1)()
9829 if not Z3_fpa_get_numeral_significand_uint64(self.ctx.ref(), self.as_ast(), ptr):
9830 raise Z3Exception("error retrieving the significand of a numeral.")
9833 """The significand of the numeral as a bit-vector expression.
9835 Remark: NaN are invalid arguments.
9838 def significand_as_bv(self):
9839 return BitVecNumRef(Z3_fpa_get_numeral_significand_bv(self.ctx.ref(), self.as_ast()), self.ctx)
9841 """The exponent of the numeral.
9843 >>> x = FPVal(2.5, FPSort(8, 24))
9848 def exponent(self, biased=True):
9849 return Z3_fpa_get_numeral_exponent_string(self.ctx.ref(), self.as_ast(), biased)
9851 """The exponent of the numeral as a long.
9853 >>> x = FPVal(2.5, FPSort(8, 24))
9854 >>> x.exponent_as_long()
9858 def exponent_as_long(self, biased=True):
9859 ptr = (ctypes.c_longlong * 1)()
9860 if not Z3_fpa_get_numeral_exponent_int64(self.ctx.ref(), self.as_ast(), ptr, biased):
9861 raise Z3Exception("error retrieving the exponent of a numeral.")
9864 """The exponent of the numeral as a bit-vector expression.
9866 Remark: NaNs are invalid arguments.
9869 def exponent_as_bv(self, biased=True):
9870 return BitVecNumRef(Z3_fpa_get_numeral_exponent_bv(self.ctx.ref(), self.as_ast(), biased), self.ctx)
9872 """Indicates whether the numeral is a NaN."""
9875 return Z3_fpa_is_numeral_nan(self.ctx.ref(), self.as_ast())
9877 """Indicates whether the numeral is +oo or -oo."""
9880 return Z3_fpa_is_numeral_inf(self.ctx.ref(), self.as_ast())
9882 """Indicates whether the numeral is +zero or -zero."""
9885 return Z3_fpa_is_numeral_zero(self.ctx.ref(), self.as_ast())
9887 """Indicates whether the numeral is normal."""
9890 return Z3_fpa_is_numeral_normal(self.ctx.ref(), self.as_ast())
9892 """Indicates whether the numeral is subnormal."""
9894 def isSubnormal(self):
9895 return Z3_fpa_is_numeral_subnormal(self.ctx.ref(), self.as_ast())
9897 """Indicates whether the numeral is positive."""
9899 def isPositive(self):
9900 return Z3_fpa_is_numeral_positive(self.ctx.ref(), self.as_ast())
9902 """Indicates whether the numeral is negative."""
9904 def isNegative(self):
9905 return Z3_fpa_is_numeral_negative(self.ctx.ref(), self.as_ast())
9908 The string representation of the numeral.
9910 >>> x = FPVal(20, FPSort(8, 24))
9915 def as_string(self):
9916 s = Z3_get_numeral_string(self.ctx.ref(), self.as_ast())
9917 return ("FPVal(%s, %s)" % (s, self.sort()))
9921 """Return `True` if `a` is a Z3 floating-point expression.
9923 >>> b = FP('b', FPSort(8, 24))
9931 return isinstance(a, FPRef)
9935 """Return `True` if `a` is a Z3 floating-point numeral value.
9937 >>> b = FP('b', FPSort(8, 24))
9940 >>> b = FPVal(1.0, FPSort(8, 24))
9946 return is_fp(a) and _is_numeral(a.ctx, a.ast)
9949def FPSort(ebits, sbits, ctx=None):
9950 """Return a Z3 floating-point sort of the given sizes. If `ctx=None`, then the global context is used.
9952 >>> Single = FPSort(8, 24)
9953 >>> Double = FPSort(11, 53)
9956 >>> x = Const('x', Single)
9957 >>> eq(x, FP('x', FPSort(8, 24)))
9961 return FPSortRef(Z3_mk_fpa_sort(ctx.ref(), ebits, sbits), ctx)
9964def _to_float_str(val, exp=0):
9965 if isinstance(val, float):
9969 sone = math.copysign(1.0, val)
9974 elif val == float("+inf"):
9976 elif val == float("-inf"):
9979 v = val.as_integer_ratio()
9982 rvs = str(num) + "/" + str(den)
9983 res = rvs + "p" + _to_int_str(exp)
9984 elif isinstance(val, bool):
9991 elif isinstance(val, str):
9992 inx = val.find("*(2**")
9995 elif val[-1] == ")":
9997 exp = str(int(val[inx + 5:-1]) + int(exp))
9999 _z3_assert(False, "String does not have floating-point numeral form.")
10001 _z3_assert(False, "Python value cannot be used to create floating-point numerals.")
10005 return res + "p" + exp
10009 """Create a Z3 floating-point NaN term.
10011 >>> s = FPSort(8, 24)
10012 >>> set_fpa_pretty(True)
10015 >>> pb = get_fpa_pretty()
10016 >>> set_fpa_pretty(False)
10018 fpNaN(FPSort(8, 24))
10019 >>> set_fpa_pretty(pb)
10021 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10022 return FPNumRef(Z3_mk_fpa_nan(s.ctx_ref(), s.ast), s.ctx)
10025def fpPlusInfinity(s):
10026 """Create a Z3 floating-point +oo term.
10028 >>> s = FPSort(8, 24)
10029 >>> pb = get_fpa_pretty()
10030 >>> set_fpa_pretty(True)
10031 >>> fpPlusInfinity(s)
10033 >>> set_fpa_pretty(False)
10034 >>> fpPlusInfinity(s)
10035 fpPlusInfinity(FPSort(8, 24))
10036 >>> set_fpa_pretty(pb)
10038 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10039 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, False), s.ctx)
10042def fpMinusInfinity(s):
10043 """Create a Z3 floating-point -oo term."""
10044 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10045 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, True), s.ctx)
10048def fpInfinity(s, negative):
10049 """Create a Z3 floating-point +oo or -oo term."""
10050 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10051 _z3_assert(isinstance(negative, bool), "expected Boolean flag")
10052 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, negative), s.ctx)
10056 """Create a Z3 floating-point +0.0 term."""
10057 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10058 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, False), s.ctx)
10062 """Create a Z3 floating-point -0.0 term."""
10063 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10064 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, True), s.ctx)
10067def fpZero(s, negative):
10068 """Create a Z3 floating-point +0.0 or -0.0 term."""
10069 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10070 _z3_assert(isinstance(negative, bool), "expected Boolean flag")
10071 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, negative), s.ctx)
10074def FPVal(sig, exp=None, fps=None, ctx=None):
10075 """Return a floating-point value of value `val` and sort `fps`.
10076 If `ctx=None`, then the global context is used.
10078 >>> v = FPVal(20.0, FPSort(8, 24))
10081 >>> print("0x%.8x" % v.exponent_as_long(False))
10083 >>> v = FPVal(2.25, FPSort(8, 24))
10086 >>> v = FPVal(-2.25, FPSort(8, 24))
10089 >>> FPVal(-0.0, FPSort(8, 24))
10091 >>> FPVal(0.0, FPSort(8, 24))
10093 >>> FPVal(+0.0, FPSort(8, 24))
10096 ctx = _get_ctx(ctx)
10097 if is_fp_sort(exp):
10101 fps = _dflt_fps(ctx)
10102 _z3_assert(is_fp_sort(fps), "sort mismatch")
10105 val = _to_float_str(sig)
10106 if val == "NaN" or val == "nan":
10108 elif val == "-0.0":
10109 return fpMinusZero(fps)
10110 elif val == "0.0" or val == "+0.0":
10111 return fpPlusZero(fps)
10112 elif val == "+oo" or val == "+inf" or val == "+Inf":
10113 return fpPlusInfinity(fps)
10114 elif val == "-oo" or val == "-inf" or val == "-Inf":
10115 return fpMinusInfinity(fps)
10117 return FPNumRef(Z3_mk_numeral(ctx.ref(), val, fps.ast), ctx)
10120def FP(name, fpsort, ctx=None):
10121 """Return a floating-point constant named `name`.
10122 `fpsort` is the floating-point sort.
10123 If `ctx=None`, then the global context is used.
10125 >>> x = FP('x', FPSort(8, 24))
10132 >>> word = FPSort(8, 24)
10133 >>> x2 = FP('x', word)
10137 if isinstance(fpsort, FPSortRef) and ctx is None:
10140 ctx = _get_ctx(ctx)
10141 return FPRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), fpsort.ast), ctx)
10144def FPs(names, fpsort, ctx=None):
10145 """Return an array of floating-point constants.
10147 >>> x, y, z = FPs('x y z', FPSort(8, 24))
10154 >>> fpMul(RNE(), fpAdd(RNE(), x, y), z)
10157 ctx = _get_ctx(ctx)
10158 if isinstance(names, str):
10159 names = names.split(" ")
10160 return [FP(name, fpsort, ctx) for name in names]
10163def fpAbs(a, ctx=None):
10164 """Create a Z3 floating-point absolute value expression.
10166 >>> s = FPSort(8, 24)
10168 >>> x = FPVal(1.0, s)
10171 >>> y = FPVal(-20.0, s)
10175 fpAbs(-1.25*(2**4))
10176 >>> fpAbs(-1.25*(2**4))
10177 fpAbs(-1.25*(2**4))
10178 >>> fpAbs(x).sort()
10181 ctx = _get_ctx(ctx)
10182 [a] = _coerce_fp_expr_list([a], ctx)
10183 return FPRef(Z3_mk_fpa_abs(ctx.ref(), a.as_ast()), ctx)
10186def fpNeg(a, ctx=None):
10187 """Create a Z3 floating-point addition expression.
10189 >>> s = FPSort(8, 24)
10194 >>> fpNeg(x).sort()
10197 ctx = _get_ctx(ctx)
10198 [a] = _coerce_fp_expr_list([a], ctx)
10199 return FPRef(Z3_mk_fpa_neg(ctx.ref(), a.as_ast()), ctx)
10202def _mk_fp_unary(f, rm, a, ctx):
10203 ctx = _get_ctx(ctx)
10204 [a] = _coerce_fp_expr_list([a], ctx)
10206 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10207 _z3_assert(is_fp(a), "Second argument must be a Z3 floating-point expression")
10208 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast()), ctx)
10211def _mk_fp_unary_pred(f, a, ctx):
10212 ctx = _get_ctx(ctx)
10213 [a] = _coerce_fp_expr_list([a], ctx)
10215 _z3_assert(is_fp(a), "First argument must be a Z3 floating-point expression")
10216 return BoolRef(f(ctx.ref(), a.as_ast()), ctx)
10219def _mk_fp_bin(f, rm, a, b, ctx):
10220 ctx = _get_ctx(ctx)
10221 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10223 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10224 _z3_assert(is_fp(a) or is_fp(b), "Second or third argument must be a Z3 floating-point expression")
10225 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast(), b.as_ast()), ctx)
10228def _mk_fp_bin_norm(f, a, b, ctx):
10229 ctx = _get_ctx(ctx)
10230 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10232 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10233 return FPRef(f(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
10236def _mk_fp_bin_pred(f, a, b, ctx):
10237 ctx = _get_ctx(ctx)
10238 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10240 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10241 return BoolRef(f(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
10244def _mk_fp_tern(f, rm, a, b, c, ctx):
10245 ctx = _get_ctx(ctx)
10246 [a, b, c] = _coerce_fp_expr_list([a, b, c], ctx)
10248 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10249 _z3_assert(is_fp(a) or is_fp(b) or is_fp(
10250 c), "Second, third or fourth argument must be a Z3 floating-point expression")
10251 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast(), b.as_ast(), c.as_ast()), ctx)
10254def fpAdd(rm, a, b, ctx=None):
10255 """Create a Z3 floating-point addition expression.
10257 >>> s = FPSort(8, 24)
10261 >>> fpAdd(rm, x, y)
10263 >>> fpAdd(RTZ(), x, y) # default rounding mode is RTZ
10265 >>> fpAdd(rm, x, y).sort()
10268 return _mk_fp_bin(Z3_mk_fpa_add, rm, a, b, ctx)
10271def fpSub(rm, a, b, ctx=None):
10272 """Create a Z3 floating-point subtraction expression.
10274 >>> s = FPSort(8, 24)
10278 >>> fpSub(rm, x, y)
10280 >>> fpSub(rm, x, y).sort()
10283 return _mk_fp_bin(Z3_mk_fpa_sub, rm, a, b, ctx)
10286def fpMul(rm, a, b, ctx=None):
10287 """Create a Z3 floating-point multiplication expression.
10289 >>> s = FPSort(8, 24)
10293 >>> fpMul(rm, x, y)
10295 >>> fpMul(rm, x, y).sort()
10298 return _mk_fp_bin(Z3_mk_fpa_mul, rm, a, b, ctx)
10301def fpDiv(rm, a, b, ctx=None):
10302 """Create a Z3 floating-point division expression.
