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at.logic.gapt.proofs

lk

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package lk

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package.scala
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Type Members

  1. case class AndLeftRule(subProof: LKProof, aux1: SequentIndex, aux2: SequentIndex) extends UnaryLKProof with CommonRule with Product with Serializable

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    An LKProof ending with a conjunction on the left:

            (π)
        A, B, Γ :- Δ
       --------------
       A ∧ B, Γ :- Δ
    

    An LKProof ending with a conjunction on the left:

            (π)
        A, B, Γ :- Δ
       --------------
       A ∧ B, Γ :- Δ
    

    subProof

    The subproof π.

    aux1

    The index of A.

    aux2

    The index of B.

  2. case class AndRightRule(leftSubProof: LKProof, aux1: SequentIndex, rightSubProof: LKProof, aux2: SequentIndex) extends BinaryLKProof with CommonRule with Product with Serializable

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    An LKProof ending with a conjunction on the right:

       (π1)         (π2)
      Γ :- Δ, A    Π :- Λ, B
    --------------------------
        Γ, Π :- Δ, Λ, A∧B
    

    An LKProof ending with a conjunction on the right:

       (π1)         (π2)
      Γ :- Δ, A    Π :- Λ, B
    --------------------------
        Γ, Π :- Δ, Λ, A∧B
    

    leftSubProof

    The proof π1.

    aux1

    The index of A.

    rightSubProof

    The proof π2

    aux2

    The index of B.

  3. abstract class BinaryLKProof extends LKProof

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    An LKProof deriving a sequent from two other sequents:

        (π1)     (π2)
       Γ :- Δ   Γ' :- Δ'
      ------------------
           Π :- Λ
    

    An LKProof deriving a sequent from two other sequents:

        (π1)     (π2)
       Γ :- Δ   Γ' :- Δ'
      ------------------
           Π :- Λ
    

  4. trait CommonRule extends LKProof with ContextRule[HOLFormula, LKProof]

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  5. case class ContractionLeftRule(subProof: LKProof, aux1: SequentIndex, aux2: SequentIndex) extends ContractionRule with Product with Serializable

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    An LKProof ending with a left contraction:

            (π)
        A, A, Γ :- Δ
       --------------
         A, Γ :- Δ
    

    An LKProof ending with a left contraction:

            (π)
        A, A, Γ :- Δ
       --------------
         A, Γ :- Δ
    

    subProof

    The subproof π.

    aux1

    The index of one occurrence of A.

    aux2

    The index of the other occurrence of A.

  6. case class ContractionRightRule(subProof: LKProof, aux1: SequentIndex, aux2: SequentIndex) extends ContractionRule with Product with Serializable

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    An LKProof ending with a right contraction:

            (π)
        Γ :- Δ, A, A
       --------------
         Γ :- Δ, A
    

    An LKProof ending with a right contraction:

            (π)
        Γ :- Δ, A, A
       --------------
         Γ :- Δ, A
    

    subProof

    The subproof π.

    aux1

    The index of one occurrence of A.

    aux2

    The index of the other occurrence of A.

  7. abstract class ContractionRule extends UnaryLKProof with CommonRule

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  8. class ConvenienceConstructor extends AnyRef

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    Class for reducing boilerplate code in LK companion objects.

  9. case class CutRule(leftSubProof: LKProof, aux1: SequentIndex, rightSubProof: LKProof, aux2: SequentIndex) extends BinaryLKProof with CommonRule with Product with Serializable

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    An LKProof ending with a cut:

         (π1)         (π2)
       Γ :- Δ, A   A, Π :- Λ
      ------------------------
           Γ, Π :- Δ, Λ
    

    An LKProof ending with a cut:

         (π1)         (π2)
       Γ :- Δ, A   A, Π :- Λ
      ------------------------
           Γ, Π :- Δ, Λ
    

    leftSubProof

    The proof π1.

    aux1

    The index of A in π1.

    rightSubProof

    The proof π2.

    aux2

    The index of A in π2.

  10. class DefinitionElimination extends Function[LambdaExpression, LambdaExpression]

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  11. case class DefinitionLeftRule(subProof: LKProof, aux: SequentIndex, main: HOLFormula) extends UnaryLKProof with CommonRule with Product with Serializable

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    An LKProof ending with a definition on the left:

    An LKProof ending with a definition on the left:

          (π)
       A, Γ :- Δ
      -----------d:l
       B, Γ :- Δ
    

    Currently, the formulas A and B can be completely arbitrary.

    subProof

    The proof π.

    aux

    The index of A in the antecedent.

    main

    The formula B that A is to be replaced with.

  12. case class DefinitionRightRule(subProof: LKProof, aux: SequentIndex, main: HOLFormula) extends UnaryLKProof with CommonRule with Product with Serializable

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    An LKProof ending with a definition on the right:

    An LKProof ending with a definition on the right:

          (π)
       Γ :- Δ, A
      -----------d:l
       Γ :- Δ, B
    

    Currently, the formulas A and B can be completely arbitrary.

    subProof

    The proof π.

    aux

    The index of A in the succedent.

    main

    The formula B that A is to be replaced with.

  13. trait Eigenvariable extends AnyRef

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    Use this trait for rules that use eigenvariables.

  14. case class EqualityLeftRule(subProof: LKProof, eq: SequentIndex, aux: SequentIndex, replacementContext: Abs) extends EqualityRule with Product with Serializable

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    An LKProof ending with a left equality rule.

    An LKProof ending with a left equality rule. There are two possible cases according to which direction the rule is applied in:

               (π)                            (π)
       A[s], s = t, Γ :- Δ            A[t], s = t, Γ :- Δ
      ---------------------eq:l      ---------------------eq:l
       A[t], s = t, Γ :- Δ            A[s], s = t, Γ :- Δ
    
    

    In either case, the rule only replaces term occurrences at parallel positions. These positions are given by the positions argument.

    subProof

    The subproof π.

    eq

    The index of s = t.

    aux

    The index of the formula in which the replacement is to be performed.

    replacementContext

    A term λx.A[x] that designates the positions to be replaced.

  15. case class EqualityRightRule(subProof: LKProof, eq: SequentIndex, aux: SequentIndex, replacementContext: Abs) extends EqualityRule with Product with Serializable

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    An LKProof ending with a right equality rule.

    An LKProof ending with a right equality rule. There are two possible cases according to which direction the rule is applied in:

               (π)                            (π)
       s = t, Γ :- Δ, A[s]            s = t, Γ :- Δ, A[t]
      ---------------------eq:r      ---------------------eq:r
       s = t, Γ :- Δ, A[t]            s = t, Γ :- Δ, A[s]
    

    In either case, the rule only replaces term occurrences at parallel positions. These positions are given by the positions argument.

    subProof

    The subproof π.

    eq

    The index of s = t.

    aux

    The index of the formula in which the replacement is to be performed.

    replacementContext

    A term λx.A[x] that designates the positions to be replaced.

  16. abstract class EqualityRule extends UnaryLKProof with CommonRule

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    Abstract class that performs most of the construction of left and right equality rules.

  17. case class ExistsLeftRule(subProof: LKProof, aux: SequentIndex, eigenVariable: Var, quantifiedVariable: Var) extends UnaryLKProof with CommonRule with Eigenvariable with Product with Serializable

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    An LKProof ending with an existential quantifier on the left:

              (π)
         A[x\α], Γ :- Δ
        ---------------∀:r
          ∃x.A Γ :- Δ
    
    This rule is only applicable if the eigenvariable condition is satisfied: α must not occur freely in Γ :- Δ.

    An LKProof ending with an existential quantifier on the left:

              (π)
         A[x\α], Γ :- Δ
        ---------------∀:r
          ∃x.A Γ :- Δ
    
    This rule is only applicable if the eigenvariable condition is satisfied: α must not occur freely in Γ :- Δ.

    subProof

    The proof π.

    aux

    The index of A[x\α].

    eigenVariable

    The variable α.

    quantifiedVariable

    The variable x.

  18. case class ExistsRightRule(subProof: LKProof, aux: SequentIndex, A: HOLFormula, term: LambdaExpression, v: Var) extends UnaryLKProof with CommonRule with Product with Serializable

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    An LKProof ending with an existential quantifier on the right:

               (π)
         Γ :- Δ, A[x\t]
        ----------------∃:r
          Γ :- Δ, ∃x.A
    

    An LKProof ending with an existential quantifier on the right:

               (π)
         Γ :- Δ, A[x\t]
        ----------------∃:r
          Γ :- Δ, ∃x.A
    

    subProof

    The proof π.

    aux

    The index of A[x\t].

    A

    The formula A.

    term

    The term t.

    v

    The variable x.

