Packages

p

gapt

cutintro

package cutintro

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  2. Protected

Type Members

  1. class ClauseWithIndexLists extends AnyRef

    Combined data of many unified literals in a clause and whether the clause is a potential part of a formula in disjunctive normal form that makes all leaves of the reduced representation true

  2. class ClausesWithIndexLists extends AnyRef

    Combined data of many clauses in a set of clauses and whether the clauses translate to a formula in disjunctive normal form that makes all leaves of the reduced representation true

  3. trait GrammarFindingMethod extends AnyRef
  4. class LeafIndex extends AnyRef

    Contains two sets to store integers

  5. class LiteralWithIndexLists extends AnyRef

    Supposed to contain the data of a unified literal and whether it makes a non-tautological leaf of the reduced representation true

  6. case class MaxSATMethod(solver: MaxSATSolver, nonTerminalLengths: Int*) extends GrammarFindingMethod with Product with Serializable
  7. case class Pi2SeHs(reducedRepresentation: Sequent[Formula], universalEigenvariable: Var, existentialEigenvariables: List[Var], substitutionsForAlpha: List[Expr], substitutionsForBetaWithAlpha: List[Expr]) extends Product with Serializable

    Schematic extended Herbrand sequent for schematic Pi-2 grammars

    Schematic extended Herbrand sequent for schematic Pi-2 grammars

    reducedRepresentation

    The schematic extended Herbrand sequent without placeholder for the cut ( F[x\U_1] |- G[y\U_2] )

    universalEigenvariable

    The variable that is introduced for the universally quantified variable of the cut formula (alpha)

    existentialEigenvariables

    The variables that are introduced for the existentially quantified variable of the cut formula (beta_1,...,beta_m)

    substitutionsForAlpha

    The terms (except from the eigenvariable) that are introduced for the universally quantified variable of the cut formula (r_1,...,r_m)

    substitutionsForBetaWithAlpha

    The terms (except from the eigenvariables) that are introduced for the existentially quantified variable of the cut formula independent from the existential eigenvariables (t_1(alpha),...,t_p(alpha))

  8. case class SchematicExtendedHerbrandSequent(us: Sequent[(FOLFormula, Seq[Seq[FOLTerm]])], ss: Seq[(Seq[FOLVar], Seq[Seq[FOLTerm]])]) extends Product with Serializable

    Represents a schematic extended Herbrand sequent.

    Represents a schematic extended Herbrand sequent.

    us

    Formulas of the original end-sequent, together with their instances.

    ss

    Instances of the cut-implications.

  9. case class SolutionStructure(sehs: SchematicExtendedHerbrandSequent, formulas: Seq[FOLFormula]) extends Product with Serializable

Value Members

  1. object CutIntroduction
  2. object MaxSATMethod extends Serializable
  3. object Pi2CutIntroduction
  4. case object ReforestMethod extends GrammarFindingMethod with Product with Serializable
  5. object beautifySolution
  6. object gStarUnify

    Computes the unified literals, i.e.

    Computes the unified literals, i.e. the set of literals that are used to contruct the cut formula

  7. object improveSolutionLK
  8. object introducePi2Cut

    Computes the cut formula for a given schematic extended Herbrand sequent

  9. object pi2GrammarToSEHS
  10. object proveWithPi2Cut

    Constructs a proof for a given schematic Pi2-grammar if a cut formula exists

  11. object sehsToVTRATG
  12. object solutionViaInterpolation

    Solution finding algorithm for Π₁-cut-introduction based on the Duality algorithm for constrained Horn clause verification[1].

    Solution finding algorithm for Π₁-cut-introduction based on the Duality algorithm for constrained Horn clause verification[1].

    [1] K. L. McMillan, A. Rybalchenko, Solving Constrained Horn Clauses using Interpolation, technical report MSR-TR-2013-6, available at https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/MSR-TR-2013-6.pdf

  13. object vtratgToSEHS

Ungrouped