10304 >>> s = FPSort(8, 24)
10308 >>> fpDiv(rm, x, y)
10310 >>> fpDiv(rm, x, y).sort()
10313 return _mk_fp_bin(Z3_mk_fpa_div, rm, a, b, ctx)
10316def fpRem(a, b, ctx=None):
10317 """Create a Z3 floating-point remainder expression.
10319 >>> s = FPSort(8, 24)
10324 >>> fpRem(x, y).sort()
10327 return _mk_fp_bin_norm(Z3_mk_fpa_rem, a, b, ctx)
10330def fpMin(a, b, ctx=None):
10331 """Create a Z3 floating-point minimum expression.
10333 >>> s = FPSort(8, 24)
10339 >>> fpMin(x, y).sort()
10342 return _mk_fp_bin_norm(Z3_mk_fpa_min, a, b, ctx)
10345def fpMax(a, b, ctx=None):
10346 """Create a Z3 floating-point maximum expression.
10348 >>> s = FPSort(8, 24)
10354 >>> fpMax(x, y).sort()
10357 return _mk_fp_bin_norm(Z3_mk_fpa_max, a, b, ctx)
10360def fpFMA(rm, a, b, c, ctx=None):
10361 """Create a Z3 floating-point fused multiply-add expression.
10363 return _mk_fp_tern(Z3_mk_fpa_fma, rm, a, b, c, ctx)
10366def fpSqrt(rm, a, ctx=None):
10367 """Create a Z3 floating-point square root expression.
10369 return _mk_fp_unary(Z3_mk_fpa_sqrt, rm, a, ctx)
10372def fpRoundToIntegral(rm, a, ctx=None):
10373 """Create a Z3 floating-point roundToIntegral expression.
10375 return _mk_fp_unary(Z3_mk_fpa_round_to_integral, rm, a, ctx)
10378def fpIsNaN(a, ctx=None):
10379 """Create a Z3 floating-point isNaN expression.
10381 >>> s = FPSort(8, 24)
10387 return _mk_fp_unary_pred(Z3_mk_fpa_is_nan, a, ctx)
10390def fpIsInf(a, ctx=None):
10391 """Create a Z3 floating-point isInfinite expression.
10393 >>> s = FPSort(8, 24)
10398 return _mk_fp_unary_pred(Z3_mk_fpa_is_infinite, a, ctx)
10401def fpIsZero(a, ctx=None):
10402 """Create a Z3 floating-point isZero expression.
10404 return _mk_fp_unary_pred(Z3_mk_fpa_is_zero, a, ctx)
10407def fpIsNormal(a, ctx=None):
10408 """Create a Z3 floating-point isNormal expression.
10410 return _mk_fp_unary_pred(Z3_mk_fpa_is_normal, a, ctx)
10413def fpIsSubnormal(a, ctx=None):
10414 """Create a Z3 floating-point isSubnormal expression.
10416 return _mk_fp_unary_pred(Z3_mk_fpa_is_subnormal, a, ctx)
10419def fpIsNegative(a, ctx=None):
10420 """Create a Z3 floating-point isNegative expression.
10422 return _mk_fp_unary_pred(Z3_mk_fpa_is_negative, a, ctx)
10425def fpIsPositive(a, ctx=None):
10426 """Create a Z3 floating-point isPositive expression.
10428 return _mk_fp_unary_pred(Z3_mk_fpa_is_positive, a, ctx)
10431def _check_fp_args(a, b):
10433 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10436def fpLT(a, b, ctx=None):
10437 """Create the Z3 floating-point expression `other < self`.
10439 >>> x, y = FPs('x y', FPSort(8, 24))
10442 >>> (x < y).sexpr()
10445 return _mk_fp_bin_pred(Z3_mk_fpa_lt, a, b, ctx)
10448def fpLEQ(a, b, ctx=None):
10449 """Create the Z3 floating-point expression `other <= self`.
10451 >>> x, y = FPs('x y', FPSort(8, 24))
10454 >>> (x <= y).sexpr()
10457 return _mk_fp_bin_pred(Z3_mk_fpa_leq, a, b, ctx)
10460def fpGT(a, b, ctx=None):
10461 """Create the Z3 floating-point expression `other > self`.
10463 >>> x, y = FPs('x y', FPSort(8, 24))
10466 >>> (x > y).sexpr()
10469 return _mk_fp_bin_pred(Z3_mk_fpa_gt, a, b, ctx)
10472def fpGEQ(a, b, ctx=None):
10473 """Create the Z3 floating-point expression `other >= self`.
10475 >>> x, y = FPs('x y', FPSort(8, 24))
10478 >>> (x >= y).sexpr()
10481 return _mk_fp_bin_pred(Z3_mk_fpa_geq, a, b, ctx)
10484def fpEQ(a, b, ctx=None):
10485 """Create the Z3 floating-point expression `fpEQ(other, self)`.
10487 >>> x, y = FPs('x y', FPSort(8, 24))
10490 >>> fpEQ(x, y).sexpr()
10493 return _mk_fp_bin_pred(Z3_mk_fpa_eq, a, b, ctx)
10496def fpNEQ(a, b, ctx=None):
10497 """Create the Z3 floating-point expression `Not(fpEQ(other, self))`.
10499 >>> x, y = FPs('x y', FPSort(8, 24))
10502 >>> (x != y).sexpr()
10505 return Not(fpEQ(a, b, ctx))
10508def fpFP(sgn, exp, sig, ctx=None):
10509 """Create the Z3 floating-point value `fpFP(sgn, sig, exp)` from the three bit-vectors sgn, sig, and exp.
10511 >>> s = FPSort(8, 24)
10512 >>> x = fpFP(BitVecVal(1, 1), BitVecVal(2**7-1, 8), BitVecVal(2**22, 23))
10514 fpFP(1, 127, 4194304)
10515 >>> xv = FPVal(-1.5, s)
10518 >>> slvr = Solver()
10519 >>> slvr.add(fpEQ(x, xv))
10522 >>> xv = FPVal(+1.5, s)
10525 >>> slvr = Solver()
10526 >>> slvr.add(fpEQ(x, xv))
10530 _z3_assert(is_bv(sgn) and is_bv(exp) and is_bv(sig), "sort mismatch")
10531 _z3_assert(sgn.sort().size() == 1, "sort mismatch")
10532 ctx = _get_ctx(ctx)
10533 _z3_assert(ctx == sgn.ctx == exp.ctx == sig.ctx, "context mismatch")
10534 return FPRef(Z3_mk_fpa_fp(ctx.ref(), sgn.ast, exp.ast, sig.ast), ctx)
10537def fpToFP(a1, a2=None, a3=None, ctx=None):
10538 """Create a Z3 floating-point conversion expression from other term sorts
10541 From a bit-vector term in IEEE 754-2008 format:
10542 >>> x = FPVal(1.0, Float32())
10543 >>> x_bv = fpToIEEEBV(x)
10544 >>> simplify(fpToFP(x_bv, Float32()))
10547 From a floating-point term with different precision:
10548 >>> x = FPVal(1.0, Float32())
10549 >>> x_db = fpToFP(RNE(), x, Float64())
10554 >>> x_r = RealVal(1.5)
10555 >>> simplify(fpToFP(RNE(), x_r, Float32()))
10558 From a signed bit-vector term:
10559 >>> x_signed = BitVecVal(-5, BitVecSort(32))
10560 >>> simplify(fpToFP(RNE(), x_signed, Float32()))
10563 ctx = _get_ctx(ctx)
10564 if is_bv(a1) and is_fp_sort(a2):
10565 return FPRef(Z3_mk_fpa_to_fp_bv(ctx.ref(), a1.ast, a2.ast), ctx)
10566 elif is_fprm(a1) and is_fp(a2) and is_fp_sort(a3):
10567 return FPRef(Z3_mk_fpa_to_fp_float(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10568 elif is_fprm(a1) and is_real(a2) and is_fp_sort(a3):
10569 return FPRef(Z3_mk_fpa_to_fp_real(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10570 elif is_fprm(a1) and is_bv(a2) and is_fp_sort(a3):
10571 return FPRef(Z3_mk_fpa_to_fp_signed(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10573 raise Z3Exception("Unsupported combination of arguments for conversion to floating-point term.")
10576def fpBVToFP(v, sort, ctx=None):
10577 """Create a Z3 floating-point conversion expression that represents the
10578 conversion from a bit-vector term to a floating-point term.
10580 >>> x_bv = BitVecVal(0x3F800000, 32)
10581 >>> x_fp = fpBVToFP(x_bv, Float32())
10587 _z3_assert(is_bv(v), "First argument must be a Z3 bit-vector expression")
10588 _z3_assert(is_fp_sort(sort), "Second argument must be a Z3 floating-point sort.")
10589 ctx = _get_ctx(ctx)
10590 return FPRef(Z3_mk_fpa_to_fp_bv(ctx.ref(), v.ast, sort.ast), ctx)
10593def fpFPToFP(rm, v, sort, ctx=None):
10594 """Create a Z3 floating-point conversion expression that represents the
10595 conversion from a floating-point term to a floating-point term of different precision.
10597 >>> x_sgl = FPVal(1.0, Float32())
10598 >>> x_dbl = fpFPToFP(RNE(), x_sgl, Float64())
10601 >>> simplify(x_dbl)
10606 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10607 _z3_assert(is_fp(v), "Second argument must be a Z3 floating-point expression.")
10608 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10609 ctx = _get_ctx(ctx)
10610 return FPRef(Z3_mk_fpa_to_fp_float(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10613def fpRealToFP(rm, v, sort, ctx=None):
10614 """Create a Z3 floating-point conversion expression that represents the
10615 conversion from a real term to a floating-point term.
10617 >>> x_r = RealVal(1.5)
10618 >>> x_fp = fpRealToFP(RNE(), x_r, Float32())
10624 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10625 _z3_assert(is_real(v), "Second argument must be a Z3 expression or real sort.")
10626 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10627 ctx = _get_ctx(ctx)
10628 return FPRef(Z3_mk_fpa_to_fp_real(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10631def fpSignedToFP(rm, v, sort, ctx=None):
10632 """Create a Z3 floating-point conversion expression that represents the
10633 conversion from a signed bit-vector term (encoding an integer) to a floating-point term.
10635 >>> x_signed = BitVecVal(-5, BitVecSort(32))
10636 >>> x_fp = fpSignedToFP(RNE(), x_signed, Float32())
10638 fpToFP(RNE(), 4294967291)
10642 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10643 _z3_assert(is_bv(v), "Second argument must be a Z3 bit-vector expression")
10644 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10645 ctx = _get_ctx(ctx)
10646 return FPRef(Z3_mk_fpa_to_fp_signed(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10649def fpUnsignedToFP(rm, v, sort, ctx=None):
10650 """Create a Z3 floating-point conversion expression that represents the
10651 conversion from an unsigned bit-vector term (encoding an integer) to a floating-point term.
10653 >>> x_signed = BitVecVal(-5, BitVecSort(32))
10654 >>> x_fp = fpUnsignedToFP(RNE(), x_signed, Float32())
10656 fpToFPUnsigned(RNE(), 4294967291)
10660 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10661 _z3_assert(is_bv(v), "Second argument must be a Z3 bit-vector expression")
10662 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10663 ctx = _get_ctx(ctx)
10664 return FPRef(Z3_mk_fpa_to_fp_unsigned(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10667def fpToFPUnsigned(rm, x, s, ctx=None):
10668 """Create a Z3 floating-point conversion expression, from unsigned bit-vector to floating-point expression."""
10670 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10671 _z3_assert(is_bv(x), "Second argument must be a Z3 bit-vector expression")
10672 _z3_assert(is_fp_sort(s), "Third argument must be Z3 floating-point sort")
10673 ctx = _get_ctx(ctx)
10674 return FPRef(Z3_mk_fpa_to_fp_unsigned(ctx.ref(), rm.ast, x.ast, s.ast), ctx)
10677def fpToSBV(rm, x, s, ctx=None):
10678 """Create a Z3 floating-point conversion expression, from floating-point expression to signed bit-vector.
10680 >>> x = FP('x', FPSort(8, 24))
10681 >>> y = fpToSBV(RTZ(), x, BitVecSort(32))
10682 >>> print(is_fp(x))
10684 >>> print(is_bv(y))
10686 >>> print(is_fp(y))
10688 >>> print(is_bv(x))
10692 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10693 _z3_assert(is_fp(x), "Second argument must be a Z3 floating-point expression")
10694 _z3_assert(is_bv_sort(s), "Third argument must be Z3 bit-vector sort")
10695 ctx = _get_ctx(ctx)
10696 return BitVecRef(Z3_mk_fpa_to_sbv(ctx.ref(), rm.ast, x.ast, s.size()), ctx)
10699def fpToUBV(rm, x, s, ctx=None):
10700 """Create a Z3 floating-point conversion expression, from floating-point expression to unsigned bit-vector.
