idp_engine.Expression¶
(They are monkey-patched by other modules)
- class ASTNode[source]
Bases:
object
superclass of all AST nodes
- check(condition, msg)[source]
raises an exception if condition is not True
- Parameters
condition (Bool) – condition to be satisfied
msg (str) – error message
- Raises
IDPZ3Error – when condition is not met
- dedup_nodes(kwargs, arg_name)[source]
pops arg_name from kwargs as a list of named items and returns a mapping from name to items
- Parameters
kwargs (Dict[str, ASTNode]) –
arg_name (str) – name of the kwargs argument, e.g. “interpretations”
- Returns
mapping from name to AST nodes
- Return type
Dict[str, ASTNode]
- Raises
AssertionError – in case of duplicate name
- class Annotations(parent, annotations)[source]
Bases:
idp_engine.Expression.ASTNode
- Parameters
annotations (List[str]) –
- __init__(parent, annotations)[source]
- Parameters
annotations (List[str]) –
- class Constructor(parent, name, args=None)[source]
Bases:
idp_engine.Expression.ASTNode
Constructor declaration
- Parameters
name (Union[UnappliedSymbol, str]) –
args (List[Accessor]) –
- name
name of the constructor
- Type
string
- sorts
types of the arguments of the constructor
- Type
List[Symbol]
- type
name of the type that contains this constructor
- Type
string
- arity
number of arguments of the constructor
- Type
Int
- tester
function to test if the constructor
- Type
SymbolDeclaration
- has been applied to some arguments
- Type
e.g., is_rgb
- symbol
only for Symbol constructors
- Type
Symbol
- __init__(parent, name, args=None)[source]
- Parameters
name (Union[idp_engine.Expression.UnappliedSymbol, str]) –
args (Optional[List[idp_engine.Expression.Accessor]]) –
- class Accessor(parent, type, accessor=None)[source]
Bases:
idp_engine.Expression.ASTNode
represents an accessor and a type
- Parameters
type (UnappliedSymbol) –
accessor (UnappliedSymbol) –
- accessor
name of accessor function
- Type
UnappliedSymbol, Optional
- type
name of the output type of the accessor
- Type
string
- decl
declaration of the accessor function
- Type
SymbolDeclaration
- __init__(parent, type, accessor=None)[source]
- Parameters
type (idp_engine.Expression.UnappliedSymbol) –
accessor (Optional[idp_engine.Expression.UnappliedSymbol]) –
- class Expression[source]
Bases:
idp_engine.Expression.ASTNode
The abstract class of AST nodes representing (sub-)expressions.
- code
Textual representation of the expression. Often used as a key.
It is generated from the sub-tree. Some tree transformations change it (e.g., instantiate), others don’t.
- Type
string
- sub_exprs
The children of the AST node.
The list may be reduced by simplification.
- Type
List[Expression]
- type
The name of the type of the expression, e.g.,
bool
.- Type
string
- co_constraint
A constraint attached to the node.
For example, the co_constraint of
square(length(top()))
issquare(length(top())) = length(top())*length(top()).
, assumingsquare
is appropriately defined.The co_constraint of a defined symbol applied to arguments is the instantiation of the definition for those arguments. This is useful for definitions over infinite domains, as well as to compute relevant questions.
- Type
Expression, optional
- simpler
A simpler, equivalent expression.
Equivalence is computed in the context of the theory and structure. Simplifying an expression is useful for efficiency and to compute relevant questions.
- Type
Expression, optional
- value
A rigid term equivalent to the expression, obtained by transformation.
Equivalence is computed in the context of the theory and structure.
- Type
Optional[Expression]
- annotations
The set of annotations given by the expert in the IDP-Z3 program.
annotations['reading']
is the annotation giving the intended meaning of the expression (in English).- Type
Dict[str, str]
- original
The original expression, before propagation and simplification.
- Type
Expression
- variables
The set of names of the variables in the expression.
