Uses of Interface
wytp.proof.Formula

Packages that use Formula

Package	Description
wytp.proof
wytp.proof.rules
wytp.proof.rules.arithmetic
wytp.proof.rules.array
wytp.proof.rules.function
wytp.proof.rules.logic
wytp.proof.rules.quantifier
wytp.proof.rules.record
wytp.proof.rules.type
wytp.proof.util
wytp.types
wytp.types.extractors

Uses of Formula in wytp.proof

Subinterfaces of Formula in wytp.proof

Modifier and Type	Interface and Description
static interface	Formula.ArithmeticEquation
static interface	Formula.Equation

Classes in wytp.proof that implement Formula

Modifier and Type	Class and Description
static class	Formula.ArithmeticEquality
static class	Formula.Conjunct
static class	Formula.Disjunct
static class	Formula.Equality
static class	Formula.Inequality
static class	Formula.Invoke
static class	Formula.Is
static class	Formula.Quantifier
static class	Formula.Truth

Methods in wytp.proof that return Formula

Modifier and Type	Method and Description
Formula	Proof.State.allocate(Formula f) Ensure a given formula is properly allocated into this state.
Formula	Formula.clone(wybs.lang.SyntacticItem[] children)
Formula	Proof.Delta.Set.get(int ith) Get the ith truth in this set
Formula	Formula.Conjunct.get(int i)
Formula	Formula.Disjunct.get(int i)
Formula[]	Formula.Conjunct.getAll()
Formula[]	Formula.Disjunct.getAll()
Formula	Formula.Quantifier.getBody()

Methods in wytp.proof that return types with arguments of type Formula

Modifier and Type	Method and Description
List<Formula>	Proof.State.getDependencies() Get the formulae on which this step depends

Methods in wytp.proof with parameters of type Formula

Modifier and Type	Method and Description
Proof.Delta	Proof.Delta.add(Formula truth) Add a new formula to this delta
Proof.Delta.Set	Proof.Delta.Set.add(Formula truth) Add a truth to this set.
Formula	Proof.State.allocate(Formula f) Ensure a given formula is properly allocated into this state.
boolean	Proof.Delta.Set.contains(Formula truth) Check whether the given formula is contained within this set or not.
Proof.State	Proof.State.infer(Proof.Rule rule, Formula truth, Formula... dependencies) Infer a new fact from one or more existing facts.
Proof.State	Proof.State.infer(Proof.Rule rule, Formula truth, Formula... dependencies) Infer a new fact from one or more existing facts.
boolean	Proof.Delta.isAddition(Formula truth) Check whether or not a given formula is in the additions set
boolean	Proof.State.isKnown(Formula truth) Determine whether a truth is already known or not.
boolean	Proof.Delta.isRemoval(Formula truth) Check whether or not a given formula is in the removals set
Proof.State	Proof.State.refine(Proof.Rule rule, WyalFile.VariableDeclaration variable, WyalFile.Type type, Formula... dependencies) Refine the type of a given variable in this state.
Proof.Delta	Proof.Delta.remove(Formula truth) Remove a truth from this delta (e.g.
Proof.Delta.Set	Proof.Delta.Set.remove(Formula truth) Remove a formula from this set
Proof.State	Proof.State.subsume(Proof.Rule rule, Formula truth, Formula replacement, Formula... dependencies) Subsume a given truth by a replacement.
Proof.State	Proof.State.subsume(Proof.Rule rule, Formula truth, Formula replacement, Formula... dependencies) Subsume a given truth by a replacement.

Constructors in wytp.proof with parameters of type Formula

Constructor and Description
Conjunct(Formula... operands)
Disjunct(Formula... operands)
Quantifier(boolean sign, wybs.util.AbstractCompilationUnit.Tuple<WyalFile.VariableDeclaration> parameters, Formula body)
Quantifier(boolean sign, WyalFile.VariableDeclaration[] parameters, Formula body)
Quantifier(boolean sign, WyalFile.VariableDeclaration parameter, Formula body)

Uses of Formula in wytp.proof.rules

Methods in wytp.proof.rules that return Formula

Modifier and Type	Method and Description
Formula	CongruenceClosure.Assignment.getDependency()
<T> Formula[]	Simplification.inlineNestedArray(Formula[] parent, int index, Formula[] child)
Formula	Simplification.simplify(Formula f) Recursively simplify a given formula by applying the "standard" simplifications for each kind.
Formula[]	Simplification.simplify(Formula[] children)
Formula	Simplification.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.
Formula	Simplification.simplifyConjunct(Formula.Conjunct conjunct)
Formula	Simplification.simplifyDisjunct(Formula.Disjunct disjunct)
Formula	Simplification.simplifyEquality(Formula.Equality eq) Simplify a non-arithmetic equality by attempting to evaluate it.
Formula	Simplification.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	Simplification.simplifyInvoke(Formula.Invoke ivk)
Formula	Simplification.simplifyIs(Formula.Is e)
Formula	Simplification.simplifyQuantifier(Formula.Quantifier quantifier) Simplify a quantified formula.