10702 >>> x = FP('x', FPSort(8, 24))
10703 >>> y = fpToUBV(RTZ(), x, BitVecSort(32))
10704 >>> print(is_fp(x))
10706 >>> print(is_bv(y))
10708 >>> print(is_fp(y))
10710 >>> print(is_bv(x))
10714 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10715 _z3_assert(is_fp(x), "Second argument must be a Z3 floating-point expression")
10716 _z3_assert(is_bv_sort(s), "Third argument must be Z3 bit-vector sort")
10717 ctx = _get_ctx(ctx)
10718 return BitVecRef(Z3_mk_fpa_to_ubv(ctx.ref(), rm.ast, x.ast, s.size()), ctx)
10721def fpToReal(x, ctx=None):
10722 """Create a Z3 floating-point conversion expression, from floating-point expression to real.
10724 >>> x = FP('x', FPSort(8, 24))
10725 >>> y = fpToReal(x)
10726 >>> print(is_fp(x))
10728 >>> print(is_real(y))
10730 >>> print(is_fp(y))
10732 >>> print(is_real(x))
10736 _z3_assert(is_fp(x), "First argument must be a Z3 floating-point expression")
10737 ctx = _get_ctx(ctx)
10738 return ArithRef(Z3_mk_fpa_to_real(ctx.ref(), x.ast), ctx)
10741def fpToIEEEBV(x, ctx=None):
10742 """\brief Conversion of a floating-point term into a bit-vector term in IEEE 754-2008 format.
10744 The size of the resulting bit-vector is automatically determined.
10746 Note that IEEE 754-2008 allows multiple different representations of NaN. This conversion
10747 knows only one NaN and it will always produce the same bit-vector representation of
10750 >>> x = FP('x', FPSort(8, 24))
10751 >>> y = fpToIEEEBV(x)
10752 >>> print(is_fp(x))
10754 >>> print(is_bv(y))
10756 >>> print(is_fp(y))
10758 >>> print(is_bv(x))
10762 _z3_assert(is_fp(x), "First argument must be a Z3 floating-point expression")
10763 ctx = _get_ctx(ctx)
10764 return BitVecRef(Z3_mk_fpa_to_ieee_bv(ctx.ref(), x.ast), ctx)
10767#########################################
10769# Strings, Sequences and Regular expressions
10771#########################################
10773class SeqSortRef(SortRef):
10774 """Sequence sort."""
10776 def is_string(self):
10777 """Determine if sort is a string
10778 >>> s = StringSort()
10781 >>> s = SeqSort(IntSort())
10785 return Z3_is_string_sort(self.ctx_ref(), self.ast)
10788 return _to_sort_ref(Z3_get_seq_sort_basis(self.ctx_ref(), self.ast), self.ctx)
10790class CharSortRef(SortRef):
10791 """Character sort."""
10794def StringSort(ctx=None):
10795 """Create a string sort
10796 >>> s = StringSort()
10800 ctx = _get_ctx(ctx)
10801 return SeqSortRef(Z3_mk_string_sort(ctx.ref()), ctx)
10803def CharSort(ctx=None):
10804 """Create a character sort
10805 >>> ch = CharSort()
10809 ctx = _get_ctx(ctx)
10810 return CharSortRef(Z3_mk_char_sort(ctx.ref()), ctx)
10814 """Create a sequence sort over elements provided in the argument
10815 >>> s = SeqSort(IntSort())
10816 >>> s == Unit(IntVal(1)).sort()
10819 return SeqSortRef(Z3_mk_seq_sort(s.ctx_ref(), s.ast), s.ctx)
10822class SeqRef(ExprRef):
10823 """Sequence expression."""
10826 return SeqSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
10828 def __add__(self, other):
10829 return Concat(self, other)
10831 def __radd__(self, other):
10832 return Concat(other, self)
10834 def __getitem__(self, i):
10836 i = IntVal(i, self.ctx)
10837 return _to_expr_ref(Z3_mk_seq_nth(self.ctx_ref(), self.as_ast(), i.as_ast()), self.ctx)
10841 i = IntVal(i, self.ctx)
10842 return SeqRef(Z3_mk_seq_at(self.ctx_ref(), self.as_ast(), i.as_ast()), self.ctx)
10844 def is_string(self):
10845 return Z3_is_string_sort(self.ctx_ref(), Z3_get_sort(self.ctx_ref(), self.as_ast()))
10847 def is_string_value(self):
10848 return Z3_is_string(self.ctx_ref(), self.as_ast())
10850 def as_string(self):
10851 """Return a string representation of sequence expression."""
10852 if self.is_string_value():
10853 string_length = ctypes.c_uint()
10854 chars = Z3_get_lstring(self.ctx_ref(), self.as_ast(), byref(string_length))
10855 return string_at(chars, size=string_length.value).decode("latin-1")
10856 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
10858 def __le__(self, other):
10859 return _to_expr_ref(Z3_mk_str_le(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
10861 def __lt__(self, other):
10862 return _to_expr_ref(Z3_mk_str_lt(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
10864 def __ge__(self, other):
10865 return _to_expr_ref(Z3_mk_str_le(self.ctx_ref(), other.as_ast(), self.as_ast()), self.ctx)
10867 def __gt__(self, other):
10868 return _to_expr_ref(Z3_mk_str_lt(self.ctx_ref(), other.as_ast(), self.as_ast()), self.ctx)
10871def _coerce_char(ch, ctx=None):
10872 if isinstance(ch, str):
10873 ctx = _get_ctx(ctx)
10874 ch = CharVal(ch, ctx)
10875 if not is_expr(ch):
10876 raise Z3Exception("Character expression expected")
10879class CharRef(ExprRef):
10880 """Character expression."""
10882 def __le__(self, other):
10883 other = _coerce_char(other, self.ctx)
10884 return _to_expr_ref(Z3_mk_char_le(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
10887 return _to_expr_ref(Z3_mk_char_to_int(self.ctx_ref(), self.as_ast()), self.ctx)
10890 return _to_expr_ref(Z3_mk_char_to_bv(self.ctx_ref(), self.as_ast()), self.ctx)
10892 def is_digit(self):
10893 return _to_expr_ref(Z3_mk_char_is_digit(self.ctx_ref(), self.as_ast()), self.ctx)
10896def CharVal(ch, ctx=None):
10897 ctx = _get_ctx(ctx)
10898 if isinstance(ch, str):
10900 if not isinstance(ch, int):
10901 raise Z3Exception("character value should be an ordinal")
10902 return _to_expr_ref(Z3_mk_char(ctx.ref(), ch), ctx)
10904def CharFromBv(ch, ctx=None):
10905 if not is_expr(ch):
10906 raise Z3Expression("Bit-vector expression needed")
10907 return _to_expr_ref(Z3_mk_char_from_bv(ch.ctx_ref(), ch.as_ast()), ch.ctx)
10909def CharToBv(ch, ctx=None):
10910 ch = _coerce_char(ch, ctx)
10913def CharToInt(ch, ctx=None):
10914 ch = _coerce_char(ch, ctx)
10917def CharIsDigit(ch, ctx=None):
10918 ch = _coerce_char(ch, ctx)
10919 return ch.is_digit()
10921def _coerce_seq(s, ctx=None):
10922 if isinstance(s, str):
10923 ctx = _get_ctx(ctx)
10924 s = StringVal(s, ctx)
10926 raise Z3Exception("Non-expression passed as a sequence")
10928 raise Z3Exception("Non-sequence passed as a sequence")
10932def _get_ctx2(a, b, ctx=None):
10943 """Return `True` if `a` is a Z3 sequence expression.
10944 >>> print (is_seq(Unit(IntVal(0))))
10946 >>> print (is_seq(StringVal("abc")))
10949 return isinstance(a, SeqRef)
10953 """Return `True` if `a` is a Z3 string expression.
10954 >>> print (is_string(StringVal("ab")))
10957 return isinstance(a, SeqRef) and a.is_string()
10960def is_string_value(a):
10961 """return 'True' if 'a' is a Z3 string constant expression.
10962 >>> print (is_string_value(StringVal("a")))
10964 >>> print (is_string_value(StringVal("a") + StringVal("b")))
10967 return isinstance(a, SeqRef) and a.is_string_value()
10969def StringVal(s, ctx=None):
10970 """create a string expression"""
10971 s = "".join(str(ch) if 32 <= ord(ch) and ord(ch) < 127 else "\\u{%x}" % (ord(ch)) for ch in s)
10972 ctx = _get_ctx(ctx)
10973 return SeqRef(Z3_mk_string(ctx.ref(), s), ctx)
10976def String(name, ctx=None):
10977 """Return a string constant named `name`. If `ctx=None`, then the global context is used.
10979 >>> x = String('x')
10981 ctx = _get_ctx(ctx)
10982 return SeqRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), StringSort(ctx).ast), ctx)
10985def Strings(names, ctx=None):
10986 """Return a tuple of String constants. """
10987 ctx = _get_ctx(ctx)
10988 if isinstance(names, str):
10989 names = names.split(" ")
10990 return [String(name, ctx) for name in names]
10993def SubString(s, offset, length):
10994 """Extract substring or subsequence starting at offset"""
10995 return Extract(s, offset, length)
10998def SubSeq(s, offset, length):
10999 """Extract substring or subsequence starting at offset"""
11000 return Extract(s, offset, length)
11004 """Create the empty sequence of the given sort
11005 >>> e = Empty(StringSort())
11006 >>> e2 = StringVal("")
11007 >>> print(e.eq(e2))
11009 >>> e3 = Empty(SeqSort(IntSort()))
11012 >>> e4 = Empty(ReSort(SeqSort(IntSort())))
11014 Empty(ReSort(Seq(Int)))
11016 if isinstance(s, SeqSortRef):
11017 return SeqRef(Z3_mk_seq_empty(s.ctx_ref(), s.ast), s.ctx)
11018 if isinstance(s, ReSortRef):
11019 return ReRef(Z3_mk_re_empty(s.ctx_ref(), s.ast), s.ctx)
11020 raise Z3Exception("Non-sequence, non-regular expression sort passed to Empty")
11024 """Create the regular expression that accepts the universal language
11025 >>> e = Full(ReSort(SeqSort(IntSort())))
11027 Full(ReSort(Seq(Int)))
11028 >>> e1 = Full(ReSort(StringSort()))
11030 Full(ReSort(String))
11032 if isinstance(s, ReSortRef):
11033 return ReRef(Z3_mk_re_full(s.ctx_ref(), s.ast), s.ctx)
11034 raise Z3Exception("Non-sequence, non-regular expression sort passed to Full")
11039 """Create a singleton sequence"""
11040 return SeqRef(Z3_mk_seq_unit(a.ctx_ref(), a.as_ast()), a.ctx)
11044 """Check if 'a' is a prefix of 'b'
11045 >>> s1 = PrefixOf("ab", "abc")
11048 >>> s2 = PrefixOf("bc", "abc")
11052 ctx = _get_ctx2(a, b)
11053 a = _coerce_seq(a, ctx)
11054 b = _coerce_seq(b, ctx)
11055 return BoolRef(Z3_mk_seq_prefix(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11059 """Check if 'a' is a suffix of 'b'
11060 >>> s1 = SuffixOf("ab", "abc")
11063 >>> s2 = SuffixOf("bc", "abc")
11067 ctx = _get_ctx2(a, b)
11068 a = _coerce_seq(a, ctx)
11069 b = _coerce_seq(b, ctx)
11070 return BoolRef(Z3_mk_seq_suffix(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11074 """Check if 'a' contains 'b'
11075 >>> s1 = Contains("abc", "ab")
11078 >>> s2 = Contains("abc", "bc")
11081 >>> x, y, z = Strings('x y z')
11082 >>> s3 = Contains(Concat(x,y,z), y)
11086 ctx = _get_ctx2(a, b)
11087 a = _coerce_seq(a, ctx)
11088 b = _coerce_seq(b, ctx)
11089 return BoolRef(Z3_mk_seq_contains(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11092def Replace(s, src, dst):
11093 """Replace the first occurrence of 'src' by 'dst' in 's'
11094 >>> r = Replace("aaa", "a", "b")
11098 ctx = _get_ctx2(dst, s)
11099 if ctx is None and is_expr(src):
11101 src = _coerce_seq(src, ctx)
11102 dst = _coerce_seq(dst, ctx)
11103 s = _coerce_seq(s, ctx)
11104 return SeqRef(Z3_mk_seq_replace(src.ctx_ref(), s.as_ast(), src.as_ast(), dst.as_ast()), s.ctx)
11107def IndexOf(s, substr, offset=None):
11108 """Retrieve the index of substring within a string starting at a specified offset.
