package cutintro
- Alphabetic
- Public
- Protected
Type Members
- 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
- 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
- trait GrammarFindingMethod extends AnyRef
- class LeafIndex extends AnyRef
Contains two sets to store integers
- 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
- case class MaxSATMethod(solver: MaxSATSolver, nonTerminalLengths: Int*) extends GrammarFindingMethod with Product with Serializable
- 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))
- 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.
- case class SolutionStructure(sehs: SchematicExtendedHerbrandSequent, formulas: Seq[FOLFormula]) extends Product with Serializable
Value Members
- object CutIntroduction
- object MaxSATMethod extends Serializable
- object Pi2CutIntroduction
- case object ReforestMethod extends GrammarFindingMethod with Product with Serializable
- object beautifySolution
- 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
- object improveSolutionLK
- object introducePi2Cut
Computes the cut formula for a given schematic extended Herbrand sequent
- object pi2GrammarToSEHS
- object proveWithPi2Cut
Constructs a proof for a given schematic Pi2-grammar if a cut formula exists
- object sehsToVTRATG
- 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
- object vtratgToSEHS
This is the API documentation for GAPT.
The main package is gapt.