package tactics
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Type Members
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case class
AndLeftTactic
(mode: TacticApplyMode = UniqueFormula) extends Tactic[(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.
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case class
AndRightTactic
(mode: TacticApplyMode = UniqueFormula) extends 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.
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case class
ChainTactic
(hyp: String, target: Option[String] = None, substitution: Map[Var, LambdaExpression] = Map()) extends Tactic[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: HOLFormula) extends 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.
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case class
DestructTactic
(applyToLabel: String) extends Tactic[Any] with Product with Serializable
Attempts to decompose a formula by trying all tactics that don't require additional information.
Attempts to decompose a formula by trying all tactics that don't require additional information.
Note that this tactic only decomposes the outermost symbol, i.e. it only performs one step.
- applyToLabel
The label of the formula to be decomposed.
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case class
EqualityTactic
(equationLabel: String, formulaLabel: String, leftToRight: Option[Boolean] = None, targetFormula: Option[HOLFormula] = None) extends Tactic[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
.
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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.
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case class
ExistsRightTactic
(mode: TacticApplyMode = UniqueFormula, terms: Seq[LambdaExpression], instantiateOnce: Boolean) extends Tactic[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 FocusTactical (index: Either[Int, OpenAssumptionIndex]) extends Tactical[Unit] with Product with Serializable
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case class
ForallLeftTactic
(mode: TacticApplyMode = UniqueFormula, terms: Seq[LambdaExpression], instantiateOnce: Boolean) extends Tactic[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.
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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.
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case class
ImpLeftTactic
(mode: TacticApplyMode = UniqueFormula) extends 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 Tactic[(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.
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case class
InductionTactic
(mode: TacticApplyMode, v: Var)(implicit ctx: Context) extends Tactic[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 at.logic.gapt.proofs.Context. Used to find the constructors of inductive types.
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case class
InsertTactic
(insertion: LKProof) extends Tactic[Unit] with Product with Serializable
Inserts an at.logic.gapt.proofs.lk.LKProof if the insertion sequent subsumes the sequent of the subgoal.
Inserts an at.logic.gapt.proofs.lk.LKProof if the insertion sequent subsumes the sequent of the subgoal.
- insertion
The at.logic.gapt.proofs.lk.LKProof to be inserted. Its end sequent must subsume the current goal.
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case class
NegLeftTactic
(mode: TacticApplyMode = UniqueFormula) extends Tactic[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 Tactic[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.
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case class
OrLeftTactic
(mode: TacticApplyMode = UniqueFormula) extends 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.
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case class
OrRightTactic
(mode: TacticApplyMode = UniqueFormula) extends Tactic[(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 RenameTactic (oldLabel: String, newLabel: String) extends Tactic[Unit] with Product with Serializable
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case class
RepeatTactic
[T](tact: Tactical[T]) extends Tactical[Unit] with Product with Serializable
Applies the given Tactical to the proof state until it fails.
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case class
RewriteTactic
(equations: Traversable[(String, Boolean)], target: Option[String], fixedSubst: Map[Var, LambdaExpression], once: Boolean) extends Tactic[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 Tactic[Var]
- case class UnfoldTactic (target: String, definition: String, definitions: Seq[String])(implicit ctx: Context) extends Tactic[Unit] with Product with Serializable
- case class UnfoldTacticHelper (definition: String, definitions: Seq[String])(implicit ctx: Context) extends Product with Serializable
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case class
WeakeningLeftTactic
(applyToLabel: String) extends Tactic[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.
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case class
WeakeningRightTactic
(applyToLabel: String) extends Tactic[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
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object
BottomAxiomTactic
extends Tactic[Unit] with Product with Serializable
Closes a goal of the form ⊥, Γ :- Δ
-
object
EscargotTactic
extends Tactic[Unit] with Product with Serializable
Calls Escargot on the subgoal.
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object
LogicalAxiomTactic
extends Tactic[Unit] with Product with Serializable
Closes a goal of the form A, Γ :- Δ, Δ
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object
PropTactic
extends Tactic[Unit] with Product with Serializable
Calls the GAPT tableau prover on the subgoal.
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object
Prover9Tactic
extends Tactic[Unit] with Product with Serializable
Calls prover9 on the subgoal.
- object QuasiPropTactic extends Tactic[Unit] with Product with Serializable
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object
ReflexivityAxiomTactic
extends Tactic[Unit] with Product with Serializable
Closes a goal of the form Γ :- Δ, s = s
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object
SkipTactical
extends Tactical[Unit] with Product with Serializable
Trivial "unit" tactical.
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object
TopAxiomTactic
extends Tactic[Unit] with Product with Serializable
Closes a goal of the form Γ :- Δ, ⊤