11109 >>> simplify(IndexOf("abcabc", "bc", 0))
11111 >>> simplify(IndexOf("abcabc", "bc", 2))
11117 if is_expr(offset):
11119 ctx = _get_ctx2(s, substr, ctx)
11120 s = _coerce_seq(s, ctx)
11121 substr = _coerce_seq(substr, ctx)
11122 if _is_int(offset):
11123 offset = IntVal(offset, ctx)
11124 return ArithRef(Z3_mk_seq_index(s.ctx_ref(), s.as_ast(), substr.as_ast(), offset.as_ast()), s.ctx)
11127def LastIndexOf(s, substr):
11128 """Retrieve the last index of substring within a string"""
11130 ctx = _get_ctx2(s, substr, ctx)
11131 s = _coerce_seq(s, ctx)
11132 substr = _coerce_seq(substr, ctx)
11133 return ArithRef(Z3_mk_seq_last_index(s.ctx_ref(), s.as_ast(), substr.as_ast()), s.ctx)
11137 """Obtain the length of a sequence 's'
11138 >>> l = Length(StringVal("abc"))
11143 return ArithRef(Z3_mk_seq_length(s.ctx_ref(), s.as_ast()), s.ctx)
11147 """Convert string expression to integer
11148 >>> a = StrToInt("1")
11149 >>> simplify(1 == a)
11151 >>> b = StrToInt("2")
11152 >>> simplify(1 == b)
11154 >>> c = StrToInt(IntToStr(2))
11155 >>> simplify(1 == c)
11159 return ArithRef(Z3_mk_str_to_int(s.ctx_ref(), s.as_ast()), s.ctx)
11163 """Convert integer expression to string"""
11166 return SeqRef(Z3_mk_int_to_str(s.ctx_ref(), s.as_ast()), s.ctx)
11170 """Convert a unit length string to integer code"""
11173 return ArithRef(Z3_mk_string_to_code(s.ctx_ref(), s.as_ast()), s.ctx)
11176 """Convert code to a string"""
11179 return SeqRef(Z3_mk_string_from_code(c.ctx_ref(), c.as_ast()), c.ctx)
11181def Re(s, ctx=None):
11182 """The regular expression that accepts sequence 's'
11184 >>> s2 = Re(StringVal("ab"))
11185 >>> s3 = Re(Unit(BoolVal(True)))
11187 s = _coerce_seq(s, ctx)
11188 return ReRef(Z3_mk_seq_to_re(s.ctx_ref(), s.as_ast()), s.ctx)
11191# Regular expressions
11193class ReSortRef(SortRef):
11194 """Regular expression sort."""
11197 return _to_sort_ref(Z3_get_re_sort_basis(self.ctx_ref(), self.ast), self.ctx)
11202 return ReSortRef(Z3_mk_re_sort(s.ctx.ref(), s.ast), s.ctx)
11203 if s is None or isinstance(s, Context):
11205 return ReSortRef(Z3_mk_re_sort(ctx.ref(), Z3_mk_string_sort(ctx.ref())), s.ctx)
11206 raise Z3Exception("Regular expression sort constructor expects either a string or a context or no argument")
11209class ReRef(ExprRef):
11210 """Regular expressions."""
11212 def __add__(self, other):
11213 return Union(self, other)
11217 return isinstance(s, ReRef)
11221 """Create regular expression membership test
11222 >>> re = Union(Re("a"),Re("b"))
11223 >>> print (simplify(InRe("a", re)))
11225 >>> print (simplify(InRe("b", re)))
11227 >>> print (simplify(InRe("c", re)))
11230 s = _coerce_seq(s, re.ctx)
11231 return BoolRef(Z3_mk_seq_in_re(s.ctx_ref(), s.as_ast(), re.as_ast()), s.ctx)
11235 """Create union of regular expressions.
11236 >>> re = Union(Re("a"), Re("b"), Re("c"))
11237 >>> print (simplify(InRe("d", re)))
11240 args = _get_args(args)
11243 _z3_assert(sz > 0, "At least one argument expected.")
11244 _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
11249 for i in range(sz):
11250 v[i] = args[i].as_ast()
11251 return ReRef(Z3_mk_re_union(ctx.ref(), sz, v), ctx)
11254def Intersect(*args):
11255 """Create intersection of regular expressions.
11256 >>> re = Intersect(Re("a"), Re("b"), Re("c"))
11258 args = _get_args(args)
11261 _z3_assert(sz > 0, "At least one argument expected.")
11262 _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
11267 for i in range(sz):
11268 v[i] = args[i].as_ast()
11269 return ReRef(Z3_mk_re_intersect(ctx.ref(), sz, v), ctx)
11273 """Create the regular expression accepting one or more repetitions of argument.
11274 >>> re = Plus(Re("a"))
11275 >>> print(simplify(InRe("aa", re)))
11277 >>> print(simplify(InRe("ab", re)))
11279 >>> print(simplify(InRe("", re)))
11282 return ReRef(Z3_mk_re_plus(re.ctx_ref(), re.as_ast()), re.ctx)
11286 """Create the regular expression that optionally accepts the argument.
11287 >>> re = Option(Re("a"))
11288 >>> print(simplify(InRe("a", re)))
11290 >>> print(simplify(InRe("", re)))
11292 >>> print(simplify(InRe("aa", re)))
11295 return ReRef(Z3_mk_re_option(re.ctx_ref(), re.as_ast()), re.ctx)
11299 """Create the complement regular expression."""
11300 return ReRef(Z3_mk_re_complement(re.ctx_ref(), re.as_ast()), re.ctx)
11304 """Create the regular expression accepting zero or more repetitions of argument.
11305 >>> re = Star(Re("a"))
11306 >>> print(simplify(InRe("aa", re)))
11308 >>> print(simplify(InRe("ab", re)))
11310 >>> print(simplify(InRe("", re)))
11313 return ReRef(Z3_mk_re_star(re.ctx_ref(), re.as_ast()), re.ctx)
11316def Loop(re, lo, hi=0):
11317 """Create the regular expression accepting between a lower and upper bound repetitions
11318 >>> re = Loop(Re("a"), 1, 3)
11319 >>> print(simplify(InRe("aa", re)))
11321 >>> print(simplify(InRe("aaaa", re)))
11323 >>> print(simplify(InRe("", re)))
11326 return ReRef(Z3_mk_re_loop(re.ctx_ref(), re.as_ast(), lo, hi), re.ctx)
11329def Range(lo, hi, ctx=None):
11330 """Create the range regular expression over two sequences of length 1
11331 >>> range = Range("a","z")
11332 >>> print(simplify(InRe("b", range)))
11334 >>> print(simplify(InRe("bb", range)))
11337 lo = _coerce_seq(lo, ctx)
11338 hi = _coerce_seq(hi, ctx)
11339 return ReRef(Z3_mk_re_range(lo.ctx_ref(), lo.ast, hi.ast), lo.ctx)
11341def Diff(a, b, ctx=None):
11342 """Create the difference regular expression
11344 return ReRef(Z3_mk_re_diff(a.ctx_ref(), a.ast, b.ast), a.ctx)
11346def AllChar(regex_sort, ctx=None):
11347 """Create a regular expression that accepts all single character strings
11349 return ReRef(Z3_mk_re_allchar(regex_sort.ctx_ref(), regex_sort.ast), regex_sort.ctx)
11354def PartialOrder(a, index):
11355 return FuncDeclRef(Z3_mk_partial_order(a.ctx_ref(), a.ast, index), a.ctx)
11358def LinearOrder(a, index):
11359 return FuncDeclRef(Z3_mk_linear_order(a.ctx_ref(), a.ast, index), a.ctx)
11362def TreeOrder(a, index):
11363 return FuncDeclRef(Z3_mk_tree_order(a.ctx_ref(), a.ast, index), a.ctx)
11366def PiecewiseLinearOrder(a, index):
11367 return FuncDeclRef(Z3_mk_piecewise_linear_order(a.ctx_ref(), a.ast, index), a.ctx)
11370def TransitiveClosure(f):
11371 """Given a binary relation R, such that the two arguments have the same sort
11372 create the transitive closure relation R+.
11373 The transitive closure R+ is a new relation.
11375 return FuncDeclRef(Z3_mk_transitive_closure(f.ctx_ref(), f.ast), f.ctx)
11379 super(ctypes.c_void_p, ast).__init__(ptr)
11382def to_ContextObj(ptr,):
11383 ctx = ContextObj(ptr)
11384 super(ctypes.c_void_p, ctx).__init__(ptr)
11387def to_AstVectorObj(ptr,):
11388 v = AstVectorObj(ptr)
11389 super(ctypes.c_void_p, v).__init__(ptr)
11392# NB. my-hacky-class only works for a single instance of OnClause
11393# it should be replaced with a proper correlation between OnClause
11394# and object references that can be passed over the FFI.
11395# for UserPropagator we use a global dictionary, which isn't great code.
11397_my_hacky_class = None
11398def on_clause_eh(ctx, p, clause):
11399 onc = _my_hacky_class
11400 p = _to_expr_ref(to_Ast(p), onc.ctx)
11401 clause = AstVector(to_AstVectorObj(clause), onc.ctx)
11402 onc.on_clause(p, clause)
11404_on_clause_eh = Z3_on_clause_eh(on_clause_eh)
11407 def __init__(self, s, on_clause):
11410 self.on_clause = on_clause
11412 global _my_hacky_class
11413 _my_hacky_class = self
11414 Z3_solver_register_on_clause(self.ctx.ref(), self.s.solver, self.idx, _on_clause_eh)
11418 def __init__(self):
11422 def set_threaded(self):
11423 if self.lock is None:
11425 self.lock = threading.Lock()
11427 def get(self, ctx):
11430 r = self.bases[ctx]
11432 r = self.bases[ctx]
11435 def set(self, ctx, r):
11438 self.bases[ctx] = r
11440 self.bases[ctx] = r
11442 def insert(self, r):
11445 id = len(self.bases) + 3
11448 id = len(self.bases) + 3
11453_prop_closures = None
11456def ensure_prop_closures():
11457 global _prop_closures
11458 if _prop_closures is None:
11459 _prop_closures = PropClosures()
11462def user_prop_push(ctx, cb):
11463 prop = _prop_closures.get(ctx)
11468def user_prop_pop(ctx, cb, num_scopes):
11469 prop = _prop_closures.get(ctx)
11471 prop.pop(num_scopes)
11474def user_prop_fresh(ctx, _new_ctx):
11475 _prop_closures.set_threaded()
11476 prop = _prop_closures.get(ctx)
11478 Z3_del_context(nctx.ctx)
11479 new_ctx = to_ContextObj(_new_ctx)
11481 nctx.eh = Z3_set_error_handler(new_ctx, z3_error_handler)
11483 new_prop = prop.fresh(nctx)
11484 _prop_closures.set(new_prop.id, new_prop)
11488def user_prop_fixed(ctx, cb, id, value):
11489 prop = _prop_closures.get(ctx)
11491 id = _to_expr_ref(to_Ast(id), prop.ctx())
11492 value = _to_expr_ref(to_Ast(value), prop.ctx())
11493 prop.fixed(id, value)
11496def user_prop_created(ctx, cb, id):
11497 prop = _prop_closures.get(ctx)
11499 id = _to_expr_ref(to_Ast(id), prop.ctx())
11503def user_prop_final(ctx, cb):
11504 prop = _prop_closures.get(ctx)
11509def user_prop_eq(ctx, cb, x, y):
11510 prop = _prop_closures.get(ctx)
11512 x = _to_expr_ref(to_Ast(x), prop.ctx())
11513 y = _to_expr_ref(to_Ast(y), prop.ctx())
11517def user_prop_diseq(ctx, cb, x, y):
11518 prop = _prop_closures.get(ctx)
11520 x = _to_expr_ref(to_Ast(x), prop.ctx())
11521 y = _to_expr_ref(to_Ast(y), prop.ctx())
11525# TODO The decision callback is not fully implemented.
11526# It needs to handle the ast*, unsigned* idx, and Z3_lbool*
11527def user_prop_decide(ctx, cb, t_ref, idx_ref, phase_ref):
11528 prop = _prop_closures.get(ctx)
11530 t = _to_expr_ref(to_Ast(t_ref), prop.ctx())
11531 t, idx, phase = prop.decide(t, idx, phase)
11538_user_prop_push = Z3_push_eh(user_prop_push)
11539_user_prop_pop = Z3_pop_eh(user_prop_pop)
11540_user_prop_fresh = Z3_fresh_eh(user_prop_fresh)
11541_user_prop_fixed = Z3_fixed_eh(user_prop_fixed)
11542_user_prop_created = Z3_created_eh(user_prop_created)
11543_user_prop_final = Z3_final_eh(user_prop_final)
11544_user_prop_eq = Z3_eq_eh(user_prop_eq)
11545_user_prop_diseq = Z3_eq_eh(user_prop_diseq)
11546_user_prop_decide = Z3_decide_eh(user_prop_decide)
11549def PropagateFunction(name, *sig):
11550 """Create a function that gets tracked by user propagator.