- Type
Set(string)
- is_type_constraint_for
name of the symbol for which the expression is a type constraint
- Type
string
- __init__()[source]
- collect(questions, all_=True, co_constraints=True)[source]
collects the questions in self.
questions is an OrderedSet of Expression Questions are the terms and the simplest sub-formula that can be evaluated. collect uses the simplified version of the expression.
all_=False : ignore expanded formulas and AppliedSymbol interpreted in a structure co_constraints=False : ignore co_constraints
default implementation for UnappliedSymbol, AIfExpr, AUnary, Variable, Number_constant, Brackets
- Parameters
questions (idp_engine.utils.OrderedSet) –
all_ (bool) –
co_constraints (bool) –
- Return type
idp_engine.utils.OrderedSet
- collect_symbols(symbols=None, co_constraints=True)[source]
returns the list of symbol declarations in self, ignoring type constraints
- Parameters
symbols (Dict[str, SymbolDeclaration]) –
co_constraints (bool) –
- Return type
Dict[str, Declaration]
- collect_nested_symbols(symbols, is_nested)[source]
returns the set of symbol declarations that occur (in)directly under an aggregate or some nested term, where is_nested is flipped to True the moment we reach such an expression
returns {SymbolDeclaration}
- Parameters
symbols (Set[SymbolDeclaration]) –
is_nested (bool) –
- Return type
Set[SymbolDeclaration]
- generate_constructors(constructors)[source]
fills the list constructors with all constructors belonging to open types.
- Parameters
constructors (Dict[str, List[idp_engine.Expression.Constructor]]) –
- co_constraints(co_constraints)[source]
collects the constraints attached to AST nodes, e.g. instantiated definitions
- Parameters
co_constraints (idp_engine.utils.OrderedSet) –
- is_assignment()[source]
- Returns
True if self assigns a rigid term to a rigid function application
- Return type
bool
- update_exprs(new_exprs)
change sub_exprs and simplify, while keeping relevant info.
- substitute(e0, e1, assignments, tag=None)
recursively substitute e0 by e1 in self (e0 is not a Variable)
if tag is present, updates assignments with symbolic propagation of co-constraints.
implementation for everything but AppliedSymbol, UnappliedSymbol and Fresh_variable
- instantiate(e0, e1, problem=None)
Recursively substitute Variable in e0 by e1 in a copy of self. Update .variables.
- instantiate1(e0, e1, problem=None)
Recursively substitute Variable in e0 by e1 in self.
Interpret appliedSymbols immediately if grounded (and not occurring in head of definition). Update .variables.
- simplify_with(assignments)
simplify the expression using the assignments
- Parameters
self (idp_engine.Expression.Expression) –
assignments (Assignments) –
- Return type
idp_engine.Expression.Expression
- symbolic_propagate(assignments, tag, truth=true)
updates assignments with the consequences of self=truth.
The consequences are obtained by symbolic processing (no calls to Z3).
- Parameters
assignments (Assignments) – The set of assignments to update.
truth (Expression, optional) – The truth value of the expression self. Defaults to TRUE.
tag (Status) –
- propagate1(assignments, tag, truth)
returns the list of symbolic_propagate of self, ignoring value and simpler
- translate(problem, vars={})
Converts the syntax tree to a Z3 expression, using .value and .simpler if present
- Parameters
problem (Theory) – holds the context for the translation (e.g. a cache of translations).
vars (Dict[id, ExprRef], optional) – mapping from Variable’s id to Z3 translation. Filled in by AQuantifier. Defaults to {}.
- Returns
Z3 expression
- Return type
ExprRef
- as_set_condition()[source]
Returns an equivalent expression of the type “x in y”, or None
- Returns
meaning “expr is (not) in enumeration”
- Return type
Tuple[Optional[AppliedSymbol], Optional[bool], Optional[Enumeration]]
- split_equivalences()[source]
Returns an equivalent expression where equivalences are replaced by implications
- Returns
Expression
- Return type
idp_engine.Expression.Expression
- add_level_mapping(level_symbols, head, pos_justification, polarity, mode)[source]
- Returns an expression where level mapping atoms (e.g., lvl_p > lvl_q)
are added to atoms containing recursive symbols.
- Parameters
level_symbols (-) – the level mapping symbols as well as their corresponding recursive symbols
head (-) – head of the rule we are adding level mapping symbols to.
pos_justification (-) – whether we are adding symbols to the direct positive justification (e.g., head => body) or direct negative justification (e.g., body => head) part of the rule.
polarity (-) – whether the current expression occurs under negation.
mode (Semantics) –
- Return type
Expression
- annotate(voc, q_vars)
annotate tree after parsing
Resolve names and determine type as well as variables in the expression
- Parameters
voc (Vocabulary) – the vocabulary
q_vars (Dict[str, Variable]) – the quantifier variables that may appear in the expression
- Returns
an equivalent AST node, with updated type, .variables
- Return type
Expression
- annotate1()
annotations that are common to __init__ and make()
- interpret(problem)
uses information in the problem and its vocabulary to: - expand quantifiers in the expression - simplify the expression using known assignments and enumerations - instantiate definitions
- Parameters
problem (Theory) – the Theory to apply
- Returns
the resulting expression
- Return type
Expression
- class Symbol(parent, name)[source]
Bases:
idp_engine.Expression.Expression
Represents a Symbol. Handles synonyms.
