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
- 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))
- Source
- introducePiCut.scala
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Instance Constructors
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new
Pi2SeHs(reducedRepresentation: Sequent[Formula], universalEigenvariable: Var, existentialEigenvariables: List[Var], substitutionsForAlpha: List[Expr], substitutionsForBetaWithAlpha: List[Expr])
- 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))
Value Members
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final
def
!=(arg0: Any): Boolean
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final
def
##(): Int
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- def +(other: String): String
- def ->[B](y: B): (Pi2SeHs, B)
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final
def
==(arg0: Any): Boolean
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final
def
asInstanceOf[T0]: T0
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def
clone(): AnyRef
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- @native() @throws( ... )
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val
dualNonTautologicalAxioms: List[Sequent[Formula]]
The set of all relevant normalized (everything is shifted to the left side) leaves
- def ensuring(cond: (Pi2SeHs) ⇒ Boolean, msg: ⇒ Any): Pi2SeHs
- def ensuring(cond: (Pi2SeHs) ⇒ Boolean): Pi2SeHs
- def ensuring(cond: Boolean, msg: ⇒ Any): Pi2SeHs
- def ensuring(cond: Boolean): Pi2SeHs
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final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
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- val existentialEigenvariables: List[Var]
-
def
finalize(): Unit
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- def formatted(fmtstr: String): String
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final
def
getClass(): Class[_]
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def
herbrandSequent(): Sequent[Formula]
Computes the Herbrand sequent that corresponds to the schematic Pi-2 grammar (F[x\T_1] |- G[y\T_2])
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final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
-
val
literalsInTheDNTAs: (Set[Formula], Set[Formula], Set[Formula])
Three sets A,B,N containing all atoms occurring in the leaves of the reduced representation (the atoms are negated if they occur on the right side of the sequent) such that in all atoms (literals) of N no eigenvariables occur, in all atoms (literals) of A only the universal eigenvariable occur, and in all atoms (literals) of B only the existential eigenvariables occur
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val
literalsInTheDNTAsAndTheDNTAs: (Set[Formula], List[Sequent[Formula]])
Computes simultaneously a set of all atoms occurring in the leaves of the reduced representation (the atoms are negated if they occur on the right side of the sequent) and a list of all relevant normalized (everything is shifted to the left side) leaves of the reduced representation
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val
multiplicityOfAlpha: Int
Number of substitutions for the eigenvariable of the universally quantified variable (m)
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val
multiplicityOfBeta: Int
Number of substitutions for the eigenvariables of the existentially quantified variable independent from the substitution of the universal eigenvariable (p)
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final
def
ne(arg0: AnyRef): Boolean
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final
def
notify(): Unit
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final
def
notifyAll(): Unit
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val
productionRulesXS: List[(Expr, Expr)]
List of all substitution pairs (alpha,r_i) and (r_i,alpha)
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val
productionRulesYS: List[(Expr, Expr)]
List of all substitution pairs (beta_j,t_i(alpha)) and (t_i(alpha),beta_j)
- val reducedRepresentation: Sequent[Formula]
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val
reducedRepresentationToFormula: Formula
Transforms the reduced representation from a sequent to a formula
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def
sortAndAtomize(literals: Set[Formula]): (Set[Formula], Set[Formula])
Computes two sets of atoms P,N for a given set of literals such that P contains all positive literals and N all atoms of the negative literals
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val
substitutionPairsAlpha: List[(Expr, Expr)]
Pairs of the universal eigenvariable with the substitutions for the universal eigenvariable ((alpha,r_1),...,(alpha,r_m))
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val
substitutionPairsBeta: List[(Expr, Expr)]
Pairs of the existential eigenvariables with the substitutions for the existential eigenvariables ((beta_1,t_1(alpha)),...,(beta_1,t_p(alpha)),...,(beta_m,t_1(alpha)),...,(beta_m,t_p(alpha)))
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def
substitutionPairsBetaI(index: Int): List[(Expr, Expr)]
Pairs of a existential eigenvariable with the substitutions for this existential eigenvariable ((beta_i,t_1(alpha)),...,(beta_i,t_p(alpha)) with i=index)
Pairs of a existential eigenvariable with the substitutions for this existential eigenvariable ((beta_i,t_1(alpha)),...,(beta_i,t_p(alpha)) with i=index)
- index
Indicates the considered existential eigenvariable (1 <= index <= m)
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val
substitutionsAlpha: List[Substitution]
List of substitutions ((alpha->r_1),...,(alpha->r_m))
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def
substitutionsBetaI(index: Int): List[Substitution]
List of substitutions ((beta_i->t_1(r_i)),...,(beta_i->t_p(r_i)) with i=index)
List of substitutions ((beta_i->t_1(r_i)),...,(beta_i->t_p(r_i)) with i=index)
- index
Indicates the considered existential eigenvariable (1 <= index <= m)
- val substitutionsForAlpha: List[Expr]
- val substitutionsForBetaWithAlpha: List[Expr]
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final
def
synchronized[T0](arg0: ⇒ T0): T0
- Definition Classes
- AnyRef
-
def
theDNTAsInTheLanguage(unifiedLiterals: Set[Formula]): List[Sequent[Formula]]
List of all relevant normalized (everything is shifted to the left side) leaves of the reduced representation in a reduced signature/language that contains the unified literals (work in progress)
List of all relevant normalized (everything is shifted to the left side) leaves of the reduced representation in a reduced signature/language that contains the unified literals (work in progress)
- unifiedLiterals
A set of formulas (unified literals) that define the reduced signature/language
- val universalEigenvariable: Var
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final
def
wait(): Unit
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final
def
wait(arg0: Long, arg1: Int): Unit
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final
def
wait(arg0: Long): Unit
- Definition Classes
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- def →[B](y: B): (Pi2SeHs, B)
This is the API documentation for GAPT.
The main package is gapt.