11551 Every term headed by this function symbol is tracked.
11552 If a term is fixed and the fixed callback is registered a
11553 callback is invoked that the term headed by this function is fixed.
11555 sig = _get_args(sig)
11557 _z3_assert(len(sig) > 0, "At least two arguments expected")
11558 arity = len(sig) - 1
11561 _z3_assert(is_sort(rng), "Z3 sort expected")
11562 dom = (Sort * arity)()
11563 for i in range(arity):
11565 _z3_assert(is_sort(sig[i]), "Z3 sort expected")
11566 dom[i] = sig[i].ast
11568 return FuncDeclRef(Z3_solver_propagate_declare(ctx.ref(), to_symbol(name, ctx), arity, dom, rng.ast), ctx)
11572class UserPropagateBase:
11575 # Either solver is set or ctx is set.
11576 # Propagators that are created throuh callbacks
11577 # to "fresh" inherit the context of that is supplied
11578 # as argument to the callback.
11579 # This context should not be deleted. It is owned by the solver.
11581 def __init__(self, s, ctx=None):
11582 assert s is None or ctx is None
11583 ensure_prop_closures()
11586 self.fresh_ctx = None
11588 self.id = _prop_closures.insert(self)
11593 self.created = None
11595 self.fresh_ctx = ctx
11597 Z3_solver_propagate_init(self.ctx_ref(),
11599 ctypes.c_void_p(self.id),
11606 self._ctx.ctx = None
11610 return self.fresh_ctx
11612 return self.solver.ctx
11615 return self.ctx().ref()
11617 def add_fixed(self, fixed):
11618 assert not self.fixed
11619 assert not self._ctx
11621 Z3_solver_propagate_fixed(self.ctx_ref(), self.solver.solver, _user_prop_fixed)
11624 def add_created(self, created):
11625 assert not self.created
11626 assert not self._ctx
11628 Z3_solver_propagate_created(self.ctx_ref(), self.solver.solver, _user_prop_created)
11629 self.created = created
11631 def add_final(self, final):
11632 assert not self.final
11633 assert not self._ctx
11635 Z3_solver_propagate_final(self.ctx_ref(), self.solver.solver, _user_prop_final)
11638 def add_eq(self, eq):
11640 assert not self._ctx
11642 Z3_solver_propagate_eq(self.ctx_ref(), self.solver.solver, _user_prop_eq)
11645 def add_diseq(self, diseq):
11646 assert not self.diseq
11647 assert not self._ctx
11649 Z3_solver_propagate_diseq(self.ctx_ref(), self.solver.solver, _user_prop_diseq)
11652 def add_decide(self, decide):
11653 assert not self.decide
11654 assert not self._ctx
11656 Z3_solver_propagate_decide(self.ctx_ref(), self.solver.solver, _user_prop_decide)
11657 self.decide = decide
11660 raise Z3Exception("push needs to be overwritten")
11662 def pop(self, num_scopes):
11663 raise Z3Exception("pop needs to be overwritten")
11665 def fresh(self, new_ctx):
11666 raise Z3Exception("fresh needs to be overwritten")
11669 assert not self._ctx
11671 Z3_solver_propagate_register(self.ctx_ref(), self.solver.solver, e.ast)
11673 Z3_solver_propagate_register_cb(self.ctx_ref(), ctypes.c_void_p(self.cb), e.ast)
11676 # Tell the solver to perform the next split on a given term
11677 # If the term is a bit-vector the index idx specifies the index of the Boolean variable being
11678 # split on. A phase of true = 1/false = -1/undef = 0 = let solver decide is the last argument.
11680 def next_split(self, t, idx, phase):
11681 Z3_solver_next_split(self.ctx_ref(), ctypes.c_void_p(self.cb), t.ast, idx, phase)
11684 # Propagation can only be invoked as during a fixed or final callback.
11686 def propagate(self, e, ids, eqs=[]):
11687 _ids, num_fixed = _to_ast_array(ids)
11689 _lhs, _num_lhs = _to_ast_array([x for x, y in eqs])
11690 _rhs, _num_rhs = _to_ast_array([y for x, y in eqs])
11691 Z3_solver_propagate_consequence(e.ctx.ref(), ctypes.c_void_p(
11692 self.cb), num_fixed, _ids, num_eqs, _lhs, _rhs, e.ast)
11694 def conflict(self, deps = [], eqs = []):
11695 self.propagate(BoolVal(False, self.ctx()), deps, eqs)
approx(self, precision=10)
__rtruediv__(self, other)
__deepcopy__(self, memo={})
__init__(self, m=None, ctx=None)
__deepcopy__(self, memo={})
__init__(self, ast, ctx=None)
__deepcopy__(self, memo={})
translate(self, other_ctx)
__init__(self, v=None, ctx=None)
__rtruediv__(self, other)
__deepcopy__(self, memo={})
__init__(self, *args, **kws)
__deepcopy__(self, memo={})
__init__(self, name, ctx=None)
declare(self, name, *args)
declare_core(self, name, rec_name, *args)
__deepcopy__(self, memo={})
__init__(self, entry, ctx)
__deepcopy__(self, memo={})
translate(self, other_ctx)
__deepcopy__(self, memo={})
assert_exprs(self, *args)
dimacs(self, include_names=True)
simplify(self, *arguments, **keywords)
convert_model(self, model)
__init__(self, models=True, unsat_cores=False, proofs=False, ctx=None, goal=None)
__deepcopy__(self, memo={})
eval(self, t, model_completion=False)
update_value(self, x, value)
evaluate(self, t, model_completion=False)
__deepcopy__(self, memo={})
__init__(self, descr, ctx=None)
get_documentation(self, n)
__deepcopy__(self, memo={})
__init__(self, ctx=None, params=None)
denominator_as_long(self)
Strings, Sequences and Regular expressions.
__init__(self, solver=None, ctx=None, logFile=None)
assert_and_track(self, a, p)
import_model_converter(self, other)
assert_exprs(self, *args)
check(self, *assumptions)
__deepcopy__(self, memo={})
__init__(self, stats, ctx)
Z3_ast Z3_API Z3_model_get_const_interp(Z3_context c, Z3_model m, Z3_func_decl a)
Return the interpretation (i.e., assignment) of constant a in the model m. Return NULL,...
Z3_sort Z3_API Z3_mk_int_sort(Z3_context c)
Create the integer type.
Z3_sort Z3_API Z3_mk_array_sort_n(Z3_context c, unsigned n, Z3_sort const *domain, Z3_sort range)
Create an array type with N arguments.
bool Z3_API Z3_open_log(Z3_string filename)
Log interaction to a file.
Z3_parameter_kind Z3_API Z3_get_decl_parameter_kind(Z3_context c, Z3_func_decl d, unsigned idx)
Return the parameter type associated with a declaration.
Z3_ast Z3_API Z3_get_denominator(Z3_context c, Z3_ast a)
Return the denominator (as a numeral AST) of a numeral AST of sort Real.
Z3_probe Z3_API Z3_probe_not(Z3_context x, Z3_probe p)
Return a probe that evaluates to "true" when p does not evaluate to true.
Z3_decl_kind Z3_API Z3_get_decl_kind(Z3_context c, Z3_func_decl d)
Return declaration kind corresponding to declaration.
void Z3_API Z3_solver_assert_and_track(Z3_context c, Z3_solver s, Z3_ast a, Z3_ast p)
Assert a constraint a into the solver, and track it (in the unsat) core using the Boolean constant p.
Z3_ast Z3_API Z3_func_interp_get_else(Z3_context c, Z3_func_interp f)
Return the 'else' value of the given function interpretation.
Z3_ast Z3_API Z3_mk_bvsge(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed greater than or equal to.
void Z3_API Z3_ast_map_inc_ref(Z3_context c, Z3_ast_map m)
Increment the reference counter of the given AST map.
Z3_ast Z3_API Z3_mk_const_array(Z3_context c, Z3_sort domain, Z3_ast v)
Create the constant array.
Z3_ast Z3_API Z3_mk_bvsle(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed less than or equal to.
Z3_func_decl Z3_API Z3_get_app_decl(Z3_context c, Z3_app a)
Return the declaration of a constant or function application.
void Z3_API Z3_del_context(Z3_context c)
Delete the given logical context.
Z3_func_decl Z3_API Z3_get_decl_func_decl_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the expression value associated with an expression parameter.
Z3_ast Z3_API Z3_ast_map_find(Z3_context c, Z3_ast_map m, Z3_ast k)
Return the value associated with the key k.
Z3_string Z3_API Z3_ast_map_to_string(Z3_context c, Z3_ast_map m)
Convert the given map into a string.
Z3_string Z3_API Z3_param_descrs_to_string(Z3_context c, Z3_param_descrs p)
Convert a parameter description set into a string. This function is mainly used for printing the cont...
Z3_ast Z3_API Z3_mk_zero_ext(Z3_context c, unsigned i, Z3_ast t1)
Extend the given bit-vector with zeros to the (unsigned) equivalent bit-vector of size m+i,...
void Z3_API Z3_solver_set_params(Z3_context c, Z3_solver s, Z3_params p)
Set the given solver using the given parameters.
Z3_ast Z3_API Z3_mk_set_intersect(Z3_context c, unsigned num_args, Z3_ast const args[])
Take the intersection of a list of sets.
Z3_params Z3_API Z3_mk_params(Z3_context c)
Create a Z3 (empty) parameter set. Starting at Z3 4.0, parameter sets are used to configure many comp...
unsigned Z3_API Z3_get_decl_num_parameters(Z3_context c, Z3_func_decl d)
Return the number of parameters associated with a declaration.
Z3_ast Z3_API Z3_mk_set_subset(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Check for subsetness of sets.
Z3_ast Z3_API Z3_mk_bvule(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned less than or equal to.
Z3_ast Z3_API Z3_mk_full_set(Z3_context c, Z3_sort domain)
Create the full set.
Z3_param_kind Z3_API Z3_param_descrs_get_kind(Z3_context c, Z3_param_descrs p, Z3_symbol n)
Return the kind associated with the given parameter name n.
void Z3_API Z3_add_rec_def(Z3_context c, Z3_func_decl f, unsigned n, Z3_ast args[], Z3_ast body)
Define the body of a recursive function.
Z3_ast Z3_API Z3_mk_true(Z3_context c)
Create an AST node representing true.
Z3_ast Z3_API Z3_mk_set_union(Z3_context c, unsigned num_args, Z3_ast const args[])
Take the union of a list of sets.
Z3_func_interp Z3_API Z3_add_func_interp(Z3_context c, Z3_model m, Z3_func_decl f, Z3_ast default_value)
Create a fresh func_interp object, add it to a model for a specified function. It has reference count...
Z3_ast Z3_API Z3_mk_bvsdiv_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed division of t1 and t2 does not overflow.
unsigned Z3_API Z3_get_arity(Z3_context c, Z3_func_decl d)
Alias for Z3_get_domain_size.
void Z3_API Z3_ast_vector_set(Z3_context c, Z3_ast_vector v, unsigned i, Z3_ast a)
Update position i of the AST vector v with the AST a.
Z3_ast Z3_API Z3_mk_bvxor(Z3_context c, Z3_ast t1, Z3_ast t2)
Bitwise exclusive-or.
Z3_string Z3_API Z3_stats_to_string(Z3_context c, Z3_stats s)
Convert a statistics into a string.
Z3_sort Z3_API Z3_mk_real_sort(Z3_context c)
Create the real type.
Z3_ast Z3_API Z3_mk_le(Z3_context c, Z3_ast t1, Z3_ast t2)
Create less than or equal to.
bool Z3_API Z3_global_param_get(Z3_string param_id, Z3_string_ptr param_value)
Get a global (or module) parameter.
bool Z3_API Z3_goal_inconsistent(Z3_context c, Z3_goal g)
Return true if the given goal contains the formula false.
Z3_ast Z3_API Z3_mk_lambda_const(Z3_context c, unsigned num_bound, Z3_app const bound[], Z3_ast body)
Create a lambda expression using a list of constants that form the set of bound variables.
void Z3_API Z3_solver_dec_ref(Z3_context c, Z3_solver s)
Decrement the reference counter of the given solver.
Z3_ast Z3_API Z3_mk_bvslt(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed less than.
Z3_func_decl Z3_API Z3_model_get_func_decl(Z3_context c, Z3_model m, unsigned i)
Return the declaration of the i-th function in the given model.
bool Z3_API Z3_ast_map_contains(Z3_context c, Z3_ast_map m, Z3_ast k)
Return true if the map m contains the AST key k.
Z3_ast Z3_API Z3_mk_numeral(Z3_context c, Z3_string numeral, Z3_sort ty)
Create a numeral of a given sort.
unsigned Z3_API Z3_func_entry_get_num_args(Z3_context c, Z3_func_entry e)
Return the number of arguments in a Z3_func_entry object.
Z3_symbol Z3_API Z3_get_decl_symbol_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the double value associated with an double parameter.
Z3_ast Z3_API Z3_get_numerator(Z3_context c, Z3_ast a)
Return the numerator (as a numeral AST) of a numeral AST of sort Real.
Z3_ast Z3_API Z3_mk_unary_minus(Z3_context c, Z3_ast arg)
Create an AST node representing - arg.
Z3_ast Z3_API Z3_mk_and(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing args[0] and ... and args[num_args-1].
void Z3_API Z3_interrupt(Z3_context c)
Interrupt the execution of a Z3 procedure. This procedure can be used to interrupt: solvers,...
void Z3_API Z3_goal_assert(Z3_context c, Z3_goal g, Z3_ast a)
Add a new formula a to the given goal. The formula is split according to the following procedure that...
Z3_symbol Z3_API Z3_param_descrs_get_name(Z3_context c, Z3_param_descrs p, unsigned i)
Return the name of the parameter at given index i.
Z3_ast Z3_API Z3_func_entry_get_value(Z3_context c, Z3_func_entry e)
Return the value of this point.
bool Z3_API Z3_is_quantifier_exists(Z3_context c, Z3_ast a)
Determine if ast is an existential quantifier.
Z3_sort Z3_API Z3_mk_uninterpreted_sort(Z3_context c, Z3_symbol s)
Create a free (uninterpreted) type using the given name (symbol).
Z3_ast Z3_API Z3_mk_false(Z3_context c)
Create an AST node representing false.
Z3_ast_vector Z3_API Z3_ast_map_keys(Z3_context c, Z3_ast_map m)
Return the keys stored in the given map.
Z3_ast Z3_API Z3_mk_bvmul(Z3_context c, Z3_ast t1, Z3_ast t2)
Standard two's complement multiplication.
Z3_model Z3_API Z3_goal_convert_model(Z3_context c, Z3_goal g, Z3_model m)
Convert a model of the formulas of a goal to a model of an original goal. The model may be null,...
void Z3_API Z3_del_constructor(Z3_context c, Z3_constructor constr)
Reclaim memory allocated to constructor.
Z3_ast Z3_API Z3_mk_bvsgt(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed greater than.
Z3_string Z3_API Z3_ast_to_string(Z3_context c, Z3_ast a)
Convert the given AST node into a string.
Z3_context Z3_API Z3_mk_context_rc(Z3_config c)
Create a context using the given configuration. This function is similar to Z3_mk_context....
Z3_string Z3_API Z3_get_full_version(void)
Return a string that fully describes the version of Z3 in use.
void Z3_API Z3_enable_trace(Z3_string tag)
Enable tracing messages tagged as tag when Z3 is compiled in debug mode. It is a NOOP otherwise.
Z3_ast Z3_API Z3_mk_set_complement(Z3_context c, Z3_ast arg)
Take the complement of a set.
unsigned Z3_API Z3_get_quantifier_num_patterns(Z3_context c, Z3_ast a)
Return number of patterns used in quantifier.
Z3_symbol Z3_API Z3_get_quantifier_bound_name(Z3_context c, Z3_ast a, unsigned i)
Return symbol of the i'th bound variable.
bool Z3_API Z3_stats_is_uint(Z3_context c, Z3_stats s, unsigned idx)
Return true if the given statistical data is a unsigned integer.
unsigned Z3_API Z3_model_get_num_consts(Z3_context c, Z3_model m)
Return the number of constants assigned by the given model.
Z3_ast Z3_API Z3_mk_extract(Z3_context c, unsigned high, unsigned low, Z3_ast t1)
Extract the bits high down to low from a bit-vector of size m to yield a new bit-vector of size n,...
Z3_ast Z3_API Z3_mk_mod(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 mod arg2.
Z3_ast Z3_API Z3_mk_bvredand(Z3_context c, Z3_ast t1)
Take conjunction of bits in vector, return vector of length 1.
Z3_ast Z3_API Z3_mk_set_add(Z3_context c, Z3_ast set, Z3_ast elem)
Add an element to a set.
Z3_ast Z3_API Z3_mk_ge(Z3_context c, Z3_ast t1, Z3_ast t2)
Create greater than or equal to.
Z3_ast Z3_API Z3_mk_bvadd_no_underflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed addition of t1 and t2 does not underflow.
Z3_ast Z3_API Z3_mk_bvadd_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2, bool is_signed)
Create a predicate that checks that the bit-wise addition of t1 and t2 does not overflow.
void Z3_API Z3_set_ast_print_mode(Z3_context c, Z3_ast_print_mode mode)
Select mode for the format used for pretty-printing AST nodes.
Z3_ast Z3_API Z3_mk_array_default(Z3_context c, Z3_ast array)
Access the array default value. Produces the default range value, for arrays that can be represented ...
unsigned Z3_API Z3_model_get_num_sorts(Z3_context c, Z3_model m)
Return the number of uninterpreted sorts that m assigns an interpretation to.
Z3_constructor Z3_API Z3_mk_constructor(Z3_context c, Z3_symbol name, Z3_symbol recognizer, unsigned num_fields, Z3_symbol const field_names[], Z3_sort_opt const sorts[], unsigned sort_refs[])
Create a constructor.
Z3_ast_vector Z3_API Z3_ast_vector_translate(Z3_context s, Z3_ast_vector v, Z3_context t)
Translate the AST vector v from context s into an AST vector in context t.
void Z3_API Z3_func_entry_inc_ref(Z3_context c, Z3_func_entry e)
Increment the reference counter of the given Z3_func_entry object.
Z3_ast Z3_API Z3_mk_fresh_const(Z3_context c, Z3_string prefix, Z3_sort ty)
Declare and create a fresh constant.
Z3_ast Z3_API Z3_mk_bvsub_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed subtraction of t1 and t2 does not overflow.
void Z3_API Z3_solver_push(Z3_context c, Z3_solver s)
Create a backtracking point.
Z3_ast Z3_API Z3_mk_bvsub_no_underflow(Z3_context c, Z3_ast t1, Z3_ast t2, bool is_signed)
Create a predicate that checks that the bit-wise subtraction of t1 and t2 does not underflow.
Z3_goal Z3_API Z3_goal_translate(Z3_context source, Z3_goal g, Z3_context target)
Copy a goal g from the context source to the context target.
Z3_ast Z3_API Z3_mk_bvudiv(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned division.
Z3_string Z3_API Z3_ast_vector_to_string(Z3_context c, Z3_ast_vector v)
Convert AST vector into a string.
Z3_ast Z3_API Z3_mk_bvshl(Z3_context c, Z3_ast t1, Z3_ast t2)
Shift left.
bool Z3_API Z3_is_numeral_ast(Z3_context c, Z3_ast a)
Z3_ast Z3_API Z3_mk_bvsrem(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed remainder (sign follows dividend).
bool Z3_API Z3_is_as_array(Z3_context c, Z3_ast a)
The (_ as-array f) AST node is a construct for assigning interpretations for arrays in Z3....
Z3_func_decl Z3_API Z3_mk_func_decl(Z3_context c, Z3_symbol s, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a constant or function.
Z3_ast Z3_API Z3_mk_is_int(Z3_context c, Z3_ast t1)
Check if a real number is an integer.
void Z3_API Z3_params_set_bool(Z3_context c, Z3_params p, Z3_symbol k, bool v)
Add a Boolean parameter k with value v to the parameter set p.
Z3_ast Z3_API Z3_mk_ite(Z3_context c, Z3_ast t1, Z3_ast t2, Z3_ast t3)
Create an AST node representing an if-then-else: ite(t1, t2, t3).
Z3_ast Z3_API Z3_mk_select(Z3_context c, Z3_ast a, Z3_ast i)
Array read. The argument a is the array and i is the index of the array that gets read.
Z3_ast Z3_API Z3_mk_sign_ext(Z3_context c, unsigned i, Z3_ast t1)
Sign-extend of the given bit-vector to the (signed) equivalent bit-vector of size m+i,...
unsigned Z3_API Z3_goal_size(Z3_context c, Z3_goal g)
Return the number of formulas in the given goal.
void Z3_API Z3_stats_inc_ref(Z3_context c, Z3_stats s)
Increment the reference counter of the given statistics object.
Z3_ast Z3_API Z3_mk_select_n(Z3_context c, Z3_ast a, unsigned n, Z3_ast const *idxs)
n-ary Array read. The argument a is the array and idxs are the indices of the array that gets read.
Z3_ast_vector Z3_API Z3_algebraic_get_poly(Z3_context c, Z3_ast a)
Return the coefficients of the defining polynomial.
Z3_ast Z3_API Z3_mk_div(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 div arg2.
void Z3_API Z3_model_dec_ref(Z3_context c, Z3_model m)
Decrement the reference counter of the given model.
void Z3_API Z3_func_interp_inc_ref(Z3_context c, Z3_func_interp f)
Increment the reference counter of the given Z3_func_interp object.
void Z3_API Z3_params_set_double(Z3_context c, Z3_params p, Z3_symbol k, double v)
Add a double parameter k with value v to the parameter set p.
Z3_string Z3_API Z3_param_descrs_get_documentation(Z3_context c, Z3_param_descrs p, Z3_symbol s)
Retrieve documentation string corresponding to parameter name s.
Z3_sort Z3_API Z3_mk_datatype_sort(Z3_context c, Z3_symbol name)
create a forward reference to a recursive datatype being declared. The forward reference can be used ...
Z3_solver Z3_API Z3_mk_solver(Z3_context c)
Create a new solver. This solver is a "combined solver" (see combined_solver module) that internally ...
Z3_model Z3_API Z3_solver_get_model(Z3_context c, Z3_solver s)
Retrieve the model for the last Z3_solver_check or Z3_solver_check_assumptions.
int Z3_API Z3_get_symbol_int(Z3_context c, Z3_symbol s)
Return the symbol int value.
Z3_func_decl Z3_API Z3_get_as_array_func_decl(Z3_context c, Z3_ast a)
Return the function declaration f associated with a (_ as_array f) node.
Z3_ast Z3_API Z3_mk_ext_rotate_left(Z3_context c, Z3_ast t1, Z3_ast t2)
Rotate bits of t1 to the left t2 times.
void Z3_API Z3_goal_inc_ref(Z3_context c, Z3_goal g)
Increment the reference counter of the given goal.
Z3_ast Z3_API Z3_mk_implies(Z3_context c, Z3_ast t1, Z3_ast t2)
Create an AST node representing t1 implies t2.
unsigned Z3_API Z3_get_datatype_sort_num_constructors(Z3_context c, Z3_sort t)
Return number of constructors for datatype.
void Z3_API Z3_params_set_uint(Z3_context c, Z3_params p, Z3_symbol k, unsigned v)
Add a unsigned parameter k with value v to the parameter set p.
Z3_lbool Z3_API Z3_solver_check_assumptions(Z3_context c, Z3_solver s, unsigned num_assumptions, Z3_ast const assumptions[])
Check whether the assertions in the given solver and optional assumptions are consistent or not.
Z3_sort Z3_API Z3_model_get_sort(Z3_context c, Z3_model m, unsigned i)
Return a uninterpreted sort that m assigns an interpretation.
Z3_ast Z3_API Z3_mk_bvashr(Z3_context c, Z3_ast t1, Z3_ast t2)
Arithmetic shift right.
Z3_ast Z3_API Z3_mk_bv2int(Z3_context c, Z3_ast t1, bool is_signed)
Create an integer from the bit-vector argument t1. If is_signed is false, then the bit-vector t1 is t...
Z3_sort Z3_API Z3_get_array_sort_domain_n(Z3_context c, Z3_sort t, unsigned idx)
Return the i'th domain sort of an n-dimensional array.
Z3_ast Z3_API Z3_mk_set_del(Z3_context c, Z3_ast set, Z3_ast elem)
Remove an element to a set.
Z3_ast Z3_API Z3_mk_bvmul_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2, bool is_signed)
Create a predicate that checks that the bit-wise multiplication of t1 and t2 does not overflow.
Z3_ast Z3_API Z3_mk_bvor(Z3_context c, Z3_ast t1, Z3_ast t2)
Bitwise or.
int Z3_API Z3_get_decl_int_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the integer value associated with an integer parameter.
unsigned Z3_API Z3_get_quantifier_num_no_patterns(Z3_context c, Z3_ast a)
Return number of no_patterns used in quantifier.
Z3_func_decl Z3_API Z3_get_datatype_sort_constructor(Z3_context c, Z3_sort t, unsigned idx)
Return idx'th constructor.
void Z3_API Z3_ast_vector_resize(Z3_context c, Z3_ast_vector v, unsigned n)
Resize the AST vector v.