  19. case class ForallLeftRule(subProof: LKProof, aux: SequentIndex, A: HOLFormula, term: LambdaExpression, v: Var) extends UnaryLKProof with CommonRule with Product with Serializable

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    An LKProof ending with a universal quantifier on the left:

               (π)
         A[x\t], Γ :- Δ
        ----------------∀:l
          ∀x.A, Γ :- Δ
    

    An LKProof ending with a universal quantifier on the left:

               (π)
         A[x\t], Γ :- Δ
        ----------------∀:l
          ∀x.A, Γ :- Δ
    

    subProof

    The proof π.

    aux

    The index of A[x\t].

    A

    The formula A.

    term

    The term t.

    v

    The variable x.

  20. case class ForallRightRule(subProof: LKProof, aux: SequentIndex, eigenVariable: Var, quantifiedVariable: Var) extends UnaryLKProof with CommonRule with Eigenvariable with Product with Serializable

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    An LKProof ending with a universal quantifier on the right:

              (π)
         Γ :- Δ, A[x\α]
        ---------------∀:r
         Γ :- Δ, ∀x.A
    
    This rule is only applicable if the eigenvariable condition is satisfied: α must not occur freely in Γ :- Δ.

    An LKProof ending with a universal quantifier on the right:

              (π)
         Γ :- Δ, A[x\α]
        ---------------∀:r
         Γ :- Δ, ∀x.A
    
    This rule is only applicable if the eigenvariable condition is satisfied: α must not occur freely in Γ :- Δ.

    subProof

    The proof π.

    aux

    The index of A[x\α].

    eigenVariable

    The variable α.

    quantifiedVariable

    The variable x.

  21. case class ImpLeftRule(leftSubProof: LKProof, aux1: SequentIndex, rightSubProof: LKProof, aux2: SequentIndex) extends BinaryLKProof with CommonRule with Product with Serializable

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    An LKProof ending with an implication on the left:

        (π1)         (π2)
      Γ :- Δ, A    B, Π :- Λ
    --------------------------
        A→B, Γ, Π :- Δ, Λ
    

    An LKProof ending with an implication on the left:

        (π1)         (π2)
      Γ :- Δ, A    B, Π :- Λ
    --------------------------
        A→B, Γ, Π :- Δ, Λ
    

    leftSubProof

    The proof π1.

    aux1

    The index of A.

    rightSubProof

    The proof π2

    aux2

    The index of B.

  22. case class ImpRightRule(subProof: LKProof, aux1: SequentIndex, aux2: SequentIndex) extends UnaryLKProof with CommonRule with Product with Serializable

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    An LKProof ending with an implication on the right:

            (π)
        A, Γ :- Δ, B
       --------------
        Γ :- Δ, A → B
    

    An LKProof ending with an implication on the right:

            (π)
        A, Γ :- Δ, B
       --------------
        Γ :- Δ, A → B
    

    subProof

    The subproof π.

    aux1

    The index of A.

    aux2

    The index of B.

  23. case class InductionCase(proof: LKProof, constructor: Const, hypotheses: Seq[SequentIndex], eigenVars: Seq[Var], conclusion: SequentIndex) extends Product with Serializable

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    Proof that a given data type constructor c preserves a formula F:

    Proof that a given data type constructor c preserves a formula F:

                                     (π)
    F(x,,1,,), F(x,,2,,), ..., F(x,,n,,), Γ :- Δ, F(c(x,,1,,,...,x,,n,,,y,,1,,,...,y,,n,,))
    

    The variables xi and yi are eigenvariables; xi are the eigenvariables of the same type as the inductive data type, yi are the other arguments of the constructor c. They can come in any order in the constructor.

    proof

    The LKProof ending in the sequent of this case.

    constructor

    The constructor c of the inductive data type that we're considering.

    hypotheses

    Indices of F(x1), ..., F(xn)

    eigenVars

    The eigenvariables of this case: x1, ..., xn, y1, ..., yn (these need to correspond to the order in c)

    conclusion

    Index of F(c(x1,...,xn,y1,...,yn))

  24. case class InductionRule(cases: Seq[InductionCase], mainFormula: HOLFormula) extends LKProof with CommonRule with Product with Serializable

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    An LKProof ending with an induction rule:

      (π,,1,,)   (π,,2,,)           (π,,n,,)
    case 1      case 2     ...     case n
    -------------------------------------(ind)
    Γ :- Δ, ∀x: indTy, F(x)
    

    An LKProof ending with an induction rule:

      (π,,1,,)   (π,,2,,)           (π,,n,,)
    case 1      case 2     ...     case n
    -------------------------------------(ind)
    Γ :- Δ, ∀x: indTy, F(x)
    

    This induction rule can handle inductive data types. The cases are proofs that the various type constructors preserve the formula we want to prove. They are provided via the InductionCase class.

    cases

    A sequence of proofs showing that each type constructor preserves the validity of the main formula.

    mainFormula

    The formula we want to prove via induction.