Methods in wytp.proof.rules with parameters of type Formula

Modifier and Type	Method and Description
Proof.State	CongruenceClosure.apply(Proof.Delta.Set existingTruths, Proof.State head, Formula newTruth)
Proof.State	Simplification.apply(Proof.State head, Formula truth)
Proof.State	EqualityCaseAnalysis.apply(Proof.State state, Formula truth)
wybs.lang.SyntacticItem	CongruenceClosure.construct(Proof.Delta.Set existingTruths, Proof.State head, wybs.lang.SyntacticItem term, Formula newTruth, List<Formula> dependencies) When generating an entirely new term within a given rule (i.e.
<T> Formula[]	Simplification.inlineNestedArray(Formula[] parent, int index, Formula[] child)
<T> Formula[]	Simplification.inlineNestedArray(Formula[] parent, int index, Formula[] child)
WyalFile.Expr	CongruenceClosure.localConstruct(Proof.Delta.Set existingTruths, Proof.State head, WyalFile.Expr term, Formula newTruth, List<Formula> dependencies)
Formula	Simplification.simplify(Formula f) Recursively simplify a given formula by applying the "standard" simplifications for each kind.
Formula[]	Simplification.simplify(Formula[] children)

Method parameters in wytp.proof.rules with type arguments of type Formula

Modifier and Type	Method and Description
wybs.lang.SyntacticItem	CongruenceClosure.construct(Proof.Delta.Set existingTruths, Proof.State head, wybs.lang.SyntacticItem term, Formula newTruth, List<Formula> dependencies) When generating an entirely new term within a given rule (i.e.
WyalFile.Expr	CongruenceClosure.localConstruct(Proof.Delta.Set existingTruths, Proof.State head, WyalFile.Expr term, Formula newTruth, List<Formula> dependencies)

Constructors in wytp.proof.rules with parameters of type Formula

Constructor and Description
Assignment(WyalFile.Expr lhs, WyalFile.Expr rhs, Formula dep)

Uses of Formula in wytp.proof.rules.arithmetic

Methods in wytp.proof.rules.arithmetic that return Formula

Modifier and Type	Method and Description
Formula	InequalityIntroduction.closeOver(Formula.Inequality ith, Formula.Inequality jth) Close over two inequalities.

Methods in wytp.proof.rules.arithmetic with parameters of type Formula

Modifier and Type	Method and Description
Proof.State	InequalityIntroduction.apply(Proof.Delta.Set existingTruths, Proof.State state, Formula newTruth)

Uses of Formula in wytp.proof.rules.array

Methods in wytp.proof.rules.array with parameters of type Formula

Modifier and Type	Method and Description
Proof.State	ArrayIndexAxiom.apply(Proof.Delta.Set existingTruths, Proof.State head, Formula truth)
Proof.State	ArrayLengthAxiom.apply(Proof.State state, Formula truth)
Proof.State	ArrayIndexCaseAnalysis.apply(Proof.State state, Formula truth)
Proof.State	ArrayEqualityCaseAnalysis.apply(Proof.State state, Formula truth)
Proof.State	ArrayIndexAxiom.attemptInstantiation(Formula source, List<WyalFile.Expr.Operator> matches, Formula target, Proof.State state)
Proof.State	ArrayIndexAxiom.attemptInstantiationByArrayAccess(Formula truth, Proof.Delta.Set existingTruths, Proof.State state)
Proof.State	ArrayIndexAxiom.attemptInstantiationByEquation(Formula truth, Proof.Delta.Set existingTruths, Proof.State state)

Uses of Formula in wytp.proof.rules.function

Methods in wytp.proof.rules.function with parameters of type Formula

Modifier and Type	Method and Description
Proof.State	MacroExpansion.apply(Proof.State state, Formula truth)
Proof.State	FunctionCallAxiom.apply(Proof.State state, Formula truth)

Uses of Formula in wytp.proof.rules.logic

Methods in wytp.proof.rules.logic with parameters of type Formula

Modifier and Type	Method and Description
Proof.State[]	OrElimination.apply(Proof.State state, Formula truth)
Proof.State	AndElimination.apply(Proof.State head, Formula truth)

Uses of Formula in wytp.proof.rules.quantifier

Methods in wytp.proof.rules.quantifier that return Formula

Modifier and Type	Method and Description
protected Formula	ExistentialElimination.expandTypeInvariants(wybs.util.AbstractCompilationUnit.Tuple<WyalFile.VariableDeclaration> declarations, TypeSystem types) For a given sequence of variable declarations expand their type invariants as appropriate.