- Parameters
name (str) –
- name
name of the symbol
- Type
string
- __init__(parent, name)[source]
- Parameters
name (str) –
- has_element(term, interpretations, extensions)[source]
Returns an expression that says whether term is in the type/predicate denoted by self.
- Parameters
term (Expression) – the argument to be checked
interpretations (Dict[str, SymbolInterpretation]) –
extensions (Dict[str, Extension]) –
- Returns
whether term is in the type denoted by self.
- Return type
Expression
- annotate(voc, q_vars)
annotate tree after parsing
Resolve names and determine type as well as variables in the expression
- Parameters
voc (Vocabulary) – the vocabulary
q_vars (Dict[str, Variable]) – the quantifier variables that may appear in the expression
- Returns
an equivalent AST node, with updated type, .variables
- Return type
Expression
- instantiate(e0, e1, problem=None)
Recursively substitute Variable in e0 by e1 in a copy of self. Update .variables.
- translate(problem, vars={})
Converts the syntax tree to a Z3 expression, using .value and .simpler if present
- Parameters
problem (Theory) – holds the context for the translation (e.g. a cache of translations).
vars (Dict[id, ExprRef], optional) – mapping from Variable’s id to Z3 translation. Filled in by AQuantifier. Defaults to {}.
- Returns
Z3 expression
- Return type
ExprRef
- class Type(parent, name, ins=None, out=None)[source]
Bases:
idp_engine.Expression.Symbol
ASTNode representing aType or Concept[aSignature], e.g., Concept[T*T->Bool]
Inherits from Symbol
- Parameters
name (Symbol) – name of the concept
ins (List[Symbol], Optional) – domain of the Concept signature, e.g., [T, T]
out (Symbol, Optional) – range of the Concept signature, e.g., Bool
- __init__(parent, name, ins=None, out=None)[source]
- Parameters
name (str) –
ins (Optional[List[idp_engine.Expression.Type]]) –
out (Optional[idp_engine.Expression.Type]) –
- extension(interpretations, extensions)
returns the extension of a Type, given some interpretations.
Normally, the extension is already in extensions. However, for Concept[T->T], an additional filtering is applied.
- Parameters
interpretations (Dict[str, SymbolInterpretation]) –
symbols (the known interpretations of types and) –
extensions (Dict[str, Tuple[Optional[List[List[idp_engine.Expression.Expression]]], Optional[Callable]]]) –
- Returns
a superset of the extension of self, and a function that, given arguments, returns an Expression that says whether the arguments are in the extension of self
- Return type
Extension
- has_element(term, interpretations, extensions)[source]
Returns an Expression that says whether term is in the type/predicate denoted by self.
- Parameters
term (Expression) – the argument to be checked
interpretations (Dict[str, SymbolInterpretation]) –
extensions (Dict[str, Extension]) –
- Returns
whether term term is in the type denoted by self.
- Return type
Expression
- annotate(voc, q_vars)
annotate tree after parsing
Resolve names and determine type as well as variables in the expression
- Parameters
voc (Vocabulary) – the vocabulary
q_vars (Dict[str, Variable]) – the quantifier variables that may appear in the expression
- Returns
an equivalent AST node, with updated type, .variables
- Return type
Expression
- class AIfExpr(parent, if_f, then_f, else_f)[source]
Bases:
idp_engine.Expression.Expression
- Parameters
if_f (Expression) –
then_f (Expression) –
else_f (Expression) –
- Return type
AIfExpr
- __init__(parent, if_f, then_f, else_f)[source]
- Parameters
if_f (idp_engine.Expression.Expression) –
then_f (idp_engine.Expression.Expression) –
else_f (idp_engine.Expression.Expression) –
- Return type
idp_engine.Expression.AIfExpr
- collect_nested_symbols(symbols, is_nested)[source]
returns the set of symbol declarations that occur (in)directly under an aggregate or some nested term, where is_nested is flipped to True the moment we reach such an expression
returns {SymbolDeclaration}
- annotate1()
annotations that are common to __init__ and make()
- translate1(problem, vars={})
Converts the syntax tree to a Z3 expression, ignoring .value and .simpler
- Parameters
problem (Theory) – holds the context for the translation (e.g. a cache of translations).
vars (Dict[id, ExprRef], optional) – mapping from Variable’s id to Z3 translation. Filled in by AQuantifier. Defaults to {}.
