package tactics
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Type Members
- case class AnalyticInductionTactic(axioms: AxiomFactory, prover: ResolutionProver)(implicit ctx: MutableContext) extends Tactical1[Unit] with Product with Serializable
Calls the analytic induction prover on the subgoal
- case class AndLeftTactic(mode: TacticApplyMode = UniqueFormula) extends Tactical1[(String, String)] with Product with Serializable
Decomposes a conjunction in the antecedent of a goal.
Decomposes a conjunction in the antecedent of a goal.
- mode
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
- case class AndRightTactic(mode: TacticApplyMode = UniqueFormula) extends Tactical1[Unit] with BinaryTactic[Unit] with Product with Serializable
Decomposes a conjunction in the succedent of a goal.
Decomposes a conjunction in the succedent of a goal.
- mode
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
- case class ChainTactic(hyp: String, target: TacticApplyMode = UniqueFormula, substitution: Map[Var, Expr] = Map()) extends Tactical1[Unit] with Product with Serializable
Performs backwards chaining: A goal of the form
∀x (P(x) → Q(x)), Γ :- Δ, Q(t)
is replaced by the goal∀x (P(x) → Q(x)), Γ :- Δ, P(t)
. - case class CutTactic(cutLabel: String, cutFormula: Formula) extends Tactical1[Unit] with BinaryTactic[Unit] with Product with Serializable
Introduces a cut, creating two new subgoals.
Introduces a cut, creating two new subgoals.
- cutLabel
The label for the cut formula.
- cutFormula
The cut formula.
- case class EqualityTactic(equationLabel: String, formulaLabel: String, leftToRight: Option[Boolean] = None, targetFormula: Option[Formula] = None) extends Tactical1[Unit] with Product with Serializable
Applies an equation in a goal.
Applies an equation in a goal.
- equationLabel
The label of the equation.
- formulaLabel
The label of the formula the equation is to be used on.
- leftToRight
If
Some(true)
, the equations = t
will be used to rewrites
tot
, and the other way around for Some(false). IfNone
, the tactic will attempt to decide the direction automatically.- targetFormula
If
Some(f)
, the tactic will attempt to producef
through application of the equality. Otherwise it will replace as many occurrences as possible according toleftToRight
.
- case class ExistsLeftTactic(mode: TacticApplyMode = UniqueFormula, eigenVariable: Option[Var] = None) extends StrongQuantTactic with Product with Serializable
Decomposes an existential quantifier in the antecedent of a goal.
Decomposes an existential quantifier in the antecedent of a goal.
- mode
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
- eigenVariable
If Some(v), the rule will attempt to use v as the eigenvariable. Otherwise it will automatically pick one.
- case class ExistsRightTactic(mode: TacticApplyMode = UniqueFormula, terms: Seq[Expr], instantiateOnce: Boolean) extends Tactical1[String] with Product with Serializable
Decomposes a block of existential quantifiers in the antecedent of a goal.
Decomposes a block of existential quantifiers in the antecedent of a goal.
- mode
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
- terms
Instantiations for the quantifiers in the block.
- instantiateOnce
Whether the quantified formula should be forgotten after instantiating.
- case class FocusTactic(index: Either[Int, OpenAssumptionIndex]) extends Tactic[Unit] with Product with Serializable
- case class ForallLeftTactic(mode: TacticApplyMode = UniqueFormula, terms: Seq[Expr], instantiateOnce: Boolean) extends Tactical1[String] with Product with Serializable
Decomposes a block of universal quantifiers in the succedent of a goal.
Decomposes a block of universal quantifiers in the succedent of a goal.
- mode
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
- terms
Instantiations for the quantifiers in the block.
- instantiateOnce
Whether the quantified formula should be forgotten after instantiating.
- case class ForallRightTactic(mode: TacticApplyMode = UniqueFormula, eigenVariable: Option[Var] = None) extends StrongQuantTactic with Product with Serializable
Decomposes a universal quantifier in the succedent of a goal.
Decomposes a universal quantifier in the succedent of a goal.
- mode
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
- eigenVariable
If Some(v), the rule will attempt to use v as the eigenvariable. Otherwise it will automatically pick one.
- case class ForwardChain(lemmaLabel: String, targetMode: TacticApplyMode = UniqueFormula, substitution: Map[Var, Expr] = Map()) extends Tactical1[Unit] with Product with Serializable
Creates forward chaining tactics.
Creates forward chaining tactics.
A forward chaining tactic replaces a goal of the form
Γ, A(t), ∀x(A(t) → B(t)) ⇒ Δ
byΓ, A(t), ∀x(A(t) → B(t)), B(t) ⇒ Δ
. - case class ImpLeftTactic(mode: TacticApplyMode = UniqueFormula) extends Tactical1[Unit] with BinaryTactic[Unit] with Product with Serializable
Decomposes an implication in the antecedent of a goal.
Decomposes an implication in the antecedent of a goal.
- mode
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
- case class ImpRightTactic(mode: TacticApplyMode = UniqueFormula) extends Tactical1[(String, String)] with Product with Serializable
Decomposes an implication in the succedent of a goal.
Decomposes an implication in the succedent of a goal.
- mode
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
- case class InductionTactic(mode: TacticApplyMode, v: Var, eigenVariables: Map[Const, Vector[Var]] = Map())(implicit ctx: Context) extends Tactical1[Unit] with Product with Serializable
Reduces a subgoal via induction.
