Package it.unive.lisa.analysis.nonRedundantSet

Class NonRedundantPowersetOfInterval

java.lang.Object

it.unive.lisa.analysis.nonRedundantSet.NonRedundantPowersetOfBaseNonRelationalValueDomain<NonRedundantPowersetOfInterval,Interval>

it.unive.lisa.analysis.nonRedundantSet.NonRedundantPowersetOfInterval

All Implemented Interfaces:

it.unive.lisa.analysis.BaseLattice<NonRedundantPowersetOfInterval>, it.unive.lisa.analysis.Lattice<NonRedundantPowersetOfInterval>, it.unive.lisa.analysis.nonrelational.NonRelationalDomain<NonRedundantPowersetOfInterval,it.unive.lisa.symbolic.value.ValueExpression,it.unive.lisa.analysis.nonrelational.value.ValueEnvironment<NonRedundantPowersetOfInterval>>, it.unive.lisa.analysis.nonrelational.NonRelationalElement<NonRedundantPowersetOfInterval,it.unive.lisa.symbolic.value.ValueExpression,it.unive.lisa.analysis.nonrelational.value.ValueEnvironment<NonRedundantPowersetOfInterval>>, it.unive.lisa.analysis.nonrelational.value.BaseNonRelationalValueDomain<NonRedundantPowersetOfInterval>, it.unive.lisa.analysis.nonrelational.value.NonRelationalValueDomain<NonRedundantPowersetOfInterval>, it.unive.lisa.analysis.SemanticEvaluator, it.unive.lisa.util.representation.StructuredObject

public class NonRedundantPowersetOfInterval
extends NonRedundantPowersetOfBaseNonRelationalValueDomain<NonRedundantPowersetOfInterval,Interval>

The finite non redundant powerset of Interval abstract domain approximating integer values as a non redundant set of interval. It is implemented as a NonRedundantPowersetOfBaseNonRelationalValueDomain, which handles most of the basic operation (such as lub, glb, widening and others operations needed to calculate the previous ones).

Nested Class Summary

Nested classes/interfaces inherited from interface it.unive.lisa.analysis.nonrelational.value.BaseNonRelationalValueDomain

it.unive.lisa.analysis.nonrelational.value.BaseNonRelationalValueDomain.EvaluationVisitor<T extends it.unive.lisa.analysis.nonrelational.value.BaseNonRelationalValueDomain<T>>

Field Summary

Fields inherited from class it.unive.lisa.analysis.nonRedundantSet.NonRedundantPowersetOfBaseNonRelationalValueDomain

elementsSet, valueDomain

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

BOTTOM_STRING, TOP_STRING

Constructor Summary

Constructors

Constructor	Description
NonRedundantPowersetOfInterval()	Constructs an empty non redundant set of intervals.
NonRedundantPowersetOfInterval(java.util.SortedSet<Interval> elements)	Constructs a non redundant set of intervals with the given intervals.

Method Summary

Modifier and Type	Method	Description
it.unive.lisa.analysis.nonrelational.value.ValueEnvironment<NonRedundantPowersetOfInterval>	assumeBinaryExpression(it.unive.lisa.analysis.nonrelational.value.ValueEnvironment<NonRedundantPowersetOfInterval> environment, it.unive.lisa.symbolic.value.operator.binary.BinaryOperator operator, it.unive.lisa.symbolic.value.ValueExpression left, it.unive.lisa.symbolic.value.ValueExpression right, it.unive.lisa.program.cfg.ProgramPoint src, it.unive.lisa.program.cfg.ProgramPoint dest, it.unive.lisa.analysis.SemanticOracle oracle)
protected NonRedundantPowersetOfInterval	EgliMilnerConnector(NonRedundantPowersetOfInterval other)	This specific Egli-Milner connector follows this definition: given two subsets S1 and S2 of a domain of a lattice:
protected it.unive.lisa.util.numeric.MathNumber	middlePoint(Interval interval)	Yields the middle point of an Interval.
protected NonRedundantPowersetOfInterval	mk(java.util.SortedSet<Interval> elements)	Utility for creating a concrete instance of NonRedundantPowersetOfBaseNonRelationalValueDomain given a set.