- Returns
Z3 expression
- Return type
ExprRef
- update_exprs(new_exprs)
change sub_exprs and simplify, while keeping relevant info.
- class Quantee(parent, vars, subtype=None, sort=None)[source]
Bases:
idp_engine.Expression.Expression
represents the description of quantification, e.g., x in T or (x,y) in P The Concept type may be qualified, e.g. Concept[Color->Bool]
- Parameters
vars (List[List[Variable]]) –
subtype (Type) –
sort (SymbolExpr) –
- vars
the (tuples of) variables being quantified
- Type
List[List[Variable]]
- subtype
a literal Type to quantify over, e.g., Color or Concept[Color->Bool].
- Type
Type, Optional
- sort
a dereferencing expression, e.g.,. $(i).
- Type
SymbolExpr, Optional
- sub_exprs
the (unqualified) type or predicate to quantify over,
- Type
List[SymbolExpr], Optional
- e.g., `[Color], [Concept] or [$
- Type
i
- arity
the length of the tuple of variables
- Type
int
- decl
the (unqualified) Declaration to quantify over, after resolution of $(i).
- Type
SymbolDeclaration, Optional
- e.g., the declaration of `Color`
- __init__(parent, vars, subtype=None, sort=None)[source]
- Parameters
vars (List[List[idp_engine.Expression.Variable]]) –
subtype (Optional[idp_engine.Expression.Type]) –
sort (Optional[idp_engine.Expression.SymbolExpr]) –
- update_exprs(new_exprs)
change sub_exprs and simplify, while keeping relevant info.
- class AQuantification(parent, annotations, q, quantees, f)[source]
Bases:
idp_engine.Expression.Expression
ASTNode representing a quantified formula
- Parameters
annotations (Dict[str, str]) –
The set of annotations given by the expert in the IDP-Z3 program.
annotations['reading']
is the annotation giving the intended meaning of the expression (in English).q (str) – either ‘∀’ or ‘∃’
quantees (List[Quantee]) – list of variable declarations
f (Expression) – the formula being quantified
- __init__(parent, annotations, q, quantees, f)[source]
- classmethod make(q, quantees, f, annotations=None)[source]
make and annotate a quantified formula
- Parameters
q (str) –
quantees (List[idp_engine.Expression.Quantee]) –
f (idp_engine.Expression.Expression) –
- Return type
AQuantification
- collect(questions, all_=True, co_constraints=True)[source]
collects the questions in self.
questions is an OrderedSet of Expression Questions are the terms and the simplest sub-formula that can be evaluated. collect uses the simplified version of the expression.
all_=False : ignore expanded formulas and AppliedSymbol interpreted in a structure co_constraints=False : ignore co_constraints
default implementation for UnappliedSymbol, AIfExpr, AUnary, Variable, Number_constant, Brackets
- collect_symbols(symbols=None, co_constraints=True)[source]
returns the list of symbol declarations in self, ignoring type constraints
- annotate(voc, q_vars)
annotate tree after parsing
Resolve names and determine type as well as variables in the expression
- Parameters
voc (Vocabulary) – the vocabulary
q_vars (Dict[str, Variable]) – the quantifier variables that may appear in the expression
- Returns
an equivalent AST node, with updated type, .variables
- Return type
Expression
- annotate1()
annotations that are common to __init__ and make()
- instantiate1(e0, e1, problem=None)
Recursively substitute Variable in e0 by e1 in self.
Interpret appliedSymbols immediately if grounded (and not occurring in head of definition). Update .variables.
- interpret(problem)
apply information in the problem and its vocabulary
- Parameters
problem (Theory) – the problem to be applied
- Returns
the expanded quantifier expression
- Return type
Expression
- symbolic_propagate(assignments, tag, truth=true)
updates assignments with the consequences of self=truth.
The consequences are obtained by symbolic processing (no calls to Z3).
- Parameters
assignments (Assignments) – The set of assignments to update.
truth (Expression, optional) – The truth value of the expression self. Defaults to TRUE.
- update_exprs(new_exprs)
change sub_exprs and simplify, while keeping relevant info.
- class Operator(parent, operator, sub_exprs, annotations=None)[source]
Bases:
idp_engine.Expression.Expression
- __init__(parent, operator, sub_exprs, annotations=None)[source]
- classmethod make(ops, operands, annotations=None)[source]
creates a BinaryOp beware: cls must be specific for ops !
- Parameters
ops (Union[str, List[str]]) –
operands (List[idp_engine.Expression.Expression]) –
- Return type
Operator
- collect(questions, all_=True, co_constraints=True)[source]
collects the questions in self.
questions is an OrderedSet of Expression Questions are the terms and the simplest sub-formula that can be evaluated. collect uses the simplified version of the expression.
all_=False : ignore expanded formulas and AppliedSymbol interpreted in a structure co_constraints=False : ignore co_constraints
default implementation for UnappliedSymbol, AIfExpr, AUnary, Variable, Number_constant, Brackets
- collect_nested_symbols(symbols, is_nested)[source]
returns the set of symbol declarations that occur (in)directly under an aggregate or some nested term, where is_nested is flipped to True the moment we reach such an expression
returns {SymbolDeclaration}
- annotate1()
annotations that are common to __init__ and make()
- class AImplication(parent, operator, sub_exprs, annotations=None)[source]
Bases:
idp_engine.Expression.Operator
- add_level_mapping(level_symbols, head, pos_justification, polarity, mode)[source]
- Returns an expression where level mapping atoms (e.g., lvl_p > lvl_q)
are added to atoms containing recursive symbols.
- Parameters
level_symbols (-) – the level mapping symbols as well as their corresponding recursive symbols
head (-) – head of the rule we are adding level mapping symbols to.
pos_justification (-) – whether we are adding symbols to the direct positive justification (e.g., head => body) or direct negative justification (e.g., body => head) part of the rule.
polarity (-) – whether the current expression occurs under negation.
- annotate1()
annotations that are common to __init__ and make()
- update_exprs(new_exprs)
change sub_exprs and simplify, while keeping relevant info.
- class AEquivalence(parent, operator, sub_exprs, annotations=None)[source]
Bases:
idp_engine.Expression.Operator
- split_equivalences()[source]
Returns an equivalent expression where equivalences are replaced by implications
- Returns
Expression
- annotate1()
annotations that are common to __init__ and make()
- update_exprs(new_exprs)
change sub_exprs and simplify, while keeping relevant info.
- class ARImplication(parent, operator, sub_exprs, annotations=None)[source]
Bases:
idp_engine.Expression.Operator
- add_level_mapping(level_symbols, head, pos_justification, polarity, mode)[source]
- Returns an expression where level mapping atoms (e.g., lvl_p > lvl_q)
are added to atoms containing recursive symbols.
- Parameters
level_symbols (-) – the level mapping symbols as well as their corresponding recursive symbols
head (-) – head of the rule we are adding level mapping symbols to.
pos_justification (-) – whether we are adding symbols to the direct positive justification (e.g., head => body) or direct negative justification (e.g., body => head) part of the rule.
polarity (-) – whether the current expression occurs under negation.
- annotate(voc, q_vars)
annotate tree after parsing
Resolve names and determine type as well as variables in the expression
- Parameters
voc (Vocabulary) – the vocabulary
q_vars (Dict[str, Variable]) – the quantifier variables that may appear in the expression
- Returns
an equivalent AST node, with updated type, .variables
- Return type
Expression
- class ADisjunction(parent, operator, sub_exprs, annotations=None)[source]
Bases:
idp_engine.Expression.Operator
- propagate1(assignments, tag, truth=true)
returns the list of symbolic_propagate of self, ignoring value and simpler
- update_exprs(new_exprs)
change sub_exprs and simplify, while keeping relevant info.
- class AConjunction(parent, operator, sub_exprs, annotations=None)[source]
Bases:
idp_engine.Expression.Operator
- propagate1(assignments, tag, truth=true)
returns the list of symbolic_propagate of self, ignoring value and simpler
- update_exprs(new_exprs)
change sub_exprs and simplify, while keeping relevant info.
- class AComparison(parent, operator, sub_exprs, annotations=None)[source]
Bases:
idp_engine.Expression.Operator
- is_assignment()[source]
- Returns
True if self assigns a rigid term to a rigid function application
- Return type
bool
- annotate(voc, q_vars)
annotate tree after parsing
Resolve names and determine type as well as variables in the expression
- Parameters
voc (Vocabulary) – the vocabulary
q_vars (Dict[str, Variable]) – the quantifier variables that may appear in the expression
- Returns
an equivalent AST node, with updated type, .variables
- Return type
Expression
- as_set_condition()
Returns an equivalent expression of the type “x in y”, or None
- Returns
meaning “expr is (not) in enumeration”
- Return type
Tuple[Optional[AppliedSymbol], Optional[bool], Optional[Enumeration]]
- propagate1(assignments, tag, truth=true)
returns the list of symbolic_propagate of self, ignoring value and simpler
- update_exprs(new_exprs)
change sub_exprs and simplify, while keeping relevant info.
- class ASumMinus(parent, operator, sub_exprs, annotations=None)[source]
Bases:
idp_engine.Expression.Operator
- update_exprs(new_exprs)
change sub_exprs and simplify, while keeping relevant info.
- class AMultDiv(parent, operator, sub_exprs, annotations=None)[source]
Bases:
idp_engine.Expression.Operator
- update_exprs(new_exprs)
change sub_exprs and simplify, while keeping relevant info.
- class APower(parent, operator, sub_exprs, annotations=None)[source]
Bases:
idp_engine.Expression.Operator
- update_exprs(new_exprs)
change sub_exprs and simplify, while keeping relevant info.
- class AUnary(parent, operators, f)[source]
Bases:
idp_engine.Expression.Expression
- Parameters
operators (List[str]) –
f (Expression) –
- __init__(parent, operators, f)[source]
- Parameters
operators (List[str]) –
f (idp_engine.Expression.Expression) –
- add_level_mapping(level_symbols, head, pos_justification, polarity, mode)[source]
- Returns an expression where level mapping atoms (e.g., lvl_p > lvl_q)
are added to atoms containing recursive symbols.
- Parameters
level_symbols (-) – the level mapping symbols as well as their corresponding recursive symbols
head (-) – head of the rule we are adding level mapping symbols to.
pos_justification (-) – whether we are adding symbols to the direct positive justification (e.g., head => body) or direct negative justification (e.g., body => head) part of the rule.
polarity (-) – whether the current expression occurs under negation.
- annotate1()
annotations that are common to __init__ and make()
- as_set_condition()
Returns an equivalent expression of the type “x in y”, or None
- Returns
meaning “expr is (not) in enumeration”
- Return type
Tuple[Optional[AppliedSymbol], Optional[bool], Optional[Enumeration]]
- propagate1(assignments, tag, truth=true)
returns the list of symbolic_propagate of self, ignoring value and simpler
- update_exprs(new_exprs)
change sub_exprs and simplify, while keeping relevant info.
- class AAggregate(parent, aggtype, quantees, f)[source]
Bases:
idp_engine.Expression.Expression
- Parameters
aggtype (str) –
quantees (List[Quantee]) –
f (Expression) –
- __init__(parent, aggtype, quantees, f)[source]
- Parameters
aggtype (str) –
quantees (List[idp_engine.Expression.Quantee]) –
f (idp_engine.Expression.Expression) –
- collect(questions, all_=True, co_constraints=True)[source]
collects the questions in self.
questions is an OrderedSet of Expression Questions are the terms and the simplest sub-formula that can be evaluated. collect uses the simplified version of the expression.
all_=False : ignore expanded formulas and AppliedSymbol interpreted in a structure co_constraints=False : ignore co_constraints
default implementation for UnappliedSymbol, AIfExpr, AUnary, Variable, Number_constant, Brackets
- collect_symbols(symbols=None, co_constraints=True)[source]
returns the list of symbol declarations in self, ignoring type constraints
- collect_nested_symbols(symbols, is_nested)[source]
returns the set of symbol declarations that occur (in)directly under an aggregate or some nested term, where is_nested is flipped to True the moment we reach such an expression
returns {SymbolDeclaration}
- annotate(voc, q_vars)
annotate tree after parsing
Resolve names and determine type as well as variables in the expression
- Parameters
voc (Vocabulary) – the vocabulary
q_vars (Dict[str, Variable]) – the quantifier variables that may appear in the expression
- Returns
an equivalent AST node, with updated type, .variables
- Return type
Expression
- annotate1()
annotations that are common to __init__ and make()
- instantiate1(e0, e1, problem=None)
Recursively substitute Variable in e0 by e1 in self.
Interpret appliedSymbols immediately if grounded (and not occurring in head of definition). Update .variables.
- interpret(problem)
uses information in the problem and its vocabulary to: - expand quantifiers in the expression - simplify the expression using known assignments and enumerations - instantiate definitions
- Parameters
problem (Theory) – the Theory to apply
- Returns
the resulting expression
- Return type
Expression
- update_exprs(new_exprs)
change sub_exprs and simplify, while keeping relevant info.