Reduces a subgoal via induction.
- mode
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
- ctx
A gapt.proofs.context.Context. Used to find the constructors of inductive types.
- case class InsertTactic(insertion: LKProof) extends Tactical1[Unit] with Product with Serializable
Inserts an gapt.proofs.lk.LKProof if the insertion sequent subsumes the sequent of the subgoal.
Inserts an gapt.proofs.lk.LKProof if the insertion sequent subsumes the sequent of the subgoal.
- insertion
The gapt.proofs.lk.LKProof to be inserted. Its end sequent must subsume the current goal.
- case class NegLeftTactic(mode: TacticApplyMode = UniqueFormula) extends Tactical1[String] with Product with Serializable
Decomposes a negation in the antecedent of a goal.
Decomposes a negation in the antecedent of a goal.
- mode
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
- case class NegRightTactic(mode: TacticApplyMode = UniqueFormula) extends Tactical1[String] with Product with Serializable
Decomposes a negation in the succedent of a goal.
Decomposes a negation in the succedent of a goal.
- mode
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
- case class OrLeftTactic(mode: TacticApplyMode = UniqueFormula) extends Tactical1[Unit] with BinaryTactic[Unit] with Product with Serializable
Decomposes a disjunction in the antecedent of a goal.
Decomposes a disjunction in the antecedent of a goal.
- mode
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
- case class OrRightTactic(mode: TacticApplyMode = UniqueFormula) extends Tactical1[(String, String)] with Product with Serializable
Decomposes a disjunction in the succedent of a goal.
Decomposes a disjunction in the succedent of a goal.
- mode
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
- case class ProofLinkTactic(proofName: String)(implicit ctx: Context) extends Tactical1[Unit] with Product with Serializable
Closes a goal with a proof link
Closes a goal with a proof link
- proofName
The name of the proof proving the goal.
- case class RenameTactic(oldLabel: String, newLabel: String) extends Tactical1[Unit] with Product with Serializable
- case class RepeatTactic[T](tact: Tactic[T]) extends Tactic[Unit] with Product with Serializable
Applies the given Tactic to the proof state until it fails.
- case class ReplaceTactic(target: String, u: Expr, v: Expr)(implicit ctx: Context) extends Tactical1[Unit] with Product with Serializable
Replaces all occurrences of a given term another term.
Replaces all occurrences of a given term another term.
- target
The label of the formula in which to replace the terms.
- u
The term to be replaced.
- v
The term by which u is replaced.
- ctx
A context.
- case class ResolutionProverTactic(prover: Prover, viaExpansionProof: Boolean = true, deskolemize: Boolean = false)(implicit ctx: MutableContext) extends Tactical1[Unit] with Product with Serializable
- case class RewriteTactic(equations: Iterable[(String, Boolean)], target: Option[String], fixedSubst: Map[Var, Expr], once: Boolean) extends Tactical1[Unit] with Product with Serializable
Rewrites using the specified equations at the target, either once or as often as possible.
Rewrites using the specified equations at the target, either once or as often as possible.
- equations
Universally quantified equations on the antecedent, with direction (left-to-right?)
- target
Formula to rewrite.
- once
Rewrite exactly once?
- abstract class StrongQuantTactic extends Tactical1[Var]
- case class SubstTactic(mode: TacticApplyMode) extends Tactical1[Unit] with Product with Serializable
- case class SuperpositionInductionTactic(opts: SpinOptions, problem: TipProblem)(implicit ctx: MutableContext) extends Tactical1[Unit] with Product with Serializable
- case class UnfoldTactic(target: String, definitions: Seq[String], maxSteps: Option[Int])(implicit ctx: Context) extends Tactical1[Unit] with Product with Serializable
- case class UnfoldTacticHelper(definitions: Seq[String], maxSteps: Option[Int] = None)(implicit ctx: Context) extends Product with Serializable
- case class WeakeningLeftTactic(applyToLabel: String) extends Tactical1[Unit] with Product with Serializable
Removes a formula from the antecedent of a goal.
Removes a formula from the antecedent of a goal.
- applyToLabel
The label of the formula to be removed.
- case class WeakeningRightTactic(applyToLabel: String) extends Tactical1[Unit] with Product with Serializable
Removes a formula from the succedent of a goal.
Removes a formula from the succedent of a goal.
- applyToLabel
The label of the formula to be removed.
Value Members
- object AnalyticInductionTactic extends Serializable
- object BottomAxiomTactic extends Tactical1[Unit] with Product with Serializable
Closes a goal of the form ⊥, Γ :- Δ
- object LogicalAxiomTactic extends Tactical1[Unit] with Product with Serializable
Closes a goal of the form A, Γ :- Δ, Δ
- object PropTactic extends Tactical1[Unit] with Product with Serializable
Calls the GAPT tableau prover on the subgoal.
- object QuasiPropTactic extends Tactical1[Unit] with Product with Serializable
- object ReflexivityAxiomTactic extends Tactical1[Unit] with Product with Serializable
Closes a goal of the form Γ :- Δ, s = s
- object TopAxiomTactic extends Tactical1[Unit] with Product with Serializable
Closes a goal of the form Γ :- Δ, ⊤
This is the API documentation for GAPT.
The main package is gapt.