wytp.proof.rules

Class Simplification

java.lang.Object

wytp.proof.util.AbstractProofRule

wytp.proof.rules.Simplification

All Implemented Interfaces:

Proof.LinearRule, Proof.Rule

public class Simplification
extends AbstractProofRule
implements Proof.LinearRule

Field Summary

Fields inherited from class wytp.proof.util.AbstractProofRule

simp, types

Constructor Summary

Constructors

Constructor and Description
Simplification(TypeSystem types)

Method Summary

Modifier and Type	Method and Description
Proof.State	apply(Proof.State head, Formula truth)
Formula.Truth	evaluateEquality(WyalFile.Opcode opcode, WyalFile.Value lhs, WyalFile.Value rhs) Evaluate a given equality whose bounds are known to be constant values of some sort.
Formula.Truth	evaluateInequality(WyalFile.Opcode opcode, WyalFile.Value.Int lhs, WyalFile.Value.Int rhs) Evaluate a given inequality whose bounds are known to be constant integer values.
Arithmetic.Polynomial	filter(Arithmetic.Polynomial p, boolean sign)
String	getName() Get the name of this rule
<T> Formula[]	inlineNestedArray(Formula[] parent, int index, Formula[] child)
WyalFile.Pair<WyalFile.Expr,WyalFile.Expr>	normaliseBounds(WyalFile.Expr lhs, WyalFile.Expr rhs) Normalise bounds of an equation to be positive.
Formula	simplify(Formula f) Recursively simplify a given formula by applying the "standard" simplifications for each kind.
Formula[]	simplify(Formula[] children)
WyalFile.Expr	simplifyArithmetic(WyalFile.Expr.Operator e)
Formula	simplifyArithmeticEquality(Formula.ArithmeticEquality eq) Simplify an arithmetic equality by canceling, evaluating and/or balancing: Canceling is the process of removing commons terms from both sides.
WyalFile.Expr	simplifyArrayIndex(WyalFile.Expr.Operator e)
WyalFile.Expr	simplifyArrayLength(WyalFile.Expr.Operator e)
WyalFile.Expr	simplifyArrayUpdate(WyalFile.Expr.Operator e)
Formula	simplifyConjunct(Formula.Conjunct conjunct)
WyalFile.Expr	simplifyConstant(WyalFile.Expr.Constant e)
WyalFile.Expr	simplifyDereference(WyalFile.Expr.Dereference e)
Formula	simplifyDisjunct(Formula.Disjunct disjunct)
Formula	simplifyEquality(Formula.Equality eq) Simplify a non-arithmetic equality by attempting to evaluate it.
WyalFile.Expr	simplifyExpression(WyalFile.Expr e) Convert an arbitrary expression to an atom.
WyalFile.Expr[]	simplifyExpressions(WyalFile.Expr[] children)
Formula	simplifyInequality(Formula.Inequality ieq) Simplify an inequality by canceling, evaluating and/or balancing: Canceling is the process of removing commons terms from both sides.
Formula	simplifyInvoke(Formula.Invoke ivk)
WyalFile.Expr	simplifyInvoke(WyalFile.Expr.Invoke ivk)
Formula	simplifyIs(Formula.Is e)
WyalFile.Expr	simplifyNonArithmetic(WyalFile.Expr.Operator e)
Formula	simplifyQuantifier(Formula.Quantifier quantifier) Simplify a quantified formula.
WyalFile.Expr	simplifyRecordAccess(WyalFile.Expr.RecordAccess e)
WyalFile.Expr	simplifyRecordInitialiser(WyalFile.Expr.RecordInitialiser e)
WyalFile.Expr	simplifyRecordUpdate(WyalFile.Expr.RecordUpdate e)

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

Simplification

public Simplification(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)
                  throws NameResolver.ResolutionError

Specified by:

apply in class AbstractProofRule

Throws:

NameResolver.ResolutionError

simplify

public Formula simplify(Formula f)
                 throws NameResolver.ResolutionError

Recursively simplify a given formula by applying the "standard" simplifications for each kind. If no simplification is performed, this returns the original object in tact.

