Z3
 
Loading...
Searching...
No Matches
QuantifierRef Class Reference

Quantifiers. More...

+ Inheritance diagram for QuantifierRef:

Public Member Functions

 as_ast (self)
 
 get_id (self)
 
 sort (self)
 
 is_forall (self)
 
 is_exists (self)
 
 is_lambda (self)
 
 __getitem__ (self, arg)
 
 weight (self)
 
 skolem_id (self)
 
 qid (self)
 
 num_patterns (self)
 
 pattern (self, idx)
 
 num_no_patterns (self)
 
 no_pattern (self, idx)
 
 body (self)
 
 num_vars (self)
 
 var_name (self, idx)
 
 var_sort (self, idx)
 
 children (self)
 
- Public Member Functions inherited from BoolRef
 __add__ (self, other)
 
 __radd__ (self, other)
 
 __rmul__ (self, other)
 
 __mul__ (self, other)
 
 __and__ (self, other)
 
 __or__ (self, other)
 
 __xor__ (self, other)
 
 __invert__ (self)
 
 py_value (self)
 
- Public Member Functions inherited from ExprRef
 sort_kind (self)
 
 __eq__ (self, other)
 
 __hash__ (self)
 
 __ne__ (self, other)
 
 params (self)
 
 decl (self)
 
 kind (self)
 
 num_args (self)
 
 arg (self, idx)
 
 from_string (self, s)
 
 serialize (self)
 
- Public Member Functions inherited from AstRef
 __init__ (self, ast, ctx=None)
 
 __del__ (self)
 
 __deepcopy__ (self, memo={})
 
 __str__ (self)
 
 __repr__ (self)
 
 __eq__ (self, other)
 
 __hash__ (self)
 
 __nonzero__ (self)
 
 __bool__ (self)
 
 sexpr (self)
 
 ctx_ref (self)
 
 eq (self, other)
 
 translate (self, target)
 
 __copy__ (self)
 
 hash (self)
 
- Public Member Functions inherited from Z3PPObject
 use_pp (self)
 

Additional Inherited Members

- Data Fields inherited from AstRef
 ast = ast
 
 ctx = _get_ctx(ctx)
 
- Protected Member Functions inherited from Z3PPObject
 _repr_html_ (self)
 

Detailed Description

Quantifiers.

Universally and Existentially quantified formulas.

Definition at line 2059 of file z3py.py.

Member Function Documentation

◆ __getitem__()

__getitem__ ( self,
arg )
Return the Z3 expression `self[arg]`.

Definition at line 2116 of file z3py.py.

2116 def __getitem__(self, arg):
2117 """Return the Z3 expression `self[arg]`.
2118 """
2119 if z3_debug():
2120 _z3_assert(self.is_lambda(), "quantifier should be a lambda expression")
2121 return _array_select(self, arg)
2122

◆ as_ast()

as_ast ( self)
Return a pointer to the corresponding C Z3_ast object.

Reimplemented from ExprRef.

Definition at line 2062 of file z3py.py.

2062 def as_ast(self):
2063 return self.ast
2064

◆ body()

body ( self)
Return the expression being quantified.

>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) == 0)
>>> q.body()
f(Var(0)) == 0

Definition at line 2187 of file z3py.py.

2187 def body(self):
2188 """Return the expression being quantified.
2189
2190 >>> f = Function('f', IntSort(), IntSort())
2191 >>> x = Int('x')
2192 >>> q = ForAll(x, f(x) == 0)
2193 >>> q.body()
2194 f(Var(0)) == 0
2195 """
2196 return _to_expr_ref(Z3_get_quantifier_body(self.ctx_ref(), self.ast), self.ctx)
2197
Z3_ast Z3_API Z3_get_quantifier_body(Z3_context c, Z3_ast a)
Return body of quantifier.

Referenced by children().

◆ children()

children ( self)
Return a list containing a single element self.body()

>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) == 0)
>>> q.children()
[f(Var(0)) == 0]

Reimplemented from ExprRef.

Definition at line 2242 of file z3py.py.