- class AppliedSymbol(parent, symbol, sub_exprs, annotations=None, is_enumerated='', is_enumeration='', in_enumeration='')[source]
Bases:
idp_engine.Expression.Expression
Represents a symbol applied to arguments
- Parameters
symbol (SymbolExpr) – the symbol to be applied to arguments
is_enumerated (string) – ‘’ or ‘is enumerated’ or ‘is not enumerated’
is_enumeration (string) – ‘’ or ‘in’ or ‘not in’
in_enumeration (Enumeration) – the enumeration following ‘in’
decl (Declaration) – the declaration of the symbol, if known
in_head (Bool) – True if the AppliedSymbol occurs in the head of a rule
- __init__(parent, symbol, sub_exprs, annotations=None, is_enumerated='', is_enumeration='', in_enumeration='')[source]
- collect(questions, all_=True, co_constraints=True)[source]
collects the questions in self.
questions is an OrderedSet of Expression Questions are the terms and the simplest sub-formula that can be evaluated. collect uses the simplified version of the expression.
all_=False : ignore expanded formulas and AppliedSymbol interpreted in a structure co_constraints=False : ignore co_constraints
default implementation for UnappliedSymbol, AIfExpr, AUnary, Variable, Number_constant, Brackets
- collect_symbols(symbols=None, co_constraints=True)[source]
returns the list of symbol declarations in self, ignoring type constraints
- collect_nested_symbols(symbols, is_nested)[source]
returns the set of symbol declarations that occur (in)directly under an aggregate or some nested term, where is_nested is flipped to True the moment we reach such an expression
returns {SymbolDeclaration}
- generate_constructors(constructors)[source]
fills the list constructors with all constructors belonging to open types.
- Parameters
constructors (dict) –
- add_level_mapping(level_symbols, head, pos_justification, polarity, mode)[source]
- Returns an expression where level mapping atoms (e.g., lvl_p > lvl_q)
are added to atoms containing recursive symbols.
- Parameters
level_symbols (-) – the level mapping symbols as well as their corresponding recursive symbols
head (-) – head of the rule we are adding level mapping symbols to.
pos_justification (-) – whether we are adding symbols to the direct positive justification (e.g., head => body) or direct negative justification (e.g., body => head) part of the rule.
polarity (-) – whether the current expression occurs under negation.
- annotate(voc, q_vars)
annotate tree after parsing
Resolve names and determine type as well as variables in the expression
- Parameters
voc (Vocabulary) – the vocabulary
q_vars (Dict[str, Variable]) – the quantifier variables that may appear in the expression
- Returns
an equivalent AST node, with updated type, .variables
- Return type
Expression
- annotate1()
annotations that are common to __init__ and make()
- as_set_condition()
Returns an equivalent expression of the type “x in y”, or None
- Returns
meaning “expr is (not) in enumeration”
- Return type
Tuple[Optional[AppliedSymbol], Optional[bool], Optional[Enumeration]]
- instantiate1(e0, e1, problem=None)
Recursively substitute Variable in e0 by e1 in self.
Interpret appliedSymbols immediately if grounded (and not occurring in head of definition). Update .variables.
- interpret(problem)
uses information in the problem and its vocabulary to: - expand quantifiers in the expression - simplify the expression using known assignments and enumerations - instantiate definitions
- Parameters
problem (Theory) – the Theory to apply
- Returns
the resulting expression
- Return type
Expression
- substitute(e0, e1, assignments, tag=None)
recursively substitute e0 by e1 in self
- update_exprs(new_exprs)
change sub_exprs and simplify, while keeping relevant info.
- class SymbolExpr(parent, s, eval='')[source]
Bases:
idp_engine.Expression.Expression
- __init__(parent, s, eval='')[source]
- annotate(voc, q_vars)
annotate tree after parsing
Resolve names and determine type as well as variables in the expression
- Parameters
voc (Vocabulary) – the vocabulary
q_vars (Dict[str, Variable]) – the quantifier variables that may appear in the expression
- Returns
an equivalent AST node, with updated type, .variables
- Return type
Expression
- update_exprs(new_exprs)
change sub_exprs and simplify, while keeping relevant info.
- class UnappliedSymbol(parent, s)[source]
Bases:
idp_engine.Expression.Expression
The result of parsing a symbol not applied to arguments. Can be a constructor or a quantified variable.
Variables are converted to Variable() by annotate().