Parameters:

f -

Returns:

Throws:

AmbiguousNameError

NameNotFoundError

NameResolver.ResolutionError

simplifyConjunct

public Formula simplifyConjunct(Formula.Conjunct conjunct)
                         throws NameResolver.ResolutionError

Throws:

NameResolver.ResolutionError

simplifyDisjunct

public Formula simplifyDisjunct(Formula.Disjunct disjunct)
                         throws NameResolver.ResolutionError

Throws:

NameResolver.ResolutionError

simplify

public Formula[] simplify(Formula[] children)
                   throws NameResolver.ResolutionError

Throws:

NameResolver.ResolutionError

simplifyQuantifier

public Formula simplifyQuantifier(Formula.Quantifier quantifier)
                           throws NameResolver.ResolutionError

Simplify a quantified formula. In essence, if the body is a truth value then that is returned. For example, forall x.true is simply true.

Parameters:

quantifier -

Returns:

Throws:

AmbiguousNameError

NameNotFoundError

NameResolver.ResolutionError

simplifyInequality

public Formula simplifyInequality(Formula.Inequality ieq)
                           throws NameResolver.ResolutionError

Simplify an inequality by canceling, evaluating and/or balancing:

1. Canceling is the process of removing commons terms from both sides. For example, in x+y < x we can cancel x to give y < 0.
2. Evaluating is the process of reducing a constant inequality to either true or false. For example, 0 < 1 reduces to true whilst 1 >= 0 reduces to false.
3. Balancing is the process of eliminating negative terms and factorising. For example, -x < 1 is balanced to 0 < 1 + x. Likewise, 2*x < 6*y is factorised to x < 3*y.

Parameters:

ieq -

Returns:

Throws:

AmbiguousNameError

NameNotFoundError

NameResolver.ResolutionError

simplifyArithmeticEquality

public Formula simplifyArithmeticEquality(Formula.ArithmeticEquality eq)
                                   throws NameResolver.ResolutionError

Simplify an arithmetic equality by canceling, evaluating and/or balancing:

1. Canceling is the process of removing commons terms from both sides. For example, in x+y == x we can cancel x to give y == 0.
2. Evaluating is the process of reducing a constant inequality to either true or false. For example, 0 == 0 reduces to true whilst 1 == 0 reduces to false.
3. Balancing is the process of eliminating negative terms and factorising. For example, -x == 1 is balanced to 0 == 1 + x. Likewise, 2*x == 6*y is factorised to x == 3*y.

Parameters:

ieq -

Returns:

Throws:

AmbiguousNameError

NameNotFoundError

NameResolver.ResolutionError

simplifyEquality

public Formula simplifyEquality(Formula.Equality eq)
                         throws NameResolver.ResolutionError

Simplify a non-arithmetic equality by attempting to evaluate it. For example, true == false reduces to false. In the case that neither side is a constant, then the original equality is returned.

Parameters:

eq -

Returns:

Throws:

AmbiguousNameError

NameNotFoundError

NameResolver.ResolutionError

simplifyInvoke

public Formula simplifyInvoke(Formula.Invoke ivk)
                       throws NameResolver.ResolutionError

Throws:

NameResolver.ResolutionError

simplifyIs

public Formula simplifyIs(Formula.Is e)
                   throws NameResolver.ResolutionError

Throws:

NameResolver.ResolutionError

simplifyExpressions

public WyalFile.Expr[] simplifyExpressions(WyalFile.Expr[] children)
                                    throws NameResolver.ResolutionError

Throws:

NameResolver.ResolutionError

simplifyExpression

public WyalFile.Expr simplifyExpression(WyalFile.Expr e)
                                 throws NameResolver.ResolutionError

Convert an arbitrary expression to an atom.

