package tactics

Content Hierarchy
Ordering
  1. Alphabetic
Visibility
  1. Public
  2. All

Type Members

  1. 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

  2. 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.

  3. 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.

  4. 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).

  5. 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.

  6. 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 equation s = t will be used to rewrite s to t, and the other way around for Some(false). If None, the tactic will attempt to decide the direction automatically.

    targetFormula

    If Some(f), the tactic will attempt to produce f through application of the equality. Otherwise it will replace as many occurrences as possible according to leftToRight.

  7. 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.

  8. 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.

  9. case class FocusTactic(index: Either[Int, OpenAssumptionIndex]) extends Tactic[Unit] with Product with Serializable
  10. 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.

  11. 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.

  12. 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 by Γ, A(t), ∀x(A(t) → B(t)), B(t) ⇒ Δ.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  21. 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.

  22. case class RenameTactic(oldLabel: String, newLabel: String) extends Tactical1[Unit] with Product with Serializable
  23. 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.

    Applies the given Tactic to the proof state until it fails.

    Note that the tactical is not required to succeed at least once, i.e. it might fail immediately.

    tact

    The Tactic to be repeated.

  24. 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.

  25. case class ResolutionProverTactic(prover: Prover, viaExpansionProof: Boolean = true, deskolemize: Boolean = false)(implicit ctx: MutableContext) extends Tactical1[Unit] with Product with Serializable
  26. 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?

  27. abstract class StrongQuantTactic extends Tactical1[Var]
  28. case class SubstTactic(mode: TacticApplyMode) extends Tactical1[Unit] with Product with Serializable
  29. case class SuperpositionInductionTactic(opts: SpinOptions, problem: TipProblem)(implicit ctx: MutableContext) extends Tactical1[Unit] with Product with Serializable
  30. case class UnfoldTactic(target: String, definitions: Seq[String], maxSteps: Option[Int])(implicit ctx: Context) extends Tactical1[Unit] with Product with Serializable
  31. case class UnfoldTacticHelper(definitions: Seq[String], maxSteps: Option[Int] = None)(implicit ctx: Context) extends Product with Serializable
  32. 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.

  33. 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

  1. object AnalyticInductionTactic extends Serializable
  2. object BottomAxiomTactic extends Tactical1[Unit] with Product with Serializable

    Closes a goal of the form ⊥, Γ :- Δ

  3. object LogicalAxiomTactic extends Tactical1[Unit] with Product with Serializable

    Closes a goal of the form A, Γ :- Δ, Δ

  4. object PropTactic extends Tactical1[Unit] with Product with Serializable

    Calls the GAPT tableau prover on the subgoal.

  5. object QuasiPropTactic extends Tactical1[Unit] with Product with Serializable
  6. object ReflexivityAxiomTactic extends Tactical1[Unit] with Product with Serializable

    Closes a goal of the form Γ :- Δ, s = s

  7. object TopAxiomTactic extends Tactical1[Unit] with Product with Serializable

    Closes a goal of the form Γ :- Δ, ⊤

Ungrouped