idp_engine.Expression

(They are monkey-patched by other modules)

class idp_engine.Expression.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 idp_engine.Expression.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())) 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-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

copy()[source]

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

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, IfExpr, AUnary, Variable, Number_constant, Brackets

collect_symbols(symbols=None, co_constraints=True)[source]

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

returns Dict[name, 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}

generate_constructors(constructors: dict)[source]

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

co_constraints(co_constraints)[source]

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

co_constraints is an OrderedSet of Expression

is_assignment()bool[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.

Interpret appliedSymbols immediately if grounded (and not occurring in head of definition). 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: idp_engine.Assignments.Assignments)idp_engine.Expression.Expression

simplify the expression using the assignments

symbolic_propagate(assignments: Assignments, tag: Status, truth: Optional[idp_engine.Expression.Expression] = 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.

propagate1(assignments, tag, truth)

returns the list of symbolic_propagate of self, ignoring value and simpler

translate(problem: Problem, vars={})z3.z3.ExprRef

Converts the syntax tree to a Z3 expression, using .value and .simpler if present

Parameters
  • problem (Problem) – 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()Tuple[Optional[AppliedSymbol], Optional[bool], Optional[Enumeration]][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

add_level_mapping(level_symbols, head, pos_justification, polarity)[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.

Returns

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)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)[source]

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

class idp_engine.Expression.IfExpr(**kwargs)[source]

Bases: idp_engine.Expression.Expression

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}

translate1(problem: Problem, vars={})z3.z3.ExprRef

Converts the syntax tree to a Z3 expression, ignoring .value and .simpler

Parameters
  • problem (Problem) – 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 idp_engine.Expression.Quantee(**kwargs)[source]

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]

sub_exprs

the type or predicate to quantify over.

Type

List[SymbolExpr], Optional

If the type is "Concept" with a particular signature, it is followed by the types in the signature.
arity

the length of the tuple of variable

Type

int

class idp_engine.Expression.AQuantification(**kwargs)[source]

Bases: idp_engine.Expression.Expression

classmethod make(q, quantees, f, annotations=None)[source]

make and annotate a quantified formula

copy()[source]

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

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, IfExpr, AUnary, Variable, Number_constant, Brackets

collect_symbols(symbols=None, co_constraints=True)[source]

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

returns Dict[name, Declaration]

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.Operator(**kwargs)[source]

Bases: idp_engine.Expression.Expression

classmethod make(ops, operands, annotations=None)[source]

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

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, IfExpr, 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}

class idp_engine.Expression.AImplication(**kwargs)[source]

Bases: idp_engine.Expression.Operator

add_level_mapping(level_symbols, head, pos_justification, polarity)[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.

Returns

Expression

class idp_engine.Expression.AEquivalence(**kwargs)[source]

Bases: idp_engine.Expression.Operator

split_equivalences()[source]

Returns an equivalent expression where equivalences are replaced by implications

Returns

Expression

class idp_engine.Expression.ARImplication(**kwargs)[source]

Bases: idp_engine.Expression.Operator

add_level_mapping(level_symbols, head, pos_justification, polarity)[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.

Returns

Expression

class idp_engine.Expression.ADisjunction(**kwargs)[source]

Bases: idp_engine.Expression.Operator

class idp_engine.Expression.AConjunction(**kwargs)[source]

Bases: idp_engine.Expression.Operator

class idp_engine.Expression.AComparison(**kwargs)[source]

Bases: idp_engine.Expression.Operator

is_assignment()[source]

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

class idp_engine.Expression.ASumMinus(**kwargs)[source]

Bases: idp_engine.Expression.Operator

class idp_engine.Expression.AMultDiv(**kwargs)[source]

Bases: idp_engine.Expression.Operator

class idp_engine.Expression.APower(**kwargs)[source]

Bases: idp_engine.Expression.Operator

class idp_engine.Expression.AUnary(**kwargs)[source]

Bases: idp_engine.Expression.Expression

add_level_mapping(level_symbols, head, pos_justification, polarity)[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.

Returns

Expression

class idp_engine.Expression.AAggregate(**kwargs)[source]

Bases: idp_engine.Expression.Expression

copy()[source]

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

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, IfExpr, AUnary, Variable, Number_constant, Brackets

collect_symbols(symbols=None, co_constraints=True)[source]

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

returns Dict[name, 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}

class idp_engine.Expression.AppliedSymbol(**kwargs)[source]

Bases: idp_engine.Expression.Expression

Represents a symbol applied to arguments

Parameters
  • symbol (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()[source]

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

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, IfExpr, AUnary, Variable, Number_constant, Brackets

collect_symbols(symbols=None, co_constraints=True)[source]

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

returns Dict[name, 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}

generate_constructors(constructors: dict)[source]

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

add_level_mapping(level_symbols, head, pos_justification, polarity)[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.

Returns

Expression

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

recursively substitute e0 by e1 in self

class idp_engine.Expression.UnappliedSymbol(**kwargs)[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().

classmethod construct(constructor: idp_engine.Expression.Constructor)[source]

Create an UnappliedSymbol from a constructor

class idp_engine.Expression.Variable(**kwargs)[source]

Bases: idp_engine.Expression.Expression

AST node for a variable in a quantification or aggregate

copy()[source]

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

annotate1()[source]

annotations that are common to __init__ and make()

class idp_engine.Expression.Number(**kwargs)[source]

Bases: idp_engine.Expression.Expression

real()[source]

converts the INT number to REAL

class idp_engine.Expression.Brackets(**kwargs)[source]

Bases: idp_engine.Expression.Expression