Parameters:

e -

Returns:

Throws:

AmbiguousNameError

NameNotFoundError

NameResolver.ResolutionError

simplifyConstant

public WyalFile.Expr simplifyConstant(WyalFile.Expr.Constant e)

simplifyRecordInitialiser

public WyalFile.Expr simplifyRecordInitialiser(WyalFile.Expr.RecordInitialiser e)
                                        throws NameResolver.ResolutionError

Throws:

NameResolver.ResolutionError

simplifyRecordAccess

public WyalFile.Expr simplifyRecordAccess(WyalFile.Expr.RecordAccess e)
                                   throws NameResolver.ResolutionError

Throws:

NameResolver.ResolutionError

simplifyRecordUpdate

public WyalFile.Expr simplifyRecordUpdate(WyalFile.Expr.RecordUpdate e)
                                   throws NameResolver.ResolutionError

Throws:

NameResolver.ResolutionError

simplifyDereference

public WyalFile.Expr simplifyDereference(WyalFile.Expr.Dereference e)
                                  throws NameResolver.ResolutionError

Throws:

NameResolver.ResolutionError

simplifyInvoke

public WyalFile.Expr simplifyInvoke(WyalFile.Expr.Invoke ivk)
                             throws NameResolver.ResolutionError

Throws:

NameResolver.ResolutionError

simplifyArrayIndex

public WyalFile.Expr simplifyArrayIndex(WyalFile.Expr.Operator e)
                                 throws NameResolver.ResolutionError

Throws:

NameResolver.ResolutionError

simplifyArrayUpdate

public WyalFile.Expr simplifyArrayUpdate(WyalFile.Expr.Operator e)
                                  throws NameResolver.ResolutionError

Throws:

NameResolver.ResolutionError

simplifyArrayLength

public WyalFile.Expr simplifyArrayLength(WyalFile.Expr.Operator e)
                                  throws NameResolver.ResolutionError

Throws:

NameResolver.ResolutionError

simplifyNonArithmetic

public WyalFile.Expr simplifyNonArithmetic(WyalFile.Expr.Operator e)
                                    throws NameResolver.ResolutionError

Throws:

NameResolver.ResolutionError

simplifyArithmetic

public WyalFile.Expr simplifyArithmetic(WyalFile.Expr.Operator e)
                                 throws NameResolver.ResolutionError

Throws:

NameResolver.ResolutionError

evaluateInequality

public Formula.Truth evaluateInequality(WyalFile.Opcode opcode,
                                        WyalFile.Value.Int lhs,
                                        WyalFile.Value.Int rhs)

Evaluate a given inequality whose bounds are known to be constant integer values. For example, 1 < 0 evaluates to false, etc.

Parameters:

opcode -

lhs -

rhs -

Returns:

evaluateEquality

public Formula.Truth evaluateEquality(WyalFile.Opcode opcode,
                                      WyalFile.Value lhs,
                                      WyalFile.Value rhs)

Evaluate a given equality whose bounds are known to be constant values of some sort. For example, true == false evaluates to false, etc.

Parameters:

opcode -

lhs -

rhs -

Returns:

normaliseBounds

public WyalFile.Pair<WyalFile.Expr,WyalFile.Expr> normaliseBounds(WyalFile.Expr lhs,
                                                                  WyalFile.Expr rhs)

Normalise bounds of an equation to be positive. For example, consider the inequality x < y - z. In this case, the right-hand side is not simplifyd because it contains a negative term. The simplifyd version of this inequality would be x + z < y.

Parameters:

lhs -

rhs -

Returns:

filter

public Arithmetic.Polynomial filter(Arithmetic.Polynomial p,
                                    boolean sign)

inlineNestedArray

public <T> Formula[] inlineNestedArray(Formula[] parent,
                                       int index,
                                       Formula[] child)