idp_engine.Expression

(They are monkey-patched by other modules)

class idp_engine.Expression.ASTNode

Bases: object

superclass of all AST nodes

check(condition, msg)

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)

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 idp_engine.Expression.Expression

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())) is square(length(top())) = length(top())*length(top())., assuming square 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 source code.

annotations['reading'] is the annotation giving the intended meaning of the expression (in English).

Type

Dict

original

The original expression, before propagation and simplification.

Type

Expression

fresh_vars

The set of names of the variables in the expression.

Type

Set(string)

copy()

create a deep copy (except for rigid terms and variables)

collect(questions, all_=True, co_constraints=True)

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, IfExpr, AUnary, Variable, Number_constant, Brackets

generate_constructors(constructors: dict)

fills the list constructors with all constructors belonging to open types.

unknown_symbols(co_constraints=True)

returns the list of symbol declarations in self, ignoring type constraints

returns Dict[name, Declaration]

co_constraints(co_constraints)

collects the constraints attached to AST nodes, e.g. instantiated definitions

`co_constraints is an OrderedSet of Expression

is_assignment() → bool

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, todo=None)

recursively substitute e0 by e1 in self (e0 is not a Variable)

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.

Interpret appliedSymbols immediately if grounded (and not occurring in head of definition). Update fresh_vars.

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 fresh_vars.

symbolic_propagate(assignments: idp_engine.Assignments.Assignments, truth: Optional[idp_engine.Expression.Expression] = true) → List[Tuple[idp_engine.Expression.Expression]]

returns the consequences of self=truth that are in assignments.

The consequences are obtained by symbolic processing (no calls to Z3).

Parameters

• assignments (Assignments) – The set of questions to chose from. Their value is ignored.

• truth (Expression, optional) – The truth value of the expression self. Defaults to TRUE.

Returns

A list of pairs (Expression, bool), descring the literals that are implicant

propagate1(assignments, truth)

returns the list of symbolic_propagate of self (default implementation)

as_set_condition() → Tuple[Optional[AppliedSymbol], Optional[bool], Optional[Enumeration]]

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]]

annotate(voc, q_vars)

annotate tree after parsing

annotate1()

annotations that are common to __init__ and make()

interpret(problem) → idp_engine.Expression.Expression

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 (Problem) – the Problem to apply

Returns

the resulting expression

Return type

Expression

class idp_engine.Expression.Constructor(**kwargs)

Bases: idp_engine.Expression.ASTNode

Constructor declaration

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

translated

the value in Z3

Type

DataTypeRef

class idp_engine.Expression.IfExpr(**kwargs)

Bases: idp_engine.Expression.Expression

class idp_engine.Expression.Quantee(**kwargs)

Bases: idp_engine.Expression.Expression

represents the description of quantification, e.g., x in T or (x,y) in P

vars

the (tuples of) variables being quantified

Type

List[List[Variable]

sort

the type or predicate to quantify over

Type

SymbolExpr, Optional

arity

the length of the tuple of variable

Type

int

copy()

create a deep copy (except for rigid terms and variables)

class idp_engine.Expression.AQuantification(**kwargs)

Bases: idp_engine.Expression.Expression

classmethod make(q, quantees, f)

make and annotate a quantified formula

copy()

create a deep copy (except for rigid terms and variables)

collect(questions, all_=True, co_constraints=True)

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, IfExpr, AUnary, Variable, Number_constant, Brackets

interpret(problem)

apply information in the problem and its vocabulary

Parameters

problem (Problem) – the problem to be applied

Returns

the expanded quantifier expression

Return type

Expression

class idp_engine.Expression.BinaryOperator(**kwargs)

Bases: idp_engine.Expression.Expression

classmethod make(ops, operands)

creates a BinaryOp beware: cls must be specific for ops !

collect(questions, all_=True, co_constraints=True)

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, IfExpr, AUnary, Variable, Number_constant, Brackets

class idp_engine.Expression.AImplication(**kwargs)

Bases: idp_engine.Expression.BinaryOperator

class idp_engine.Expression.AEquivalence(**kwargs)

Bases: idp_engine.Expression.BinaryOperator

class idp_engine.Expression.ARImplication(**kwargs)

Bases: idp_engine.Expression.BinaryOperator

class idp_engine.Expression.ADisjunction(**kwargs)

Bases: idp_engine.Expression.BinaryOperator

class idp_engine.Expression.AConjunction(**kwargs)

Bases: idp_engine.Expression.BinaryOperator

class idp_engine.Expression.AComparison(**kwargs)

Bases: idp_engine.Expression.BinaryOperator

is_assignment()

Returns: bool: True if self assigns a rigid term to a rigid function application

class idp_engine.Expression.ASumMinus(**kwargs)

Bases: idp_engine.Expression.BinaryOperator

class idp_engine.Expression.AMultDiv(**kwargs)

Bases: idp_engine.Expression.BinaryOperator

class idp_engine.Expression.APower(**kwargs)

Bases: idp_engine.Expression.BinaryOperator

class idp_engine.Expression.AUnary(**kwargs)

Bases: idp_engine.Expression.Expression

class idp_engine.Expression.AAggregate(**kwargs)

Bases: idp_engine.Expression.Expression

copy()

create a deep copy (except for rigid terms and variables)

collect(questions, all_=True, co_constraints=True)

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, IfExpr, AUnary, Variable, Number_constant, Brackets

class idp_engine.Expression.AppliedSymbol(**kwargs)

Bases: idp_engine.Expression.Expression

Represents a symbol applied to arguments

Parameters

• eval (string) – ‘$’ if the symbol must be evaluated, else ‘’

• s (Expression) – 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

copy()

create a deep copy (except for rigid terms and variables)

collect(questions, all_=True, co_constraints=True)

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, IfExpr, AUnary, Variable, Number_constant, Brackets

generate_constructors(constructors: dict)

fills the list constructors with all constructors belonging to open types.

substitute(e0, e1, assignments, todo=None)

recursively substitute e0 by e1 in self

class idp_engine.Expression.UnappliedSymbol(**kwargs)

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().

classmethod construct(constructor: idp_engine.Expression.Constructor)

Create an UnappliedSymbol from a constructor

class idp_engine.Expression.Variable(**kwargs)

Bases: idp_engine.Expression.Expression

AST node for a variable in a quantification or aggregate

copy()

create a deep copy (except for rigid terms and variables)

class idp_engine.Expression.Number(**kwargs)

Bases: idp_engine.Expression.Expression

class idp_engine.Expression.Brackets(**kwargs)

Bases: idp_engine.Expression.Expression