wytp.proof.rules.arithmetic

Class InequalityIntroduction

java.lang.Object

wytp.proof.util.AbstractProofRule

wytp.proof.util.AbstractClosureRule

wytp.proof.rules.arithmetic.InequalityIntroduction

All Implemented Interfaces:

Proof.LinearRule, Proof.Rule

public class InequalityIntroduction
extends AbstractClosureRule
implements Proof.LinearRule

Responsible for emplying a form of transitive closure over inequalities. For example, if x < y and y < z then this rule might infer that x < z. To reduce the number of unnecessary inferences, the rule is selective about how to determine new inequalities. Specifically, it relies on a lexiographic ordering of terms and will only produce inferences for the least ordered term in any given pair of inequualities.

Author:

David J. Pearce

Field Summary

Fields inherited from class wytp.proof.util.AbstractProofRule

simp, types

Constructor Summary

Constructors

Constructor and Description
InequalityIntroduction(Simplification simp, TypeSystem types)

Method Summary

Modifier and Type	Method and Description
Proof.State	apply(Proof.Delta.Set existingTruths, Proof.State state, Formula newTruth)
Formula	closeOver(Formula.Inequality ith, Formula.Inequality jth) Close over two inequalities.
String	getName() Get the name of this rule

Methods inherited from class wytp.proof.util.AbstractClosureRule

apply, apply, getExistingTruths

Methods inherited from class wytp.proof.util.AbstractProofRule

extractDefinedTerms, findAllInstances, substitute

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface wytp.proof.Proof.LinearRule

apply

Constructor Detail

InequalityIntroduction

public InequalityIntroduction(Simplification simp,
                              TypeSystem types)

Method Detail

getName

public String getName()

Description copied from interface: Proof.Rule

Get the name of this rule

Specified by:

getName in interface Proof.Rule

Returns:

apply

public Proof.State apply(Proof.Delta.Set existingTruths,
                         Proof.State state,
                         Formula newTruth)
                  throws wybs.lang.NameResolver.ResolutionError

Specified by:

apply in class AbstractClosureRule

Throws:

wybs.lang.NameResolver.ResolutionError

closeOver

public Formula closeOver(Formula.Inequality ith,
                         Formula.Inequality jth)
                  throws wybs.lang.NameResolver.ResolutionError

Close over two inequalities. This may or may not produce a new inequality as a result. For example, closing over 3 < x and x < y gives 3 < y. Observe that, for this operation to succeed, there must exist a term common to both inequalities. In the case that multiple candidate terms exist, then the lexiographically least is selected.

This operation always closes in the same direction. If ith is "p1 >= p2" and jth is "p3 >= p4" then it attempts to generate the inequality of the form "p1 >= p4", but never of the form "p4 >= p1". In otherwords, the ith inequality always provides the lower bound and the jth inequality always provides the upper bound.

NOTE: this currently assumes that the inequalities are balanced.

Parameters:

ith -

jth -

Returns:

Throws:

wybs.lang.NameResolver.ResolutionError