wytp.proof.util

Class Formulae

java.lang.Object

wytp.proof.util.Formulae

public class Formulae
extends Object

Provides a range of different algorithms for manipulating formula. The idea is that these provide the building blocks on which different automated theorem provers can be built and experimented with. Each of the algorithms contained here attempts to perform a single task and to do it with at least moderate efficiency (though there is room for improvement there).

Author:

David J. Pearce

Constructor Summary

Constructors

Constructor and Description
Formulae()

Method Summary

Modifier and Type	Method and Description
static Formula	and(Formula lhs, Formula rhs)
static Formula.Inequality	greaterOrEqual(WyalFile.Expr lhs, WyalFile.Expr rhs)
static Formula	implies(Formula lhs, Formula rhs)
static Formula	invert(Formula f) Logically invert a given formula.
static Formula.Inequality	lessThan(WyalFile.Expr lhs, WyalFile.Expr rhs)
static Formula	or(Formula lhs, Formula rhs)
static Formula	toFormula(WyalFile.Stmt stmt, TypeSystem types) Take a tree of statements and expressions, and return a formula.
static Formula[]	toFormulae(WyalFile.Stmt[] stmts, TypeSystem types) Convert an array of statements into an array of (equivalent) formulae.

Methods inherited from class java.lang.Object

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

Constructor Detail

Formulae

public Formulae()

Method Detail

toFormula

public static Formula toFormula(WyalFile.Stmt stmt,
                                TypeSystem types)
                         throws wybs.lang.NameResolver.ResolutionError

Take a tree of statements and expressions, and return a formula. This is the first part of the process in discharging a given assertion. The purpose of a formula is just to provide a more "structured" form of the logical expression. The interface Formula also provides useful functions form manipulating formulae.

Observe that after this conversion the resulting formula is not necessarily in simplified form. For example, conjuncts may contain nested conjuncts or equations may be unbalanced.

Parameters:

stmt - The statement being converted into a formula

types - The type system is required for the translation, as some aspects depend upon the types of expressions involved.

Returns:

Throws:

AmbiguousNameError

NameNotFoundError

wybs.lang.NameResolver.ResolutionError

toFormulae

public static Formula[] toFormulae(WyalFile.Stmt[] stmts,
                                   TypeSystem types)
                            throws wybs.lang.NameResolver.ResolutionError

Convert an array of statements into an array of (equivalent) formulae.

Parameters:

stmts -

Returns:

Throws:

AmbiguousNameError

NameNotFoundError

wybs.lang.NameResolver.ResolutionError

lessThan

public static Formula.Inequality lessThan(WyalFile.Expr lhs,
                                          WyalFile.Expr rhs)

greaterOrEqual

public static Formula.Inequality greaterOrEqual(WyalFile.Expr lhs,
                                                WyalFile.Expr rhs)

implies

public static Formula implies(Formula lhs,
                              Formula rhs)

and

public static Formula and(Formula lhs,
                          Formula rhs)

or

public static Formula or(Formula lhs,
                         Formula rhs)

invert

public static Formula invert(Formula f)

Logically invert a given formula. This pushes through all inversions as far as possible. For example, !(x == 0 && y < x) becomes x != 0 || y >= x. This method is useful (amongst other things) for beginning a proof-by-contradiction. In such a proof, we first invert the formula in question and then establish that this reduces to a contradiction.

Parameters:

f -

Returns: