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.lattices.FunctionalLattice<M,Identifier,T>

it.unive.lisa.analysis.nonrelational.Environment<InferenceSystem<T>,ValueExpression,T,InferredValue.InferredPair<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,InferredValue.InferredPair<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 class it.unive.lisa.analysis.lattices.FunctionalLattice

FunctionalLattice.FunctionalLift<V extends Lattice<V>>, FunctionalLattice.KeyFunctionalLift<K>

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

SemanticDomain.Satisfiability

Field Summary

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

function, lattice

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

BOTTOM_STRING, TOP_STRING

Constructor Summary

Constructors

Constructor	Description
InferenceSystem(InferenceSystem<T> other, T state)	Builds an inference system identical to the given one, except for the execution state that will be set to the given one.
InferenceSystem(T domain)	Builds an empty inference system.
InferenceSystem(T domain, java.util.Map<Identifier,T> function, InferredValue.InferredPair<T> inferred)	Builds an environment containing the given mapping.

Method Summary

Modifier and Type	Method	Description
InferenceSystem<T>	assignAux(Identifier id, ValueExpression expression, java.util.Map<Identifier,T> function, T value, InferredValue.InferredPair<T> eval, ProgramPoint pp)	Auxiliary function of Environment.assign(Identifier, SymbolicExpression, ProgramPoint) that is invoked after the evaluation of the expression.
InferenceSystem<T>	assumeSatisfied(InferredValue.InferredPair<T> eval)	Assumes that an expression, that evaluated to eval, is always satisfied by this environment.
InferenceSystem<T>	bottom()	Yields the bottom element of this lattice.
boolean	equals(java.lang.Object obj)
org.apache.commons.lang3.tuple.Pair<T,InferredValue.InferredPair<T>>	eval(ValueExpression expression, ProgramPoint pp)	Yields the evaluation of the given expression, happening at the given program point.
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).
InferenceSystem<T>	glbAux(T lattice, java.util.Map<Identifier,T> function, InferenceSystem<T> other)	Auxiliary glb operation, invoked after the result has been computed to create the concrete instance of environment.
int	hashCode()
boolean	isBottom()	Yields true if and only if this object represents the bottom of the lattice.
boolean	isTop()	Yields true if and only if this object represents the top of the lattice.
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.
InferenceSystem<T>	mk(T lattice, java.util.Map<Identifier,T> function)	Builds a instance of this class from the given lattice instance and the given mapping.
DomainRepresentation	representation()	Yields a DomainRepresentation of the information contained in 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, forgetIdentifier, forgetIdentifiersIf, glb, lubKeys, popScope, pushScope, satisfies

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

functionalLift, getKeys, getMap, getState, getValues, glbKeys, iterator, mkNewFunction, putState, toString

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

lessOrEqual, lub, widening

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

assign, assume, forgetIdentifier, forgetIdentifiers, forgetIdentifiersIf, getDomainInstance, popScope, pushScope, satisfies

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

InferenceSystem

public InferenceSystem(InferenceSystem<T> other,
                       T state)

Builds an inference system identical to the given one, except for the execution state that will be set to the given one.

Parameters:

other - the inference system to copy

state - the new execution state

InferenceSystem

public InferenceSystem(T domain,
                       java.util.Map<Identifier,T> function,
                       InferredValue.InferredPair<T> inferred)

Builds an environment containing the given mapping. If function is null, the new environment is the top environment if lattice.isTop() holds, and it is the bottom environment if lattice.isBottom() holds.

Parameters:

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

function - the function representing the mapping contained in the new environment; can be null

inferred - the inferred pair for the last computed expression, that is left on the top of the stack

Method Detail

mk

public InferenceSystem<T> mk(T lattice,
                             java.util.Map<Identifier,T> function)

Description copied from class: FunctionalLattice

Builds a instance of this class from the given lattice instance and the given mapping.

