wytp.proof.rules.logic

Class AndElimination

java.lang.Object

wytp.proof.util.AbstractProofRule

wytp.proof.rules.logic.AndElimination

All Implemented Interfaces:

Proof.LinearRule, Proof.Rule

public class AndElimination
extends AbstractProofRule
implements Proof.LinearRule

Responsible for breaking conjuncts down into their individual terms. This is perhaps the most simple implementation of a Proof.Rule which is also useful. For example, consider this simple assertion:

 assert:
   forall(int x):
       if:
           x > 0
       then:
           x >= 0
 

To prove this by contradiction, we invert the term and look for a contradiction. Eventually, we will encounter the conjunct (x > 0) && (x < 0) and, in order to proceed, this is broken down (by this rule) into the atomic truths x > 0 and x < 0. From there a separate rule shows the final contradiction.

Author:

David J. Pearce

Field Summary

Fields inherited from class wytp.proof.util.AbstractProofRule

simp, types

Constructor Summary

Constructors

Constructor and Description
AndElimination(Simplification simplify, TypeSystem types)

Method Summary

Modifier and Type	Method and Description
Proof.State	apply(Proof.State head, Formula truth)
String	getName() Get the name of this rule

Methods inherited from class wytp.proof.util.AbstractProofRule

apply, 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

AndElimination

public AndElimination(Simplification simplify,
                      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.State head,
                         Formula truth)

Specified by:

apply in class AbstractProofRule