Methods inherited from class it.unive.lisa.analysis.nonRedundantSet.NonRedundantPowersetOfBaseNonRelationalValueDomain

bottom, equals, evalBinaryExpression, evalNonNullConstant, evalUnaryExpression, extrapolationHeuristic, glbAux, hashCode, isBottom, isTop, lessOrEqualAux, lessOrEqualEgliMilner, lubAux, removeOverlapping, removeOverlappingBetweenElements, removeRedundancy, representation, satisfiesBinaryExpression, top, toString, wideningAux

Methods inherited from class java.lang.Object

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

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

glb, lessOrEqual, lub, narrowing, narrowingAux, widening

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

assume, assumeTernaryExpression, assumeUnaryExpression, canProcess, eval, evalIdentifier, evalNullConstant, evalPushAny, evalPushInv, evalSkip, evalTernaryExpression, evalTypeCast, evalTypeConv, evalValueExpression, satisfies, satisfiesAbstractValue, satisfiesNonNullConstant, satisfiesNullConstant, satisfiesTernaryExpression, satisfiesUnaryExpression

Methods inherited from interface it.unive.lisa.analysis.nonrelational.NonRelationalElement

fixedVariable, unknownVariable

Constructor Detail

NonRedundantPowersetOfInterval

public NonRedundantPowersetOfInterval()

Constructs an empty non redundant set of intervals.

NonRedundantPowersetOfInterval

public NonRedundantPowersetOfInterval(java.util.SortedSet<Interval> elements)

Constructs a non redundant set of intervals with the given intervals.

Parameters:

elements - the set of intervals

Method Detail

EgliMilnerConnector

protected NonRedundantPowersetOfInterval EgliMilnerConnector(NonRedundantPowersetOfInterval other)
                                                      throws it.unive.lisa.analysis.SemanticException

This specific Egli-Milner connector follows this definition:
given two subsets S₁ and S₂ of a domain of a lattice:

S₁ +_EM S₂ = {s₂ ∋ S₂ | ∃ s₁ ∋ S₁ : s₁ ≤ s₂} ∪ {lub(s'₁, s₂) | s'₁ ∋ S₁, s₂ ∋ S₂, NOT ∃ s₁ ∋ S₁ : s₁ ≤ s₂}

s'₁ can be chosen randomly but in this case is chosen to be the closest interval to s₂ (closest based on middle point).

Overrides:

EgliMilnerConnector in class NonRedundantPowersetOfBaseNonRelationalValueDomain<NonRedundantPowersetOfInterval,Interval>

Parameters:

other - the other concrete element

Returns:

a new set that is ≤_EM than both this and other

Throws:

it.unive.lisa.analysis.SemanticException - if an error occurs during the computation

middlePoint

protected it.unive.lisa.util.numeric.MathNumber middlePoint(Interval interval)

Yields the middle point of an Interval. If both extremes are non-infinite the middle point is the sum of the two divided by two. If only one of the two extreme is infinite the middle point is said to be the non-infinite extreme. If both the extremes are infinite the middle point is said to be 0.

Parameters:

interval - the interval to calculate the middle point of

Returns:

the middle point of the interval

assumeBinaryExpression

public it.unive.lisa.analysis.nonrelational.value.ValueEnvironment<NonRedundantPowersetOfInterval> assumeBinaryExpression(it.unive.lisa.analysis.nonrelational.value.ValueEnvironment<NonRedundantPowersetOfInterval> environment,
                                                                                                                          it.unive.lisa.symbolic.value.operator.binary.BinaryOperator operator,
                                                                                                                          it.unive.lisa.symbolic.value.ValueExpression left,
                                                                                                                          it.unive.lisa.symbolic.value.ValueExpression right,
                                                                                                                          it.unive.lisa.program.cfg.ProgramPoint src,
                                                                                                                          it.unive.lisa.program.cfg.ProgramPoint dest,
                                                                                                                          it.unive.lisa.analysis.SemanticOracle oracle)
                                                                                                                   throws it.unive.lisa.analysis.SemanticException

Throws:

it.unive.lisa.analysis.SemanticException

mk

protected NonRedundantPowersetOfInterval mk(java.util.SortedSet<Interval> elements)

Description copied from class: NonRedundantPowersetOfBaseNonRelationalValueDomain

Utility for creating a concrete instance of NonRedundantPowersetOfBaseNonRelationalValueDomain given a set.

Specified by:

mk in class NonRedundantPowersetOfBaseNonRelationalValueDomain<NonRedundantPowersetOfInterval,Interval>

Parameters:

elements - the set containing the elements that must be included in the lattice instance

Returns:

a new concrete instance of NonRedundantPowerset containing the elements of the given set