Package it.unive.lisa.analysis.nonrelational.inference

Class InferenceSystem<T extends InferredValue<T>>

java.lang.Object

it.unive.lisa.analysis.BaseLattice<F>

it.unive.lisa.analysis.FunctionalLattice<M,Identifier,T>

it.unive.lisa.analysis.nonrelational.Environment<InferenceSystem<T>,ValueExpression,T>

it.unive.lisa.analysis.nonrelational.inference.InferenceSystem<T>

Type Parameters:

T - the type of InferredValue in this inference system

All Implemented Interfaces:

Lattice<InferenceSystem<T>>, SemanticDomain<InferenceSystem<T>,ValueExpression,Identifier>, ValueDomain<InferenceSystem<T>>, java.lang.Iterable<java.util.Map.Entry<Identifier,T>>

public class InferenceSystem<T extends InferredValue<T>>
extends Environment<InferenceSystem<T>,ValueExpression,T>
implements ValueDomain<InferenceSystem<T>>

An inference system that model standard derivation systems (e.g., types systems, small step semantics, big step semantics, ...). An inference system is an Environment that work on InferredValues, and that exposes the last inferred value (getInferredValue()) and the execution state (getExecutionState()).

Nested Class Summary

Nested classes/interfaces inherited from interface it.unive.lisa.analysis.SemanticDomain

SemanticDomain.Satisfiability

Field Summary

Fields inherited from class it.unive.lisa.analysis.FunctionalLattice

function, lattice

Fields inherited from interface it.unive.lisa.analysis.Lattice

BOTTOM_STRING, TOP_STRING

Constructor Summary

Constructors

Constructor	Description
InferenceSystem(T domain)	Builds an empty inference system.

Method Summary

Modifier and Type	Method	Description
protected InferenceSystem<T>	assignAux(Identifier id, ValueExpression value, java.util.Map<Identifier,T> function, T eval, ProgramPoint pp)	Auxiliary function of Environment.assign(Identifier, SymbolicExpression, ProgramPoint) that is invoked after the evaluation of the expression.
InferenceSystem<T>	bottom()	Yields the bottom element of this lattice.
protected InferenceSystem<T>	copy()	Copies this environment.
T	getExecutionState()	Yields the execution state (also called program counter), that might change when evaluating an expression.
T	getInferredValue()	Yields the inferred value of the last SymbolicExpression handled by this domain, either through Environment.assign(Identifier, SymbolicExpression, ProgramPoint) or smallStepSemantics(ValueExpression, ProgramPoint).
boolean	lessOrEqualAux(InferenceSystem<T> other)	Yields true if and only if this lattice element is in relation with (usually represented through ≤) the given one, assuming that base cases have already been handled.
InferenceSystem<T>	lubAux(InferenceSystem<T> other)	Performs the least upper bound operation between this lattice element and the given one, assuming that base cases have already been handled.
java.lang.String	representation()	Yields a textual representation of the content of this domain's instance.
InferenceSystem<T>	smallStepSemantics(ValueExpression expression, ProgramPoint pp)	Yields a copy of this domain, that has been modified accordingly to the semantics of the given expression.
InferenceSystem<T>	top()	Yields the top element of this lattice.
InferenceSystem<T>	wideningAux(InferenceSystem<T> other)	Performs the widening operation between this lattice element and the given one, assuming that base cases have already been handled.

Methods inherited from class it.unive.lisa.analysis.nonrelational.Environment

assign, assume, assumeAux, forgetIdentifier, isBottom, isTop, satisfies, toString

Methods inherited from class it.unive.lisa.analysis.FunctionalLattice

equals, getKeys, getState, hashCode, iterator, mkNewFunction

Methods inherited from class it.unive.lisa.analysis.BaseLattice

lessOrEqual, lub, widening

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Methods inherited from interface it.unive.lisa.analysis.Lattice

isBottom, isTop, lessOrEqual, lub, widening

Methods inherited from interface it.unive.lisa.analysis.SemanticDomain

assign, assume, forgetIdentifier, forgetIdentifiers, satisfies

Methods inherited from interface it.unive.lisa.analysis.ValueDomain

applySubstitution

Constructor Detail

InferenceSystem

public InferenceSystem(T domain)

Builds an empty inference system.

Parameters:

domain - a singleton instance to be used during semantic operations to retrieve top and bottom values

Method Detail

getExecutionState

public T getExecutionState()

Yields the execution state (also called program counter), that might change when evaluating an expression.

Returns:

the execution state

getInferredValue

public T getInferredValue()

Yields the inferred value of the last SymbolicExpression handled by this domain, either through Environment.assign(Identifier, SymbolicExpression, ProgramPoint) or smallStepSemantics(ValueExpression, ProgramPoint).

Returns:

the value inferred for the last expression

copy

protected InferenceSystem<T> copy()

Description copied from class: Environment

Copies this environment. The function of the returned environment must be a (shallow) copy of the one of the given environment.