Z3_ast Z3_API Z3_mk_quantifier_const_ex(Z3_context c, bool is_forall, unsigned weight, Z3_symbol quantifier_id, Z3_symbol skolem_id, unsigned num_bound, Z3_app const bound[], unsigned num_patterns, Z3_pattern const patterns[], unsigned num_no_patterns, Z3_ast const no_patterns[], Z3_ast body)
Create a universal or existential quantifier using a list of constants that will form the set of boun...
Z3_pattern Z3_API Z3_mk_pattern(Z3_context c, unsigned num_patterns, Z3_ast const terms[])
Create a pattern for quantifier instantiation.
Z3_symbol_kind Z3_API Z3_get_symbol_kind(Z3_context c, Z3_symbol s)
Return Z3_INT_SYMBOL if the symbol was constructed using Z3_mk_int_symbol, and Z3_STRING_SYMBOL if th...
bool Z3_API Z3_is_lambda(Z3_context c, Z3_ast a)
Determine if ast is a lambda expression.
unsigned Z3_API Z3_stats_get_uint_value(Z3_context c, Z3_stats s, unsigned idx)
Return the unsigned value of the given statistical data.
Z3_sort Z3_API Z3_get_array_sort_domain(Z3_context c, Z3_sort t)
Return the domain of the given array sort. In the case of a multi-dimensional array,...
Z3_ast Z3_API Z3_mk_bvmul_no_underflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed multiplication of t1 and t2 does not underflo...
Z3_ast Z3_API Z3_func_decl_to_ast(Z3_context c, Z3_func_decl f)
Convert a Z3_func_decl into Z3_ast. This is just type casting.
void Z3_API Z3_add_const_interp(Z3_context c, Z3_model m, Z3_func_decl f, Z3_ast a)
Add a constant interpretation.
Z3_ast Z3_API Z3_mk_bvadd(Z3_context c, Z3_ast t1, Z3_ast t2)
Standard two's complement addition.
unsigned Z3_API Z3_algebraic_get_i(Z3_context c, Z3_ast a)
Return which root of the polynomial the algebraic number represents.
void Z3_API Z3_params_dec_ref(Z3_context c, Z3_params p)
Decrement the reference counter of the given parameter set.
Z3_ast Z3_API Z3_get_app_arg(Z3_context c, Z3_app a, unsigned i)
Return the i-th argument of the given application.
Z3_string Z3_API Z3_model_to_string(Z3_context c, Z3_model m)
Convert the given model into a string.
Z3_func_decl Z3_API Z3_mk_fresh_func_decl(Z3_context c, Z3_string prefix, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a fresh constant or function.
unsigned Z3_API Z3_ast_map_size(Z3_context c, Z3_ast_map m)
Return the size of the given map.
unsigned Z3_API Z3_param_descrs_size(Z3_context c, Z3_param_descrs p)
Return the number of parameters in the given parameter description set.
Z3_string Z3_API Z3_goal_to_dimacs_string(Z3_context c, Z3_goal g, bool include_names)
Convert a goal into a DIMACS formatted string. The goal must be in CNF. You can convert a goal to CNF...
Z3_ast Z3_API Z3_mk_lt(Z3_context c, Z3_ast t1, Z3_ast t2)
Create less than.
Z3_ast Z3_API Z3_get_quantifier_no_pattern_ast(Z3_context c, Z3_ast a, unsigned i)
Return i'th no_pattern.
double Z3_API Z3_stats_get_double_value(Z3_context c, Z3_stats s, unsigned idx)
Return the double value of the given statistical data.
Z3_ast Z3_API Z3_mk_bvugt(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned greater than.
unsigned Z3_API Z3_goal_depth(Z3_context c, Z3_goal g)
Return the depth of the given goal. It tracks how many transformations were applied to it.
Z3_string Z3_API Z3_get_symbol_string(Z3_context c, Z3_symbol s)
Return the symbol name.
Z3_ast Z3_API Z3_pattern_to_ast(Z3_context c, Z3_pattern p)
Convert a Z3_pattern into Z3_ast. This is just type casting.
Z3_ast Z3_API Z3_mk_bvnot(Z3_context c, Z3_ast t1)
Bitwise negation.
Z3_ast Z3_API Z3_mk_bvurem(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned remainder.
void Z3_API Z3_mk_datatypes(Z3_context c, unsigned num_sorts, Z3_symbol const sort_names[], Z3_sort sorts[], Z3_constructor_list constructor_lists[])
Create mutually recursive datatypes.
unsigned Z3_API Z3_func_interp_get_arity(Z3_context c, Z3_func_interp f)
Return the arity (number of arguments) of the given function interpretation.
Z3_ast Z3_API Z3_mk_bvsub(Z3_context c, Z3_ast t1, Z3_ast t2)
Standard two's complement subtraction.
Z3_ast Z3_API Z3_get_algebraic_number_upper(Z3_context c, Z3_ast a, unsigned precision)
Return a upper bound for the given real algebraic number. The interval isolating the number is smalle...
Z3_ast Z3_API Z3_mk_power(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 ^ arg2.
Z3_ast Z3_API Z3_mk_seq_concat(Z3_context c, unsigned n, Z3_ast const args[])
Concatenate sequences.
Z3_sort Z3_API Z3_mk_enumeration_sort(Z3_context c, Z3_symbol name, unsigned n, Z3_symbol const enum_names[], Z3_func_decl enum_consts[], Z3_func_decl enum_testers[])
Create a enumeration sort.
unsigned Z3_API Z3_get_bv_sort_size(Z3_context c, Z3_sort t)
Return the size of the given bit-vector sort.
Z3_ast Z3_API Z3_mk_set_member(Z3_context c, Z3_ast elem, Z3_ast set)
Check for set membership.
void Z3_API Z3_ast_vector_dec_ref(Z3_context c, Z3_ast_vector v)
Decrement the reference counter of the given AST vector.
void Z3_API Z3_func_interp_dec_ref(Z3_context c, Z3_func_interp f)
Decrement the reference counter of the given Z3_func_interp object.
void Z3_API Z3_params_inc_ref(Z3_context c, Z3_params p)
Increment the reference counter of the given parameter set.
void Z3_API Z3_set_error_handler(Z3_context c, Z3_error_handler h)
Register a Z3 error handler.
Z3_ast Z3_API Z3_mk_distinct(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing distinct(args[0], ..., args[num_args-1]).
Z3_config Z3_API Z3_mk_config(void)
Create a configuration object for the Z3 context object.
void Z3_API Z3_set_param_value(Z3_config c, Z3_string param_id, Z3_string param_value)
Set a configuration parameter.
Z3_sort Z3_API Z3_mk_bv_sort(Z3_context c, unsigned sz)
Create a bit-vector type of the given size.
Z3_ast Z3_API Z3_mk_bvult(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned less than.
void Z3_API Z3_ast_map_dec_ref(Z3_context c, Z3_ast_map m)
Decrement the reference counter of the given AST map.
Z3_string Z3_API Z3_params_to_string(Z3_context c, Z3_params p)
Convert a parameter set into a string. This function is mainly used for printing the contents of a pa...
Z3_param_descrs Z3_API Z3_get_global_param_descrs(Z3_context c)
Retrieve description of global parameters.
Z3_func_decl Z3_API Z3_model_get_const_decl(Z3_context c, Z3_model m, unsigned i)
Return the i-th constant in the given model.
Z3_ast Z3_API Z3_translate(Z3_context source, Z3_ast a, Z3_context target)
Translate/Copy the AST a from context source to context target. AST a must have been created using co...
Z3_sort Z3_API Z3_get_range(Z3_context c, Z3_func_decl d)
Return the range of the given declaration.
void Z3_API Z3_global_param_set(Z3_string param_id, Z3_string param_value)
Set a global (or module) parameter. This setting is shared by all Z3 contexts.
Z3_ast_vector Z3_API Z3_model_get_sort_universe(Z3_context c, Z3_model m, Z3_sort s)
Return the finite set of distinct values that represent the interpretation for sort s.
void Z3_API Z3_func_entry_dec_ref(Z3_context c, Z3_func_entry e)
Decrement the reference counter of the given Z3_func_entry object.
unsigned Z3_API Z3_stats_size(Z3_context c, Z3_stats s)
Return the number of statistical data in s.
void Z3_API Z3_append_log(Z3_string string)
Append user-defined string to interaction log.
Z3_ast Z3_API Z3_get_quantifier_body(Z3_context c, Z3_ast a)
Return body of quantifier.
void Z3_API Z3_param_descrs_dec_ref(Z3_context c, Z3_param_descrs p)
Decrement the reference counter of the given parameter description set.
Z3_model Z3_API Z3_mk_model(Z3_context c)
Create a fresh model object. It has reference count 0.
Z3_symbol Z3_API Z3_get_decl_name(Z3_context c, Z3_func_decl d)
Return the constant declaration name as a symbol.
Z3_ast Z3_API Z3_mk_bvneg_no_overflow(Z3_context c, Z3_ast t1)
Check that bit-wise negation does not overflow when t1 is interpreted as a signed bit-vector.
Z3_string Z3_API Z3_stats_get_key(Z3_context c, Z3_stats s, unsigned idx)
Return the key (a string) for a particular statistical data.
Z3_ast Z3_API Z3_mk_bvand(Z3_context c, Z3_ast t1, Z3_ast t2)
Bitwise and.
Z3_ast_kind Z3_API Z3_get_ast_kind(Z3_context c, Z3_ast a)
Return the kind of the given AST.
Z3_ast Z3_API Z3_mk_bvsmod(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed remainder (sign follows divisor).
Z3_model Z3_API Z3_model_translate(Z3_context c, Z3_model m, Z3_context dst)
translate model from context c to context dst.
void Z3_API Z3_get_version(unsigned *major, unsigned *minor, unsigned *build_number, unsigned *revision_number)
Return Z3 version number information.
Z3_ast Z3_API Z3_mk_int2bv(Z3_context c, unsigned n, Z3_ast t1)
Create an n bit bit-vector from the integer argument t1.
void Z3_API Z3_solver_assert(Z3_context c, Z3_solver s, Z3_ast a)
Assert a constraint into the solver.
unsigned Z3_API Z3_ast_vector_size(Z3_context c, Z3_ast_vector v)
Return the size of the given AST vector.
unsigned Z3_API Z3_get_quantifier_weight(Z3_context c, Z3_ast a)
Obtain weight of quantifier.
bool Z3_API Z3_model_eval(Z3_context c, Z3_model m, Z3_ast t, bool model_completion, Z3_ast *v)
Evaluate the AST node t in the given model. Return true if succeeded, and store the result in v.
unsigned Z3_API Z3_solver_get_num_scopes(Z3_context c, Z3_solver s)
Return the number of backtracking points.
Z3_sort Z3_API Z3_get_array_sort_range(Z3_context c, Z3_sort t)
Return the range of the given array sort.
void Z3_API Z3_del_constructor_list(Z3_context c, Z3_constructor_list clist)
Reclaim memory allocated for constructor list.
Z3_ast Z3_API Z3_mk_bound(Z3_context c, unsigned index, Z3_sort ty)
Create a variable.
unsigned Z3_API Z3_get_app_num_args(Z3_context c, Z3_app a)
Return the number of argument of an application. If t is an constant, then the number of arguments is...
Z3_ast Z3_API Z3_func_entry_get_arg(Z3_context c, Z3_func_entry e, unsigned i)
Return an argument of a Z3_func_entry object.
Z3_ast Z3_API Z3_mk_eq(Z3_context c, Z3_ast l, Z3_ast r)
Create an AST node representing l = r.
void Z3_API Z3_ast_vector_inc_ref(Z3_context c, Z3_ast_vector v)
Increment the reference counter of the given AST vector.
unsigned Z3_API Z3_model_get_num_funcs(Z3_context c, Z3_model m)
Return the number of function interpretations in the given model.
void Z3_API Z3_dec_ref(Z3_context c, Z3_ast a)
Decrement the reference counter of the given AST. The context c should have been created using Z3_mk_...
Z3_ast_vector Z3_API Z3_mk_ast_vector(Z3_context c)
Return an empty AST vector.
Z3_ast Z3_API Z3_mk_empty_set(Z3_context c, Z3_sort domain)
Create the empty set.
Z3_ast Z3_API Z3_mk_set_has_size(Z3_context c, Z3_ast set, Z3_ast k)
Create predicate that holds if Boolean array set has k elements set to true.
Z3_ast Z3_API Z3_mk_repeat(Z3_context c, unsigned i, Z3_ast t1)
Repeat the given bit-vector up length i.
