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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final
def
##(): Int
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def
+(other: String): String
- Implicit
- This member is added by an implicit conversion from InstanceTermEncoding to any2stringadd[InstanceTermEncoding] performed by method any2stringadd in scala.Predef.
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def
->[B](y: B): (InstanceTermEncoding, B)
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- This member is added by an implicit conversion from InstanceTermEncoding to ArrowAssoc[InstanceTermEncoding] performed by method ArrowAssoc in scala.Predef.
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- def decode(recursionScheme: RecursionScheme): RecursionScheme
- def decodeOption(term: LambdaExpression): Option[(SequentIndex, Substitution)]
- def decodeToExpansionSequent(terms: Iterable[LambdaExpression]): ExpansionSequent
- def decodeToInstanceSequent(terms: Iterable[LambdaExpression]): HOLSequent
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def
decodeToPolarizedFormula(term: LambdaExpression): (HOLFormula, 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: LambdaExpression): HOLFormula
- def encode(recursionScheme: RecursionScheme): RecursionScheme
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def
encode(instance: ExpansionProof): Set[LambdaExpression]
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.
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def
encode(instance: ExpansionSequent)(implicit dummyImplicit: DummyImplicit): Set[LambdaExpression]
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.
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def
encode(instance: HOLSequent): Set[LambdaExpression]
Encodes a sequent consisting of instances of an instance sequent.
- def encode(signedInstance: HOLFormula): LambdaExpression
- def encodeOption(signedInstance: HOLFormula): Option[LambdaExpression]
- val endSequent: HOLSequent
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def
ensuring(cond: (InstanceTermEncoding) ⇒ Boolean, msg: ⇒ Any): InstanceTermEncoding
- Implicit
- This member is added by an implicit conversion from InstanceTermEncoding to Ensuring[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 to Ensuring[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 to Ensuring[InstanceTermEncoding] performed by method Ensuring in scala.Predef.
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- Ensuring
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def
ensuring(cond: Boolean): InstanceTermEncoding
- Implicit
- This member is added by an implicit conversion from InstanceTermEncoding to Ensuring[InstanceTermEncoding] performed by method Ensuring in scala.Predef.
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- Ensuring
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final
def
eq(arg0: AnyRef): Boolean
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def
equals(arg0: Any): Boolean
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def
finalize(): Unit
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def
findESFormula(sym: Const): Option[HOLFormula]
Maps a function symbol to its corresponding formula in the end-sequent.
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def
findESIndex(sym: Const): Option[SequentIndex]
Maps a function symbol to the index of its corresponding formula in the end-sequent.
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def
formatted(fmtstr: String): String
- Implicit
- This member is added by an implicit conversion from InstanceTermEncoding to StringFormat[InstanceTermEncoding] performed by method StringFormat in scala.Predef.
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- StringFormat
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final
def
getClass(): Class[_]
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def
hashCode(): Int
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- val instanceTermType: Ty
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final
def
isInstanceOf[T0]: Boolean
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val
matrices: Sequent[HOLFormula]
The propositional matrices phi of the end-sequent.
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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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final
def
ne(arg0: AnyRef): Boolean
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final
def
notify(): Unit
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final
def
notifyAll(): Unit
- Definition Classes
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val
quantVars: Sequent[Seq[Var]]
The quantified variables of each formula in the end-sequent.
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val
signedMatrices: Sequent[HOLFormula]
The propositional matrices of the end-sequent, where the formulas in the succedent are negated.
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val
symbols: Sequent[Const]
The function symbols used to encode the instances of each formula in the end-sequent.
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final
def
synchronized[T0](arg0: ⇒ T0): T0
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def
toString(): String
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def
wait(): Unit
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def
wait(arg0: Long, arg1: Int): Unit
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def
wait(arg0: Long): Unit
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def
→[B](y: B): (InstanceTermEncoding, B)
- Implicit
- This member is added by an implicit conversion from InstanceTermEncoding to ArrowAssoc[InstanceTermEncoding] performed by method ArrowAssoc in scala.Predef.
- Definition Classes
- ArrowAssoc