wytp.proof.util

Class AbstractProofRule

java.lang.Object

wytp.proof.util.AbstractProofRule

All Implemented Interfaces:

Proof.Rule

Direct Known Subclasses:

AbstractClosureRule, AndElimination, ArrayEqualityCaseAnalysis, ArrayIndexCaseAnalysis, ArrayLengthAxiom, EqualityCaseAnalysis, ExistentialElimination, FunctionCallAxiom, MacroExpansion, RecordEqualityCaseAnalysis, Simplification

public abstract class AbstractProofRule
extends Object
implements Proof.Rule

Field Summary

Fields

Modifier and Type	Field and Description
protected Simplification	simp
protected TypeSystem	types

Constructor Summary

Constructors

Constructor and Description
AbstractProofRule(Simplification simp, TypeSystem types)

Method Summary

Modifier and Type	Method and Description
abstract Proof.State	apply(Proof.State head, Formula truth)
Proof.State	apply(Proof.State current, Proof.State head)
static <T extends WyalFile.Expr> List<T>	extractDefinedTerms(wybs.lang.SyntacticItem item, int kind, Formula.Quantifier... stack) Search through a given syntactic item looking for matching ground terms which are guaranteed to be defined in the given state.
protected static <T extends wybs.lang.SyntacticItem> List<T>	findAllInstances(wybs.lang.SyntacticItem e, Class<T> kind)
wybs.lang.SyntacticItem	substitute(wybs.lang.SyntacticItem from, wybs.lang.SyntacticItem to, wybs.lang.SyntacticItem item) Substitute for a given variable within a given syntactic item.

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.Rule

getName

Field Detail

simp

protected final Simplification simp

types

protected final TypeSystem types

Constructor Detail

AbstractProofRule

public AbstractProofRule(Simplification simp,
                         TypeSystem types)

Method Detail

apply

public Proof.State apply(Proof.State current,
                         Proof.State head)
                  throws wybs.lang.NameResolver.ResolutionError

Throws:

wybs.lang.NameResolver.ResolutionError

apply

public abstract Proof.State apply(Proof.State head,
                                  Formula truth)
                           throws wybs.lang.NameResolver.ResolutionError

Throws:

wybs.lang.NameResolver.ResolutionError

findAllInstances

protected static <T extends wybs.lang.SyntacticItem> List<T> findAllInstances(wybs.lang.SyntacticItem e,
                                                                              Class<T> kind)

extractDefinedTerms

public static <T extends WyalFile.Expr> List<T> extractDefinedTerms(wybs.lang.SyntacticItem item,
                                                                    int kind,
                                                                    Formula.Quantifier... stack)

Search through a given syntactic item looking for matching ground terms which are guaranteed to be defined in the given state. This is useful for a number of different rules which attempt to extract information from formulae, even when they are universally quantified or contained in disjunctions. As an example, consider the following:

 type nat is (int n) where n >= 0
 function f(int x) -> (nat r)

 define invariant(int[] xs, int x) is:
   forall(int k):
      (f(x) > xs[k]) || (f(x) < xs[k])

 assert:
   forall (int[] ys, int i):
     if:
       i < 0
       invariant(ys,i)
     then:
       false
 

The key is that, since invarint(ys,i) is asserted, it follows that f(i) is defined in the antecedent. As a result, the postcondition of f() dictates that i >= 0 must follow. This gives a contradiction in the antecedent, meaning the overall assertion holds.

Parameters:

item - SyntacticItem to search through

kind - Instances of this class will be extracted

Returns:

substitute

public wybs.lang.SyntacticItem substitute(wybs.lang.SyntacticItem from,
                                          wybs.lang.SyntacticItem to,
                                          wybs.lang.SyntacticItem item)

Substitute for a given variable within a given syntactic item. Specifically, this replaces all instances of VariableAccess which match the given declaration. Observe that the substitution is performed verbatim and (for example) without simplifying the underlying item.

This function preserves the aliasing structure of the original item up to the substitution itself. Furthermore, if no substitution was performed then the original item is returned as is.

Parameters:

from -

to -

item -

Returns: