class InstanceTermEncoding extends AnyRef
Encodes instances of an end-sequent as terms.
Only instances of weak quantifiers are recorded, instances of strong quantifiers or free variables are ignored.
The end-sequent will be internally transformed into one which is in variable normal form.
In the case of cut-introduction, the end-sequent has no free variables and no strong quantifiers and we're encoding a Herbrand sequent as a set of terms. A term r_i(t_1,...,t_n) encodes an instance of the formula "forall x_1 ... x_n, phi(x_1,...,x_n)" using the instances (t_1,...,t_n).
In the case of inductive proofs, the end-sequent contains strong quantifiers variable (alpha). Here, we consider proofs of instance sequents, which are obtained by e.g. substituting a numeral for alpha. Hence the formulas occurring in the end-sequents of instance proofs are substitution instances of endSequent; the encoded terms still only capture the instances used in the instance proofs--i.e. not alpha.
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- termExtraction.scala
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- def +(other: String): String
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- This member is added by an implicit conversion from InstanceTermEncoding toany2stringadd[InstanceTermEncoding] performed by method any2stringadd in scala.Predef.
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- any2stringadd
- def ->[B](y: B): (InstanceTermEncoding, B)
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- This member is added by an implicit conversion from InstanceTermEncoding toArrowAssoc[InstanceTermEncoding] performed by method ArrowAssoc in scala.Predef.
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- def decode(recursionScheme: RecursionScheme): RecursionScheme
- def decodeOption(term: Expr): Option[(SequentIndex, Substitution)]
- def decodeToExpansionProof(terms: Iterable[Expr]): ExpansionProof
- def decodeToExpansionSequent(terms: Iterable[Expr]): ExpansionSequent
- def decodeToInstanceSequent(terms: Iterable[Expr]): HOLSequent
- def decodeToPolarizedFormula(term: Expr): (Formula, Polarity)
Decodes a term into its corresponding instance.
Decodes a term into its corresponding instance.
The resulting instance can contain alpha in the inductive case.
- def decodeToSignedFormula(term: Expr): Formula
- def encode(recursionScheme: RecursionScheme): RecursionScheme
- def encode(instance: ExpansionProof): Set[Expr]
Encodes an expansion proof (of an instance proof).
Encodes an expansion proof (of an instance proof).
The shallow formulas of the expansion sequents should be subsumed by formulas in the end-sequent.
- def encode(instance: ExpansionSequent)(implicit dummyImplicit: DummyImplicit): Set[Expr]
Encodes an expansion sequent (of an instance proof).
Encodes an expansion sequent (of an instance proof).
The shallow formulas of the expansion sequents should be subsumed by formulas in the end-sequent.
- def encode(instance: HOLSequent): Set[Expr]
Encodes a sequent consisting of instances of an instance sequent.
- def encode(signedInstance: Formula): Expr
- def encodeOption(signedInstance: Formula): Option[Expr]
- val endSequent: HOLSequent
- def ensuring(cond: (InstanceTermEncoding) => Boolean, msg: => Any): InstanceTermEncoding
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- This member is added by an implicit conversion from InstanceTermEncoding toEnsuring[InstanceTermEncoding] performed by method Ensuring in scala.Predef.
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- def ensuring(cond: (InstanceTermEncoding) => Boolean): InstanceTermEncoding
- Implicit
- This member is added by an implicit conversion from InstanceTermEncoding toEnsuring[InstanceTermEncoding] performed by method Ensuring in scala.Predef.
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- def ensuring(cond: Boolean, msg: => Any): InstanceTermEncoding
- Implicit
- This member is added by an implicit conversion from InstanceTermEncoding toEnsuring[InstanceTermEncoding] performed by method Ensuring in scala.Predef.
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- def ensuring(cond: Boolean): InstanceTermEncoding
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- This member is added by an implicit conversion from InstanceTermEncoding toEnsuring[InstanceTermEncoding] performed by method Ensuring in scala.Predef.
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- final def eq(arg0: AnyRef): Boolean
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- def equals(arg0: AnyRef): Boolean
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- def findESFormula(sym: Const): Option[Formula]
Maps a function symbol to its corresponding formula in the end-sequent.
- def findESIndex(sym: Const): Option[SequentIndex]
Maps a function symbol to the index of its corresponding formula in the end-sequent.
- def formatted(fmtstr: String): String
- Implicit
- This member is added by an implicit conversion from InstanceTermEncoding toStringFormat[InstanceTermEncoding] performed by method StringFormat in scala.Predef.
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- val instanceTermType: Ty
- final def isInstanceOf[T0]: Boolean
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- val matrices: Sequent[Formula]
The propositional matrices phi of the end-sequent.
- def mkSym(idx: SequentIndex): String
Assigns each formula in the end-sequent a fresh function symbol name used to encode its instances.
Assigns each formula in the end-sequent a fresh function symbol name used to encode its instances.
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- val quantVars: Sequent[Seq[Var]]
The quantified variables of each formula in the end-sequent.
- val signedMatrices: Sequent[Formula]
The propositional matrices of the end-sequent, where the formulas in the succedent are negated.
- val symbols: Sequent[Const]
The function symbols used to encode the instances of each formula in the end-sequent.
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(Since version ) see corresponding Javadoc for more information.
- def →[B](y: B): (InstanceTermEncoding, B)
- Implicit
- This member is added by an implicit conversion from InstanceTermEncoding toArrowAssoc[InstanceTermEncoding] performed by method ArrowAssoc in scala.Predef.
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This is the API documentation for GAPT.
The main package is gapt.