  25. abstract class InitialSequent extends LKProof

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    An LKProof consisting of a single sequent:

        --------ax
         Γ :- Δ
    

    An LKProof consisting of a single sequent:

        --------ax
         Γ :- Δ
    

  26. class InterpolationException extends Exception

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  27. abstract class LKProof extends SequentProof[HOLFormula, LKProof]

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  28. class LKProofReplacer extends LKVisitor[Unit]

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  29. class LKProofSubstitutable extends Substitutable[Substitution, LKProof, LKProof]

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    Class that describes how LKProofs can be substituted.

  30. class LKRuleCreationException extends Exception

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  31. class LKToLKsk extends Logger

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  32. trait LKVisitor[T] extends AnyRef

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    Implementation of the visitor pattern for at.logic.gapt.proofs.lk.LKProof.

    Implementation of the visitor pattern for at.logic.gapt.proofs.lk.LKProof. Proof transformations can implement this trait to reduce boilerplate code.

    T

    Type of additional arguments that may be used in the transformation.

  33. case class LogicalAxiom(A: HOLFormula) extends InitialSequent with Product with Serializable

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    An LKProof consisting of a logical axiom:

       --------ax
        A :- A
    
    with A atomic.

    An LKProof consisting of a logical axiom:

       --------ax
        A :- A
    
    with A atomic.

    A

    The atom A.

  34. case class NegLeftRule(subProof: LKProof, aux: SequentIndex) extends UnaryLKProof with CommonRule with Product with Serializable

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    Index of the left cut formula or the formula itself.

    Index of the left cut formula or the formula itself. An LKProof ending with a negation on the left:

          (π)
       Γ :- Δ, A
      -----------¬:l
      ¬A, Γ :- Δ
    

    subProof

    The proof π.

    aux

    The index of A in the succedent.

  35. case class NegRightRule(subProof: LKProof, aux: SequentIndex) extends UnaryLKProof with CommonRule with Product with Serializable

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    An LKProof ending with a negation on the right:Index of the left cut formula or the formula itself.

    An LKProof ending with a negation on the right:Index of the left cut formula or the formula itself.

          (π)
       A, Γ :- Δ
      -----------¬:r
      Γ :- Δ, ¬A
    

    subProof

    The proof π.

    aux

    The index of A in the antecedent.

  36. case class OrLeftRule(leftSubProof: LKProof, aux1: SequentIndex, rightSubProof: LKProof, aux2: SequentIndex) extends BinaryLKProof with CommonRule with Product with Serializable

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    An LKProof ending with a disjunction on the left:

        (π1)         (π2)
      A, Γ :- Δ    B, Π :- Λ
    --------------------------
        A∨B, Γ, Π :- Δ, Λ
    

    An LKProof ending with a disjunction on the left:

        (π1)         (π2)
      A, Γ :- Δ    B, Π :- Λ
    --------------------------
        A∨B, Γ, Π :- Δ, Λ
    

    leftSubProof

    The proof π1.

    aux1

    The index of A.

    rightSubProof

    The proof π2

    aux2

    The index of B.

  37. case class OrRightRule(subProof: LKProof, aux1: SequentIndex, aux2: SequentIndex) extends UnaryLKProof with CommonRule with Product with Serializable

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    An LKProof ending with a disjunction on the right:

            (π)
        Γ :- Δ, A, B
       --------------
        Γ :- Δ, A ∨ B
    

    An LKProof ending with a disjunction on the right:

            (π)
        Γ :- Δ, A, B
       --------------
        Γ :- Δ, A ∨ B
    

    subProof

    The subproof π.

    aux1

    The index of A.

    aux2

    The index of B.

  38. class ProofBuilder extends AnyRef

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    Class for convenient construction of proofs.

    Class for convenient construction of proofs. Allows you to write proofs post-order style (à la Bussproofs). Example:

    (ProofBuilder
    c LogicalAxiom(A)
    c LogicalAxiom(B)
    u (WeakeningLeftRule(_, C))
    b (AndRightRule(_,_, And(A, B))
    qed)
    
    The constructor is private, so the only way to instantiate this class is by using the ProofBuilder object. This means that the stack will always be empty in the beginning.