- __init__(parent, s)[source]
- classmethod construct(constructor)[source]
Create an UnappliedSymbol from a constructor
- Parameters
constructor (idp_engine.Expression.Constructor) –
- annotate(voc, q_vars)
annotate tree after parsing
Resolve names and determine type as well as variables in the expression
- Parameters
voc (Vocabulary) – the vocabulary
q_vars (Dict[str, Variable]) – the quantifier variables that may appear in the expression
- Returns
an equivalent AST node, with updated type, .variables
- Return type
Expression
- class Variable(parent, name, sort=None)[source]
Bases:
idp_engine.Expression.Expression
AST node for a variable in a quantification or aggregate
- Parameters
name (str) – name of the variable
sort (Optional[Union[Type, Symbol]]) – sort of the variable, if known
- __init__(parent, name, sort=None)[source]
- Parameters
name (str) –
sort (Optional[Union[idp_engine.Expression.Type, idp_engine.Expression.Symbol]]) –
- annotate1()[source]
annotations that are common to __init__ and make()
- annotate(voc, q_vars)
annotate tree after parsing
Resolve names and determine type as well as variables in the expression
- Parameters
voc (Vocabulary) – the vocabulary
q_vars (Dict[str, Variable]) – the quantifier variables that may appear in the expression
- Returns
an equivalent AST node, with updated type, .variables
- Return type
Expression
- instantiate1(e0, e1, problem=None)
Recursively substitute Variable in e0 by e1 in self.
Interpret appliedSymbols immediately if grounded (and not occurring in head of definition). Update .variables.
- interpret(problem)
uses information in the problem and its vocabulary to: - expand quantifiers in the expression - simplify the expression using known assignments and enumerations - instantiate definitions
- Parameters
problem (Theory) – the Theory to apply
- Returns
the resulting expression
- Return type
Expression
- substitute(e0, e1, assignments, tag=None)
recursively substitute e0 by e1 in self (e0 is not a Variable)
if tag is present, updates assignments with symbolic propagation of co-constraints.
implementation for everything but AppliedSymbol, UnappliedSymbol and Fresh_variable
- translate(problem, vars={})
Converts the syntax tree to a Z3 expression, using .value and .simpler if present
- Parameters
problem (Theory) – holds the context for the translation (e.g. a cache of translations).
vars (Dict[id, ExprRef], optional) – mapping from Variable’s id to Z3 translation. Filled in by AQuantifier. Defaults to {}.
- Returns
Z3 expression
- Return type
ExprRef
- class Number(**kwargs)[source]
Bases:
idp_engine.Expression.Expression
- __init__(**kwargs)[source]
- real()[source]
converts the INT number to REAL
- annotate(voc, q_vars)
annotate tree after parsing
Resolve names and determine type as well as variables in the expression
- Parameters
voc (Vocabulary) – the vocabulary
q_vars (Dict[str, Variable]) – the quantifier variables that may appear in the expression
- Returns
an equivalent AST node, with updated type, .variables
- Return type
Expression
- translate(problem, vars={})
Converts the syntax tree to a Z3 expression, using .value and .simpler if present
- Parameters
problem (Theory) – holds the context for the translation (e.g. a cache of translations).
vars (Dict[id, ExprRef], optional) – mapping from Variable’s id to Z3 translation. Filled in by AQuantifier. Defaults to {}.
- Returns
Z3 expression
- Return type
ExprRef
- class Date(**kwargs)[source]
Bases:
idp_engine.Expression.Expression
- __init__(**kwargs)[source]
- translate(problem, vars={})
Converts the syntax tree to a Z3 expression, using .value and .simpler if present
- Parameters
problem (Theory) – holds the context for the translation (e.g. a cache of translations).
vars (Dict[id, ExprRef], optional) – mapping from Variable’s id to Z3 translation. Filled in by AQuantifier. Defaults to {}.
- Returns
Z3 expression
- Return type
ExprRef
- class Brackets(**kwargs)[source]
Bases:
idp_engine.Expression.Expression
- annotate1()
annotations that are common to __init__ and make()
- symbolic_propagate(assignments, tag, truth=true)
updates assignments with the consequences of self=truth.
The consequences are obtained by symbolic processing (no calls to Z3).
- Parameters
assignments (Assignments) – The set of assignments to update.
truth (Expression, optional) – The truth value of the expression self. Defaults to TRUE.
- update_exprs(new_exprs)
change sub_exprs and simplify, while keeping relevant info.
- __init__(**kwargs)[source]