Specified by:

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

Parameters:

lattice - an instance of lattice to be used during semantic operations to retrieve top and bottom values

function - the function representing the mapping contained in the new environment; can be null

Returns:

a new instance of this class

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

eval

public org.apache.commons.lang3.tuple.Pair<T,InferredValue.InferredPair<T>> eval(ValueExpression expression,
                                                                                       ProgramPoint pp)
                                                                                throws SemanticException

Description copied from class: Environment

Yields the evaluation of the given expression, happening at the given program point. The result of the evaluation is in the form of <abstract element, evaluation result>, where evaluation result is the true result of the evaluation, while abstract element is the element derived by the result that is to be stored inside the environment mapped to an identifier.

Specified by:

eval in class Environment<InferenceSystem<T extends InferredValue<T>>,ValueExpression,T extends InferredValue<T>,InferredValue.InferredPair<T extends InferredValue<T>>>

Parameters:

expression - the expression to evaluate

pp - the program point where the evaluation happens

Returns:

the result of the evaluation

Throws:

SemanticException - if something goes wrong during the evaluation

assignAux

public InferenceSystem<T> assignAux(Identifier id,
                                    ValueExpression expression,
                                    java.util.Map<Identifier,T> function,
                                    T value,
                                    InferredValue.InferredPair<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>,InferredValue.InferredPair<T extends InferredValue<T>>>

Parameters:

id - the identifier that has been assigned

expression - the expression that has been evaluated and assigned

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

value - the final value stored for id, after considering applying NonRelationalElement.variable(Identifier, ProgramPoint) and Identifier.isWeak()

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

isTop

public boolean isTop()

Description copied from class: FunctionalLattice

Yields true if and only if this object represents the top of the lattice. The default implementation of this method uses reference equality between this and the value returned by Lattice.top(), thus assuming that the top element is a singleton. If this is not the case, override this method accordingly to provide a coherent test.

By default, a functional lattice is the top lattice if the underlying lattice's isTop() holds and its function is null.

Specified by:

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

Overrides:

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

Returns:

true if this is the top of the lattice

isBottom

public boolean isBottom()

Description copied from class: FunctionalLattice

Yields true if and only if this object represents the bottom of the lattice. The default implementation of this method uses reference equality between this and the value returned by Lattice.bottom(), thus assuming that the bottom element is a singleton. If this is not the case, override this method accordingly to provide a coherent test.

By default, a functional lattice is the top lattice if the underlying lattice's isBottom() holds and its function is null.

Specified by:

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

Overrides:

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

Returns:

true if this is the bottom of the lattice

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 least upper bound 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))

The default implementation of this method delegates to BaseLattice.lubAux(BaseLattice), and is thus safe for finite lattices and ACC ones.

Overrides:

wideningAux 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

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

assumeSatisfied

public InferenceSystem<T> assumeSatisfied(InferredValue.InferredPair<T> eval)

Description copied from class: Environment

Assumes that an expression, that evaluated to eval, is always satisfied by this environment. This auxiliary method serves as a constructor for the final concrete instance of environment.

Specified by:

assumeSatisfied in class Environment<InferenceSystem<T extends InferredValue<T>>,ValueExpression,T extends InferredValue<T>,InferredValue.InferredPair<T extends InferredValue<T>>>

Parameters:

eval - the result of the evaluation of the expression that is always satisfied

Returns:

the (possibly) updated environment

glbAux

public InferenceSystem<T> glbAux(T lattice,
                                 java.util.Map<Identifier,T> function,
                                 InferenceSystem<T> other)

Description copied from class: Environment

Auxiliary glb operation, invoked after the result has been computed to create the concrete instance of environment. Note that any additional information that is instance-specific (i.e. anything but function and lattice singleton) has to be computed by this method.

Specified by:

glbAux in class Environment<InferenceSystem<T extends InferredValue<T>>,ValueExpression,T extends InferredValue<T>,InferredValue.InferredPair<T extends InferredValue<T>>>

Parameters:

lattice - the lattice that is the result of the glb

function - the function that is the result of the glb (might be null

other - the other environment

Returns:

the final instance of the glb

hashCode

public int hashCode()

Overrides:

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

equals

public boolean equals(java.lang.Object obj)

Overrides:

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

representation

public DomainRepresentation representation()

Description copied from interface: SemanticDomain

Yields a DomainRepresentation of the information contained in 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>,InferredValue.InferredPair<T extends InferredValue<T>>>

Returns:

the representation