  39. class ReductiveCutElimException extends Exception

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  40. class ReductiveCutElimination extends AnyRef

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  41. case class ReflexivityAxiom(s: LambdaExpression) extends InitialSequent with Product with Serializable

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    An LKProof consisting of a reflexivity axiom:

       ------------ax
         :- s = s
    
    with s a term.

    An LKProof consisting of a reflexivity axiom:

       ------------ax
         :- s = s
    
    with s a term.

    s

    The term s.

  42. trait SolveUtils extends AnyRef

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  43. case class TheoryAxiom(conclusion: Sequent[HOLAtom]) extends InitialSequent with Product with Serializable

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  44. abstract class UnaryLKProof extends LKProof

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    An LKProof deriving a sequent from another sequent:

           (π)
         Γ :- Δ
       ----------
        Γ' :- Δ'
    

    An LKProof deriving a sequent from another sequent:

           (π)
         Γ :- Δ
       ----------
        Γ' :- Δ'
    

  45. case class WeakeningLeftRule(subProof: LKProof, formula: HOLFormula) extends UnaryLKProof with CommonRule with Product with Serializable

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    An LKProof ending with a left weakening:

           (π)
          Γ :- Δ
        ---------w:l
        A, Γ :- Δ
    

    An LKProof ending with a left weakening:

           (π)
          Γ :- Δ
        ---------w:l
        A, Γ :- Δ
    

    subProof

    The subproof π.

    formula

    The formula A.

  46. case class WeakeningRightRule(subProof: LKProof, formula: HOLFormula) extends UnaryLKProof with CommonRule with Product with Serializable

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    An LKProof ending with a right weakening:

           (π)
          Γ :- Δ
        ---------w:r
        Γ :- Δ, A
    

    An LKProof ending with a right weakening:

           (π)
          Γ :- Δ
        ---------w:r
        Γ :- Δ, A
    

    subProof

    The subproof π.

    formula

    The formula A.

Value Members

  1. object AndLeftMacroRule extends ConvenienceConstructor

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  2. object AndLeftRule extends ConvenienceConstructor with Serializable

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  3. object AndRightRule extends ConvenienceConstructor with Serializable

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  4. object AtomicExpansion

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  5. object Axiom

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    Convenience object for constructing Axioms.

  6. object BinaryLKProof

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  7. object BottomAxiom extends InitialSequent with Product with Serializable

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    An LKProof introducing ⊥ on the left:

          --------⊥:l
            ⊥ :-
    

    An LKProof introducing ⊥ on the left:

          --------⊥:l
            ⊥ :-
    

  8. object ContractionLeftMacroRule

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    This macro rule simulates a series of contractions in the antecedent.

  9. object ContractionLeftRule extends ConvenienceConstructor with Serializable

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  10. object ContractionMacroRule extends ConvenienceConstructor

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    This macro rule simulates a series of contractions in both cedents.

  11. object ContractionRightMacroRule

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    This macro rule simulates a series of contractions in the succedent.

  12. object ContractionRightRule extends ConvenienceConstructor with Serializable

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  13. object CutRule extends ConvenienceConstructor with Serializable

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  14. object DefinitionElimination

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  15. object DefinitionLeftRule extends ConvenienceConstructor with Serializable

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  16. object DefinitionRightRule extends ConvenienceConstructor with Serializable

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  17. object DefinitionRule

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  18. object Eigenvariable

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  19. object EqualityLeftMacroRule extends ConvenienceConstructor

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  20. object EqualityLeftRule extends ConvenienceConstructor with Serializable

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  21. object EqualityRightMacroRule extends ConvenienceConstructor

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  22. object EqualityRightRule extends ConvenienceConstructor with Serializable

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  23. object ExchangeLeftMacroRule

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    Move a formula to the beginning of the antecedent, where the main formula is customarily placed.

    Move a formula to the beginning of the antecedent, where the main formula is customarily placed.

             (π)
        Γ, A, Γ' :- Δ
       --------------
        A, Γ, Γ' :- Δ
    

  24. object ExchangeRightMacroRule

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    Move a formula to the end of the succedent, where the main formula is customarily placed.

    Move a formula to the end of the succedent, where the main formula is customarily placed.