Z3_goal_prec Z3_API Z3_goal_precision(Z3_context c, Z3_goal g)
Return the "precision" of the given goal. Goals can be transformed using over and under approximation...
void Z3_API Z3_solver_pop(Z3_context c, Z3_solver s, unsigned n)
Backtrack n backtracking points.
void Z3_API Z3_ast_map_erase(Z3_context c, Z3_ast_map m, Z3_ast k)
Erase a key from the map.
Z3_ast Z3_API Z3_mk_int2real(Z3_context c, Z3_ast t1)
Coerce an integer to a real.
unsigned Z3_API Z3_get_index_value(Z3_context c, Z3_ast a)
Return index of de-Bruijn bound variable.
Z3_goal Z3_API Z3_mk_goal(Z3_context c, bool models, bool unsat_cores, bool proofs)
Create a goal (aka problem). A goal is essentially a set of formulas, that can be solved and/or trans...
double Z3_API Z3_get_decl_double_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the double value associated with an double parameter.
unsigned Z3_API Z3_get_ast_hash(Z3_context c, Z3_ast a)
Return a hash code for the given AST. The hash code is structural but two different AST objects can m...
Z3_symbol Z3_API Z3_get_sort_name(Z3_context c, Z3_sort d)
Return the sort name as a symbol.
void Z3_API Z3_params_validate(Z3_context c, Z3_params p, Z3_param_descrs d)
Validate the parameter set p against the parameter description set d.
Z3_func_decl Z3_API Z3_get_datatype_sort_recognizer(Z3_context c, Z3_sort t, unsigned idx)
Return idx'th recognizer.
void Z3_API Z3_global_param_reset_all(void)
Restore the value of all global (and module) parameters. This command will not affect already created...
Z3_ast Z3_API Z3_mk_gt(Z3_context c, Z3_ast t1, Z3_ast t2)
Create greater than.
Z3_ast Z3_API Z3_mk_store(Z3_context c, Z3_ast a, Z3_ast i, Z3_ast v)
Array update.
Z3_string Z3_API Z3_get_decl_rational_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the rational value, as a string, associated with a rational parameter.
void Z3_API Z3_ast_vector_push(Z3_context c, Z3_ast_vector v, Z3_ast a)
Add the AST a in the end of the AST vector v. The size of v is increased by one.
bool Z3_API Z3_is_eq_ast(Z3_context c, Z3_ast t1, Z3_ast t2)
Compare terms.
bool Z3_API Z3_is_quantifier_forall(Z3_context c, Z3_ast a)
Determine if an ast is a universal quantifier.
Z3_ast_map Z3_API Z3_mk_ast_map(Z3_context c)
Return an empty mapping from AST to AST.
Z3_ast Z3_API Z3_mk_xor(Z3_context c, Z3_ast t1, Z3_ast t2)
Create an AST node representing t1 xor t2.
Z3_ast Z3_API Z3_mk_map(Z3_context c, Z3_func_decl f, unsigned n, Z3_ast const *args)
Map f on the argument arrays.
Z3_ast Z3_API Z3_mk_const(Z3_context c, Z3_symbol s, Z3_sort ty)
Declare and create a constant.
Z3_symbol Z3_API Z3_mk_string_symbol(Z3_context c, Z3_string s)
Create a Z3 symbol using a C string.
void Z3_API Z3_param_descrs_inc_ref(Z3_context c, Z3_param_descrs p)
Increment the reference counter of the given parameter description set.
void Z3_API Z3_stats_dec_ref(Z3_context c, Z3_stats s)
Decrement the reference counter of the given statistics object.
Z3_ast Z3_API Z3_mk_array_ext(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create array extensionality index given two arrays with the same sort. The meaning is given by the ax...
Z3_ast Z3_API Z3_mk_re_concat(Z3_context c, unsigned n, Z3_ast const args[])
Create the concatenation of the regular languages.
Z3_ast Z3_API Z3_sort_to_ast(Z3_context c, Z3_sort s)
Convert a Z3_sort into Z3_ast. This is just type casting.
Z3_func_entry Z3_API Z3_func_interp_get_entry(Z3_context c, Z3_func_interp f, unsigned i)
Return a "point" of the given function interpretation. It represents the value of f in a particular p...
Z3_func_decl Z3_API Z3_mk_rec_func_decl(Z3_context c, Z3_symbol s, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a recursive function.
unsigned Z3_API Z3_get_ast_id(Z3_context c, Z3_ast t)
Return a unique identifier for t. The identifier is unique up to structural equality....
Z3_ast Z3_API Z3_mk_concat(Z3_context c, Z3_ast t1, Z3_ast t2)
Concatenate the given bit-vectors.
unsigned Z3_API Z3_get_quantifier_num_bound(Z3_context c, Z3_ast a)
Return number of bound variables of quantifier.
Z3_sort Z3_API Z3_get_decl_sort_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the sort value associated with a sort parameter.
Z3_constructor_list Z3_API Z3_mk_constructor_list(Z3_context c, unsigned num_constructors, Z3_constructor const constructors[])
Create list of constructors.
Z3_ast Z3_API Z3_mk_app(Z3_context c, Z3_func_decl d, unsigned num_args, Z3_ast const args[])
Create a constant or function application.
Z3_sort_kind Z3_API Z3_get_sort_kind(Z3_context c, Z3_sort t)
Return the sort kind (e.g., array, tuple, int, bool, etc).
Z3_ast Z3_API Z3_mk_bvneg(Z3_context c, Z3_ast t1)
Standard two's complement unary minus.
Z3_ast Z3_API Z3_mk_store_n(Z3_context c, Z3_ast a, unsigned n, Z3_ast const *idxs, Z3_ast v)
n-ary Array update.
Z3_sort Z3_API Z3_get_domain(Z3_context c, Z3_func_decl d, unsigned i)
Return the sort of the i-th parameter of the given function declaration.
Z3_sort Z3_API Z3_mk_bool_sort(Z3_context c)
Create the Boolean type.
void Z3_API Z3_params_set_symbol(Z3_context c, Z3_params p, Z3_symbol k, Z3_symbol v)
Add a symbol parameter k with value v to the parameter set p.
Z3_ast Z3_API Z3_ast_vector_get(Z3_context c, Z3_ast_vector v, unsigned i)
Return the AST at position i in the AST vector v.
Z3_func_decl Z3_API Z3_to_func_decl(Z3_context c, Z3_ast a)
Convert an AST into a FUNC_DECL_AST. This is just type casting.
Z3_ast Z3_API Z3_mk_set_difference(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Take the set difference between two sets.
Z3_ast Z3_API Z3_mk_bvsdiv(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed division.
Z3_ast Z3_API Z3_mk_bvlshr(Z3_context c, Z3_ast t1, Z3_ast t2)
Logical shift right.
Z3_ast Z3_API Z3_get_decl_ast_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the expression value associated with an expression parameter.
Z3_pattern Z3_API Z3_get_quantifier_pattern_ast(Z3_context c, Z3_ast a, unsigned i)
Return i'th pattern.
void Z3_API Z3_goal_dec_ref(Z3_context c, Z3_goal g)
Decrement the reference counter of the given goal.
Z3_ast Z3_API Z3_mk_not(Z3_context c, Z3_ast a)
Create an AST node representing not(a).
Z3_ast Z3_API Z3_mk_or(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing args[0] or ... or args[num_args-1].
Z3_sort Z3_API Z3_mk_array_sort(Z3_context c, Z3_sort domain, Z3_sort range)
Create an array type.
void Z3_API Z3_model_inc_ref(Z3_context c, Z3_model m)
Increment the reference counter of the given model.
Z3_ast Z3_API Z3_mk_seq_extract(Z3_context c, Z3_ast s, Z3_ast offset, Z3_ast length)
Extract subsequence starting at offset of length.
Z3_string Z3_API Z3_get_numeral_string(Z3_context c, Z3_ast a)
Return numeral value, as a decimal string of a numeric constant term.
void Z3_API Z3_func_interp_add_entry(Z3_context c, Z3_func_interp fi, Z3_ast_vector args, Z3_ast value)
add a function entry to a function interpretation.
Z3_ast Z3_API Z3_mk_bvuge(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned greater than or equal to.
Z3_string Z3_API Z3_get_numeral_binary_string(Z3_context c, Z3_ast a)
Return numeral value, as a binary string of a numeric constant term.
Z3_sort Z3_API Z3_get_quantifier_bound_sort(Z3_context c, Z3_ast a, unsigned i)
Return sort of the i'th bound variable.
void Z3_API Z3_disable_trace(Z3_string tag)
Disable tracing messages tagged as tag when Z3 is compiled in debug mode. It is a NOOP otherwise.
Z3_ast Z3_API Z3_goal_formula(Z3_context c, Z3_goal g, unsigned idx)
Return a formula from the given goal.
Z3_symbol Z3_API Z3_mk_int_symbol(Z3_context c, int i)
Create a Z3 symbol using an integer.
unsigned Z3_API Z3_func_interp_get_num_entries(Z3_context c, Z3_func_interp f)
Return the number of entries in the given function interpretation.
void Z3_API Z3_ast_map_insert(Z3_context c, Z3_ast_map m, Z3_ast k, Z3_ast v)
Store/Replace a new key, value pair in the given map.
Z3_string Z3_API Z3_goal_to_string(Z3_context c, Z3_goal g)
Convert a goal into a string.
bool Z3_API Z3_is_eq_sort(Z3_context c, Z3_sort s1, Z3_sort s2)
compare sorts.
void Z3_API Z3_del_config(Z3_config c)
Delete the given configuration object.
void Z3_API Z3_inc_ref(Z3_context c, Z3_ast a)
Increment the reference counter of the given AST. The context c should have been created using Z3_mk_...
Z3_ast Z3_API Z3_mk_real2int(Z3_context c, Z3_ast t1)
Coerce a real to an integer.
Z3_func_interp Z3_API Z3_model_get_func_interp(Z3_context c, Z3_model m, Z3_func_decl f)
Return the interpretation of the function f in the model m. Return NULL, if the model does not assign...
void Z3_API Z3_solver_inc_ref(Z3_context c, Z3_solver s)
Increment the reference counter of the given solver.
Z3_ast Z3_API Z3_mk_ext_rotate_right(Z3_context c, Z3_ast t1, Z3_ast t2)
Rotate bits of t1 to the right t2 times.
Z3_string Z3_API Z3_get_numeral_decimal_string(Z3_context c, Z3_ast a, unsigned precision)
Return numeral as a string in decimal notation. The result has at most precision decimal places.
Z3_sort Z3_API Z3_get_sort(Z3_context c, Z3_ast a)
Return the sort of an AST node.
Z3_func_decl Z3_API Z3_get_datatype_sort_constructor_accessor(Z3_context c, Z3_sort t, unsigned idx_c, unsigned idx_a)
Return idx_a'th accessor for the idx_c'th constructor.
Z3_ast Z3_API Z3_mk_bvredor(Z3_context c, Z3_ast t1)
Take disjunction of bits in vector, return vector of length 1.
void Z3_API Z3_ast_map_reset(Z3_context c, Z3_ast_map m)
Remove all keys from the given map.
void Z3_API Z3_solver_reset(Z3_context c, Z3_solver s)
Remove all assertions from the solver.
bool Z3_API Z3_is_algebraic_number(Z3_context c, Z3_ast a)
Return true if the given AST is a real algebraic number.
BitVecVal(val, bv, ctx=None)
_coerce_exprs(a, b, ctx=None)
_ctx_from_ast_args(*args)
_to_func_decl_ref(a, ctx)
_valid_accessor(acc)
Datatypes.
BitVec(name, bv, ctx=None)
DeclareSort(name, ctx=None)
RecAddDefinition(f, args, body)
_z3_check_cint_overflow(n, name)
TupleSort(name, sorts, ctx=None)
_coerce_expr_list(alist, ctx=None)
RealVector(prefix, sz, ctx=None)
BitVecs(names, bv, ctx=None)
BoolVector(prefix, sz, ctx=None)
FreshConst(sort, prefix="c")
EnumSort(name, values, ctx=None)
simplify(a, *arguments, **keywords)
Utils.
BV2Int(a, is_signed=False)
FreshInt(prefix="x", ctx=None)
_to_func_decl_array(args)
args2params(arguments, keywords, ctx=None)
Cond(p, t1, t2, ctx=None)
FreshReal(prefix="b", ctx=None)
_reduce(func, sequence, initial)
BVAddNoOverflow(a, b, signed)
FreshBool(prefix="b", ctx=None)
_ctx_from_ast_arg_list(args, default_ctx=None)
IntVector(prefix, sz, ctx=None)
RealVarVector(n, ctx=None)
DisjointSum(name, sorts, ctx=None)
Exists(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])
ForAll(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])
BVSubNoUnderflow(a, b, signed)
DatatypeSort(name, ctx=None)
BVMulNoOverflow(a, b, signed)
_mk_quantifier(is_forall, vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])