2242 def children(self):
2243 """Return a list containing a single element self.body()
2244
2245 >>> f = Function('f', IntSort(), IntSort())
2246 >>> x = Int('x')
2247 >>> q = ForAll(x, f(x) == 0)
2248 >>> q.children()
2249 [f(Var(0)) == 0]
2250 """
2251 return [self.body()]
2252
2253

◆ get_id()

get_id ( self)
Return unique identifier for object. It can be used for hash-tables and maps.

Reimplemented from ExprRef.

Definition at line 2065 of file z3py.py.

2065 def get_id(self):
2066 return Z3_get_ast_id(self.ctx_ref(), self.as_ast())
2067
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....

◆ is_exists()

is_exists ( self)
Return `True` if `self` is an existential quantifier.

>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) == 0)
>>> q.is_exists()
False
>>> q = Exists(x, f(x) != 0)
>>> q.is_exists()
True

Definition at line 2088 of file z3py.py.

2088 def is_exists(self):
2089 """Return `True` if `self` is an existential quantifier.
2090
2091 >>> f = Function('f', IntSort(), IntSort())
2092 >>> x = Int('x')
2093 >>> q = ForAll(x, f(x) == 0)
2094 >>> q.is_exists()
2095 False
2096 >>> q = Exists(x, f(x) != 0)
2097 >>> q.is_exists()
2098 True
2099 """
2100 return Z3_is_quantifier_exists(self.ctx_ref(), self.ast)
2101
bool Z3_API Z3_is_quantifier_exists(Z3_context c, Z3_ast a)
Determine if ast is an existential quantifier.

◆ is_forall()

is_forall ( self)
Return `True` if `self` is a universal quantifier.

>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) == 0)
>>> q.is_forall()
True
>>> q = Exists(x, f(x) != 0)
>>> q.is_forall()
False

Definition at line 2074 of file z3py.py.

2074 def is_forall(self):
2075 """Return `True` if `self` is a universal quantifier.
2076
2077 >>> f = Function('f', IntSort(), IntSort())
2078 >>> x = Int('x')
2079 >>> q = ForAll(x, f(x) == 0)
2080 >>> q.is_forall()
2081 True
2082 >>> q = Exists(x, f(x) != 0)
2083 >>> q.is_forall()
2084 False
2085 """
2086 return Z3_is_quantifier_forall(self.ctx_ref(), self.ast)
2087
bool Z3_API Z3_is_quantifier_forall(Z3_context c, Z3_ast a)
Determine if an ast is a universal quantifier.

◆ is_lambda()

is_lambda ( self)
Return `True` if `self` is a lambda expression.

>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> q = Lambda(x, f(x))
>>> q.is_lambda()
True
>>> q = Exists(x, f(x) != 0)
>>> q.is_lambda()
False

Definition at line 2102 of file z3py.py.

2102 def is_lambda(self):
2103 """Return `True` if `self` is a lambda expression.
2104
2105 >>> f = Function('f', IntSort(), IntSort())
2106 >>> x = Int('x')
2107 >>> q = Lambda(x, f(x))
2108 >>> q.is_lambda()
2109 True
2110 >>> q = Exists(x, f(x) != 0)
2111 >>> q.is_lambda()
2112 False
2113 """
2114 return Z3_is_lambda(self.ctx_ref(), self.ast)
2115
bool Z3_API Z3_is_lambda(Z3_context c, Z3_ast a)
Determine if ast is a lambda expression.

Referenced by __getitem__(), and sort().

◆ no_pattern()

no_pattern ( self,
idx )
Return a no-pattern.

Definition at line 2181 of file z3py.py.

2181 def no_pattern(self, idx):
2182 """Return a no-pattern."""
2183 if z3_debug():
2184 _z3_assert(idx < self.num_no_patterns(), "Invalid no-pattern idx")
2185 return _to_expr_ref(Z3_get_quantifier_no_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
2186
Z3_ast Z3_API Z3_get_quantifier_no_pattern_ast(Z3_context c, Z3_ast a, unsigned i)
Return i'th no_pattern.