             (π)
        Γ :- Δ, A, Δ'
       --------------
        Γ :- Δ, Δ', A
    

  25. object ExistsLeftBlock

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  26. object ExistsLeftRule extends ConvenienceConstructor with Serializable

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  27. object ExistsRightBlock

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  28. object ExistsRightRule extends ConvenienceConstructor with Serializable

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  29. object ExtractInterpolant

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  30. object ForallLeftBlock

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  31. object ForallLeftRule extends ConvenienceConstructor with Serializable

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  32. object ForallRightBlock

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  33. object ForallRightRule extends ConvenienceConstructor with Serializable

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  34. object ImpLeftRule extends ConvenienceConstructor with Serializable

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  35. object ImpRightMacroRule extends ConvenienceConstructor

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  36. object ImpRightRule extends ConvenienceConstructor with Serializable

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  37. object InitialSequent

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  38. object Interpolate

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  39. implicit object LKProofSubstitutableDefault extends LKProofSubstitutable

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  40. object LKProver extends OneShotProver

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  41. object LKToExpansionProof

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  42. object LKToLKsk

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  43. object LKToLKsk2

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  44. implicit def LeftSequentIndex(i: SequentIndex): Either[SequentIndex, HOLFormula]

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  45. object NaturalNumberInductionRule extends ConvenienceConstructor

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  46. object NegLeftRule extends ConvenienceConstructor with Serializable

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  47. object NegRightRule extends ConvenienceConstructor with Serializable

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  48. object OrLeftRule extends ConvenienceConstructor with Serializable

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  49. object OrRightMacroRule extends ConvenienceConstructor

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  50. object OrRightRule extends ConvenienceConstructor with Serializable

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  51. object ParamodulationLeftRule extends ConvenienceConstructor

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  52. object ParamodulationRightRule extends ConvenienceConstructor

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  53. object ProofBuilder extends ProofBuilder

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  54. object ReductiveCutElimination

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    This object implements a version of Gentzen's cut-elimination proof for our sequent calculus LK.

    This object implements a version of Gentzen's cut-elimination proof for our sequent calculus LK. For details, please refer to the documentation of the apply methods.

  55. implicit def RightFormula(f: HOLFormula): Either[SequentIndex, HOLFormula]

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  56. object StrongQuantifierRule

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  57. object TopAxiom extends InitialSequent with Product with Serializable

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    An LKProof introducing ⊤ on the right:

          --------⊤:r
            :- ⊤
    

    An LKProof introducing ⊤ on the right:

          --------⊤:r
            :- ⊤
    

  58. object TransRule

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  59. object UnaryLKProof

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  60. object WeakQuantifierRule

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  61. object WeakeningContractionMacroRule extends ConvenienceConstructor

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    This macro rule simulates multiple weakenings and contractions in both cedents.

  62. object WeakeningLeftMacroRule

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    This macro rule simulates a series of weakenings in the antecedent.

  63. object WeakeningMacroRule extends ConvenienceConstructor

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    This macro rule simulates a series of weakenings in both cedents.

  64. object WeakeningRightMacroRule

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    This macro rule simulates a series of weakenings in the succedent.

  65. object cleanStructuralRules

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  66. object consoleString

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  67. object containsEqualityReasoning

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  68. object cutFormulas

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  69. object cutsNumber

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  70. object eliminateTheoryAxioms extends LKVisitor[HOLFormula]

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    Object for calling the eliminateTheoryAxiom transformation.

  71. object extractRecSchem

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  72. object freeVariablesLK

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  73. object groundFreeVarsLK

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  74. object isRegular

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  75. object lkNew2Old

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    Conversion algorithm for new LK => old LK

  76. object lkOld2New

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    Conversion algorithm for old LK => new LK.

  77. implicit object lkProofReplaceable extends ClosedUnderReplacement[LKProof]

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  78. object makeInductionExplicit extends LKVisitor[Unit]

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  79. object moveStrongQuantifierRulesDown

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    Modifies an LK proof to introduce strong quantifiers as soon as possible.

  80. object printProofStats

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  81. object proofFromInstances

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    Computes a proof of F from a proof of some instances of F

  82. object quantRulesNumber

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  83. object regularize extends LKVisitor[Set[Var]]

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    Proof regularization

  84. object rulesNumber

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  85. object skolemize

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  86. object solve

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    Bottom-up construction of sequent calculus proofs.

    Bottom-up construction of sequent calculus proofs.

    Currently supports propositional logic as well as proof construction using expansion trees.

  87. object solvePropositional extends SolveUtils

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  88. object strongQuantRulesNumber

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  89. object weakQuantRulesNumber

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Inherited from AnyRef

Inherited from Any

Ungrouped