Package it.unive.lisa.analysis

Interface Lattice<L extends Lattice<L>>

Type Parameters:

L - the concrete Lattice instance

All Superinterfaces:

StructuredObject

All Known Subinterfaces:

AbstractState<A>, BaseHeapDomain<H>, BaseInferredValue<T>, BaseLattice<L>, BaseNonRelationalTypeDomain<T>, BaseNonRelationalValueDomain<T>, HeapDomain<D>, InferredValue<T>, NonRelationalDomain<T,E,F>, NonRelationalElement<T,E,F>, NonRelationalHeapDomain<T>, NonRelationalTypeDomain<T>, NonRelationalValueDomain<T>, TypeDomain<T>, ValueDomain<D>

All Known Implementing Classes:

Aliases, AnalysisState, AnalyzedCFG, BackwardAnalyzedCFG, BackwardOptimizedAnalyzedCFG, CFGFixpoint.CompoundState, CFGResults, DataflowDomain, DefiniteDataflowDomain, Environment, ExpressionInverseSet, ExpressionSet, FixpointInfo, FixpointResults, FunctionalLattice, GenericInverseSetLattice, GenericMapLattice, GenericSetLattice, HeapEnvironment, InferenceSystem, InferredValue.InferredPair, InverseSetLattice, OptimizedAnalyzedCFG, PossibleDataflowDomain, Satisfiability, SetLattice, StatementStore, SymbolAliasing, TypeEnvironment, ValueEnvironment, VariableLift

public interface Lattice<L extends Lattice<L>>
extends StructuredObject

An interface for elements that follow a lattice structure. Implementers of this interface should inherit from BaseLattice, unless explicitly needed.

Field Summary

Fields

Modifier and Type	Field	Description
static java.lang.String	BOTTOM_STRING	A string constant that can be used to represent bottom values.
static java.lang.String	TOP_STRING	A string constant that can be used to represent top values.

Method Summary

Modifier and Type	Method	Description
L	bottom()	Yields the bottom element of this lattice.
static StructuredRepresentation	bottomRepresentation()	Yields a fresh StructuredRepresentation that can be used to represent bottom values through StructuredObject.representation().
default L	glb(L other)	Performs the greatest lower upper bound operation between this lattice element and the given one.
default boolean	isBottom()	Yields true if and only if this object represents the bottom of the lattice.
default boolean	isTop()	Yields true if and only if this object represents the top of the lattice.
boolean	lessOrEqual(L other)	Yields true if and only if this lattice element is in relation with (usually represented through ≤) the given one.
L	lub(L other)	Performs the least upper bound operation between this lattice element and the given one.
default L	narrowing(L other)	Performs the narrowing operation between this lattice element and the given one.
L	top()	Yields the top element of this lattice.
static StructuredRepresentation	topRepresentation()	Yields a fresh StructuredRepresentation that can be used to represent top values through StructuredObject.representation().
default L	widening(L other)	Performs the widening operation between this lattice element and the given one.

Methods inherited from interface it.unive.lisa.util.representation.StructuredObject

representation

Field Detail

TOP_STRING

static final java.lang.String TOP_STRING

A string constant that can be used to represent top values.

See Also:

Constant Field Values

BOTTOM_STRING

static final java.lang.String BOTTOM_STRING

A string constant that can be used to represent bottom values.

See Also:

Constant Field Values

Method Detail

topRepresentation

static StructuredRepresentation topRepresentation()

Yields a fresh StructuredRepresentation that can be used to represent top values through StructuredObject.representation().

Returns:

the representation

bottomRepresentation

static StructuredRepresentation bottomRepresentation()

Yields a fresh StructuredRepresentation that can be used to represent bottom values through StructuredObject.representation().

Returns:

the representation

lessOrEqual

boolean lessOrEqual(L other)
             throws SemanticException

Yields true if and only if this lattice element is in relation with (usually represented through ≤) the given one. This operation is not commutative.

Parameters:

other - the other lattice element

Returns:

true if and only if that condition holds

Throws:

SemanticException - if an error occurs during the computation

lub

L lub(L other)
throws SemanticException

Performs the least upper bound operation between this lattice element and the given one. This operation is commutative.

Parameters:

other - the other lattice element

Returns:

the least upper bound

Throws:

SemanticException - if an error occurs during the computation

glb

default L glb(L other)
       throws SemanticException

Performs the greatest lower upper bound operation between this lattice element and the given one. This operation is commutative.

Parameters:

other - the other lattice element

Returns:

the greatest lower bound

Throws:

SemanticException - if an error occurs during the computation

top

L top()

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

Returns:

the top element

bottom

L bottom()

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

Returns:

the bottom element

isTop

default boolean isTop()

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 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.

Returns:

true if this is the top of the lattice

isBottom

default boolean isBottom()

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 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.

Returns:

true if this is the bottom of the lattice

widening

default L widening(L other)
            throws SemanticException

Performs the widening operation between this lattice element and the given one. This operation is not commutative. The default implementation of this method delegates to lub(Lattice), and is thus safe for finite lattices and ACC ones.

Parameters:

other - the other lattice element

Returns:

the widening between this and other

Throws:

SemanticException - if an error occurs during the computation

narrowing

default L narrowing(L other)
             throws SemanticException

Performs the narrowing operation between this lattice element and the given one. This operation is not commutative. The default implementation of this method delegates to glb(Lattice), and is thus safe for finite lattices and DCC ones.

Parameters:

other - the other lattice element

Returns:

the narrowing between this and other

Throws:

SemanticException - if an error occurs during the computation