◆ num_no_patterns()

num_no_patterns ( self)
Return the number of no-patterns.

Definition at line 2177 of file z3py.py.

2177 def num_no_patterns(self):
2178 """Return the number of no-patterns."""
2179 return Z3_get_quantifier_num_no_patterns(self.ctx_ref(), self.ast)
2180
unsigned Z3_API Z3_get_quantifier_num_no_patterns(Z3_context c, Z3_ast a)
Return number of no_patterns used in quantifier.

Referenced by no_pattern().

◆ num_patterns()

num_patterns ( self)
Return the number of patterns (i.e., quantifier instantiation hints) in `self`.

>>> f = Function('f', IntSort(), IntSort())
>>> g = Function('g', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
>>> q.num_patterns()
2

Definition at line 2147 of file z3py.py.

2147 def num_patterns(self):
2148 """Return the number of patterns (i.e., quantifier instantiation hints) in `self`.
2149
2150 >>> f = Function('f', IntSort(), IntSort())
2151 >>> g = Function('g', IntSort(), IntSort())
2152 >>> x = Int('x')
2153 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2154 >>> q.num_patterns()
2155 2
2156 """
2157 return int(Z3_get_quantifier_num_patterns(self.ctx_ref(), self.ast))
2158
unsigned Z3_API Z3_get_quantifier_num_patterns(Z3_context c, Z3_ast a)
Return number of patterns used in quantifier.

Referenced by pattern().

◆ num_vars()

num_vars ( self)
Return the number of variables bounded by this quantifier.

>>> f = Function('f', IntSort(), IntSort(), IntSort())
>>> x = Int('x')
>>> y = Int('y')
>>> q = ForAll([x, y], f(x, y) >= x)
>>> q.num_vars()
2

Definition at line 2198 of file z3py.py.

2198 def num_vars(self):
2199 """Return the number of variables bounded by this quantifier.
2200
2201 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2202 >>> x = Int('x')
2203 >>> y = Int('y')
2204 >>> q = ForAll([x, y], f(x, y) >= x)
2205 >>> q.num_vars()
2206 2
2207 """
2208 return int(Z3_get_quantifier_num_bound(self.ctx_ref(), self.ast))
2209
unsigned Z3_API Z3_get_quantifier_num_bound(Z3_context c, Z3_ast a)
Return number of bound variables of quantifier.

Referenced by var_name(), and var_sort().

◆ pattern()

pattern ( self,
idx )
Return a pattern (i.e., quantifier instantiation hints) in `self`.

>>> f = Function('f', IntSort(), IntSort())
>>> g = Function('g', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
>>> q.num_patterns()
2
>>> q.pattern(0)
f(Var(0))
>>> q.pattern(1)
g(Var(0))

Definition at line 2159 of file z3py.py.

2159 def pattern(self, idx):
2160 """Return a pattern (i.e., quantifier instantiation hints) in `self`.
2161
2162 >>> f = Function('f', IntSort(), IntSort())
2163 >>> g = Function('g', IntSort(), IntSort())
2164 >>> x = Int('x')
2165 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2166 >>> q.num_patterns()
2167 2
2168 >>> q.pattern(0)
2169 f(Var(0))
2170 >>> q.pattern(1)
2171 g(Var(0))
2172 """
2173 if z3_debug():
2174 _z3_assert(idx < self.num_patterns(), "Invalid pattern idx")
2175 return PatternRef(Z3_get_quantifier_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
2176
Z3_pattern Z3_API Z3_get_quantifier_pattern_ast(Z3_context c, Z3_ast a, unsigned i)
Return i'th pattern.

◆ qid()

qid ( self)
Return the quantifier id of `self`.

Definition at line 2142 of file z3py.py.

2142 def qid(self):
2143 """Return the quantifier id of `self`.
2144 """
2145 return _symbol2py(self.ctx, Z3_get_quantifier_id(self.ctx_ref(), self.ast))
2146
Z3_symbol Z3_API Z3_get_quantifier_id(Z3_context c, Z3_ast a)
Obtain id of quantifier.