Methods in wytp.proof.rules.quantifier with parameters of type Formula

Modifier and Type	Method and Description
Proof.State	ExhaustiveQuantifierInstantiation.apply(Proof.Delta.Set existingTruths, Proof.State state, Formula newTruth)
Proof.State	ExistentialElimination.apply(Proof.State head, Formula truth)

Uses of Formula in wytp.proof.rules.record

Methods in wytp.proof.rules.record with parameters of type Formula

Modifier and Type	Method and Description
Proof.State	RecordEqualityCaseAnalysis.apply(Proof.State state, Formula truth)

Uses of Formula in wytp.proof.rules.type

Methods in wytp.proof.rules.type with parameters of type Formula

Modifier and Type	Method and Description
Proof.State	TypeTestNormalisation.apply(Proof.Delta.Set existingTruths, Proof.State head, Formula newTruth)
Proof.State	TypeTestClosure.apply(Proof.Delta.Set existingTruths, Proof.State head, Formula newTruth)

Uses of Formula in wytp.proof.util

Fields in wytp.proof.util with type parameters of type Formula

Modifier and Type	Field and Description
protected List<Formula>	AbstractProof.AbstractState.dependencies

Methods in wytp.proof.util that return Formula

Modifier and Type	Method and Description
Formula	DeltaProof.State.allocate(Formula truth)
static Formula	Formulae.and(Formula lhs, Formula rhs)
Formula	FastDelta.Set.get(int ith)
static Formula	Formulae.implies(Formula lhs, Formula rhs)
static Formula	Formulae.invert(Formula f) Logically invert a given formula.
static Formula	Formulae.or(Formula lhs, Formula rhs)
static Formula	Formulae.toFormula(WyalFile.Stmt stmt, TypeSystem types) Take a tree of statements and expressions, and return a formula.
static Formula[]	Formulae.toFormulae(WyalFile.Stmt[] stmts, TypeSystem types) Convert an array of statements into an array of (equivalent) formulae.

Methods in wytp.proof.util that return types with arguments of type Formula

Modifier and Type	Method and Description
List<Formula>	AbstractProof.AbstractState.getDependencies()

Methods in wytp.proof.util with parameters of type Formula

Modifier and Type	Method and Description
FastDelta	FastDelta.add(Formula truth)
FastDelta.Set	FastDelta.Set.add(Formula truth)
Formula	DeltaProof.State.allocate(Formula truth)
static Formula	Formulae.and(Formula lhs, Formula rhs)
abstract Proof.State	AbstractClosureRule.apply(Proof.Delta.Set existingTruths, Proof.State head, Formula truth)
abstract Proof.State	AbstractProofRule.apply(Proof.State head, Formula truth)
Proof.State	AbstractClosureRule.apply(Proof.State head, Formula truth)
boolean	FastDelta.Set.contains(Formula truth)
static Formula	Formulae.implies(Formula lhs, Formula rhs)
DeltaProof.State	DeltaProof.State.infer(Proof.Rule rule, Formula truth, Formula... dependencies)
DeltaProof.State	DeltaProof.State.infer(Proof.Rule rule, Formula truth, Formula... dependencies)
static Formula	Formulae.invert(Formula f) Logically invert a given formula.
boolean	FastDelta.isAddition(Formula truth)
boolean	DeltaProof.State.isKnown(Formula truth) Determine whether a given truth is known or not.
boolean	FastDelta.isRemoval(Formula truth)
static Formula	Formulae.or(Formula lhs, Formula rhs)
Proof.State	DeltaProof.State.refine(Proof.Rule rule, WyalFile.VariableDeclaration variable, WyalFile.Type type, Formula... dependencies)
FastDelta	FastDelta.remove(Formula truth)
FastDelta.Set	FastDelta.Set.remove(Formula truth)
DeltaProof.State	DeltaProof.State.subsume(Proof.Rule rule, Formula from, Formula to, Formula... deps) Subume one formula with one or more formulae.
DeltaProof.State	DeltaProof.State.subsume(Proof.Rule rule, Formula from, Formula to, Formula... deps) Subume one formula with one or more formulae.

Constructors in wytp.proof.util with parameters of type Formula

Constructor and Description
AbstractState(AbstractProof<T> proof, T parent, Proof.Rule rule, Formula... dependencies)
DeltaProof(WyalFile.Declaration.Assert assertion, wybs.lang.SyntacticHeap heap, Formula axiom)
Set(Formula f)
State(DeltaProof proof, Formula axiom)

Uses of Formula in wytp.types

Methods in wytp.types that return Formula

Modifier and Type	Method and Description
Formula	TypeSystem.extractInvariant(WyalFile.Type type, WyalFile.Expr root) Extracting the invariant (if any) from a given type.

Uses of Formula in wytp.types.extractors

Methods in wytp.types.extractors that return Formula

Modifier and Type	Method and Description
Formula	TypeInvariantExtractor.extract(WyalFile.Type type, WyalFile.Expr root)
Formula	TypeInvariantExtractor.extractTypeInvariantInner(WyalFile.Type type, WyalFile.Expr root, HashSet<WyalFile.Type> visited)