Specified by:

copy in class Environment<InferenceSystem<T extends InferredValue<T>>,ValueExpression,T extends InferredValue<T>>

Returns:

a copy of the given environment

assignAux

protected InferenceSystem<T> assignAux(Identifier id,
                                       ValueExpression value,
                                       java.util.Map<Identifier,T> function,
                                       T eval,
                                       ProgramPoint pp)

Description copied from class: Environment

Auxiliary function of Environment.assign(Identifier, SymbolicExpression, ProgramPoint) that is invoked after the evaluation of the expression.

Specified by:

assignAux in class Environment<InferenceSystem<T extends InferredValue<T>>,ValueExpression,T extends InferredValue<T>>

Parameters:

id - the identifier that has been assigned

value - the expression that has been evaluated and assigned

function - a copy of the current function, where the id has been assigned to eval

eval - the abstract value that is the result of the evaluation of value

pp - the program point that where this operation is being evaluated

Returns:

a new instance of this environment containing the given function, obtained by assigning id to eval

smallStepSemantics

public InferenceSystem<T> smallStepSemantics(ValueExpression expression,
                                             ProgramPoint pp)
                                      throws SemanticException

Description copied from interface: SemanticDomain

Yields a copy of this domain, that has been modified accordingly to the semantics of the given expression.

Specified by:

smallStepSemantics in interface SemanticDomain<InferenceSystem<T extends InferredValue<T>>,ValueExpression,Identifier>

Parameters:

expression - the expression whose semantics need to be computed

pp - the program point that where this operation is being evaluated

Returns:

a copy of this domain, modified accordingly to the semantics of expression

Throws:

SemanticException - if an error occurs during the computation

top

public InferenceSystem<T> top()

Description copied from interface: Lattice

Yields the top element of this lattice. The returned element should be unique across different calls to this method, since Lattice.isTop() uses reference equality by default. If the value returned by this method is not a singleton, override Lattice.isTop() accordingly to provide a coherent test.

Specified by:

top in interface Lattice<T extends InferredValue<T>>

Returns:

the top element

bottom

public InferenceSystem<T> bottom()

Description copied from interface: Lattice

Yields the bottom element of this lattice. The returned element should be unique across different calls to this method, since Lattice.isBottom() uses reference equality by default. If the value returned by this method is not a singleton, override Lattice.isBottom() accordingly to provide a coherent test.

Specified by:

bottom in interface Lattice<T extends InferredValue<T>>

Returns:

the bottom element

lubAux

public InferenceSystem<T> lubAux(InferenceSystem<T> other)
                          throws SemanticException

Description copied from class: BaseLattice

Performs the least upper bound operation between this lattice element and the given one, assuming that base cases have already been handled. In particular, it is guaranteed that:

• other is not null
• other is neither top nor bottom
• this is neither top nor bottom
• this and other are not the same object (according both to == and to Object.equals(Object))

Overrides:

lubAux in class FunctionalLattice<InferenceSystem<T extends InferredValue<T>>,Identifier,T extends InferredValue<T>>

Parameters:

other - the other lattice element

Returns:

the widening between this and other

Throws:

SemanticException - if an error occurs during the computation

wideningAux

public InferenceSystem<T> wideningAux(InferenceSystem<T> other)
                               throws SemanticException

Description copied from class: BaseLattice

Performs the widening operation between this lattice element and the given one, assuming that base cases have already been handled. In particular, it is guaranteed that:

• other is not null
• other is neither top nor bottom
• this is neither top nor bottom
• this and other are not the same object (according both to == and to Object.equals(Object))

Overrides:

wideningAux in class FunctionalLattice<InferenceSystem<T extends InferredValue<T>>,Identifier,T extends InferredValue<T>>

Parameters:

other - the other lattice element

Returns:

the least upper bound

Throws:

SemanticException - if an error occurs during the computation

lessOrEqualAux

public boolean lessOrEqualAux(InferenceSystem<T> other)
                       throws SemanticException

Description copied from class: BaseLattice

Yields true if and only if this lattice element is in relation with (usually represented through ≤) the given one, assuming that base cases have already been handled. In particular, it is guaranteed that:

• other is not null
• other is neither top nor bottom
• this is neither top nor bottom
• this and other are not the same object (according both to == and to Object.equals(Object))

Overrides:

lessOrEqualAux in class FunctionalLattice<InferenceSystem<T extends InferredValue<T>>,Identifier,T extends InferredValue<T>>

Parameters:

other - the other lattice element

Returns:

true if and only if that condition holds

Throws:

SemanticException - if an error occurs during the computation

representation

public java.lang.String representation()

Description copied from interface: SemanticDomain

Yields a textual representation of the content of this domain's instance.

Specified by:

representation in interface SemanticDomain<InferenceSystem<T extends InferredValue<T>>,ValueExpression,Identifier>

Overrides:

representation in class Environment<InferenceSystem<T extends InferredValue<T>>,ValueExpression,T extends InferredValue<T>>

Returns:

the textual representation