◆ skolem_id()

skolem_id ( self)
Return the skolem id of `self`.

Definition at line 2137 of file z3py.py.

2137 def skolem_id(self):
2138 """Return the skolem id of `self`.
2139 """
2140 return _symbol2py(self.ctx, Z3_get_quantifier_skolem_id(self.ctx_ref(), self.ast))
2141
Z3_symbol Z3_API Z3_get_quantifier_skolem_id(Z3_context c, Z3_ast a)
Obtain skolem id of quantifier.

◆ sort()

sort ( self)
Return the Boolean sort or sort of Lambda.

Reimplemented from BoolRef.

Definition at line 2068 of file z3py.py.

2068 def sort(self):
2069 """Return the Boolean sort or sort of Lambda."""
2070 if self.is_lambda():
2071 return _sort(self.ctx, self.as_ast())
2072 return BoolSort(self.ctx)
2073

◆ var_name()

var_name ( self,
idx )
Return a string representing a name used when displaying the quantifier.

>>> f = Function('f', IntSort(), IntSort(), IntSort())
>>> x = Int('x')
>>> y = Int('y')
>>> q = ForAll([x, y], f(x, y) >= x)
>>> q.var_name(0)
'x'
>>> q.var_name(1)
'y'

Definition at line 2210 of file z3py.py.

2210 def var_name(self, idx):
2211 """Return a string representing a name used when displaying the quantifier.
2212
2213 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2214 >>> x = Int('x')
2215 >>> y = Int('y')
2216 >>> q = ForAll([x, y], f(x, y) >= x)
2217 >>> q.var_name(0)
2218 'x'
2219 >>> q.var_name(1)
2220 'y'
2221 """
2222 if z3_debug():
2223 _z3_assert(idx < self.num_vars(), "Invalid variable idx")
2224 return _symbol2py(self.ctx, Z3_get_quantifier_bound_name(self.ctx_ref(), self.ast, idx))
2225
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.

◆ var_sort()

var_sort ( self,
idx )
Return the sort of a bound variable.

>>> f = Function('f', IntSort(), RealSort(), IntSort())
>>> x = Int('x')
>>> y = Real('y')
>>> q = ForAll([x, y], f(x, y) >= x)
>>> q.var_sort(0)
Int
>>> q.var_sort(1)
Real

Definition at line 2226 of file z3py.py.

2226 def var_sort(self, idx):
2227 """Return the sort of a bound variable.
2228
2229 >>> f = Function('f', IntSort(), RealSort(), IntSort())
2230 >>> x = Int('x')
2231 >>> y = Real('y')
2232 >>> q = ForAll([x, y], f(x, y) >= x)
2233 >>> q.var_sort(0)
2234 Int
2235 >>> q.var_sort(1)
2236 Real
2237 """
2238 if z3_debug():
2239 _z3_assert(idx < self.num_vars(), "Invalid variable idx")
2240 return _to_sort_ref(Z3_get_quantifier_bound_sort(self.ctx_ref(), self.ast, idx), self.ctx)
2241
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.

◆ weight()

weight ( self)
Return the weight annotation of `self`.

>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) == 0)
>>> q.weight()
1
>>> q = ForAll(x, f(x) == 0, weight=10)
>>> q.weight()
10

Definition at line 2123 of file z3py.py.

2123 def weight(self):
2124 """Return the weight annotation of `self`.
2125
2126 >>> f = Function('f', IntSort(), IntSort())
2127 >>> x = Int('x')
2128 >>> q = ForAll(x, f(x) == 0)
2129 >>> q.weight()
2130 1
2131 >>> q = ForAll(x, f(x) == 0, weight=10)
2132 >>> q.weight()
2133 10
2134 """
2135 return int(Z3_get_quantifier_weight(self.ctx_ref(), self.ast))
2136
unsigned Z3_API Z3_get_quantifier_weight(Z3_context c, Z3_ast a)
Obtain weight of quantifier.