Class/Object

at.logic.gapt.proofs.expansion

InstanceTermEncoding

Related Docs: object InstanceTermEncoding | package expansion

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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.

Source
termExtraction.scala
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  1. final def !=(arg0: Any): Boolean

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  2. final def ##(): Int

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  3. def +(other: String): String

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    Implicit information
    This member is added by an implicit conversion from InstanceTermEncoding to any2stringadd[InstanceTermEncoding] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (InstanceTermEncoding, B)

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    Implicit information
    This member is added by an implicit conversion from InstanceTermEncoding to ArrowAssoc[InstanceTermEncoding] performed by method ArrowAssoc in scala.Predef.
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    ArrowAssoc
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    @inline()
  5. final def ==(arg0: Any): Boolean

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  6. final def asInstanceOf[T0]: T0

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  7. def clone(): AnyRef

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    @throws( ... )
  8. def decode(recursionScheme: RecursionScheme): RecursionScheme

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  9. def decodeOption(term: LambdaExpression): Option[(SequentIndex, Substitution)]

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  10. def decodeToExpansionSequent(terms: Iterable[LambdaExpression]): ExpansionSequent

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  11. def decodeToInstanceSequent(terms: Iterable[LambdaExpression]): HOLSequent

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  12. def decodeToPolarizedFormula(term: LambdaExpression): (HOLFormula, Boolean)

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    Decodes a term into its corresponding instance.

    Decodes a term into its corresponding instance.

    The resulting instance can contain alpha in the inductive case.

  13. def decodeToSignedFormula(term: LambdaExpression): HOLFormula

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  14. def encode(recursionScheme: RecursionScheme): RecursionScheme

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  15. def encode(instance: ExpansionProof): Set[LambdaExpression]

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    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.

  16. def encode(instance: ExpansionSequent)(implicit dummyImplicit: DummyImplicit): Set[LambdaExpression]

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    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.

  17. def encode(instance: HOLSequent): Set[LambdaExpression]

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    Encodes a sequent consisting of instances of an instance sequent.

  18. def encode(signedInstance: HOLFormula): LambdaExpression

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  19. def encodeOption(signedInstance: HOLFormula): Option[LambdaExpression]

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  20. val endSequent: HOLSequent

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  21. def ensuring(cond: (InstanceTermEncoding) ⇒ Boolean, msg: ⇒ Any): InstanceTermEncoding

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    Implicit information
    This member is added by an implicit conversion from InstanceTermEncoding to Ensuring[InstanceTermEncoding] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  22. def ensuring(cond: (InstanceTermEncoding) ⇒ Boolean): InstanceTermEncoding

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    Implicit information
    This member is added by an implicit conversion from InstanceTermEncoding to Ensuring[InstanceTermEncoding] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  23. def ensuring(cond: Boolean, msg: ⇒ Any): InstanceTermEncoding

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    Implicit information
    This member is added by an implicit conversion from InstanceTermEncoding to Ensuring[InstanceTermEncoding] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  24. def ensuring(cond: Boolean): InstanceTermEncoding

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    Implicit information
    This member is added by an implicit conversion from InstanceTermEncoding to Ensuring[InstanceTermEncoding] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  25. final def eq(arg0: AnyRef): Boolean

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  26. def equals(arg0: Any): Boolean

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  27. def finalize(): Unit

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    @throws( classOf[java.lang.Throwable] )
  28. def findESFormula(sym: Const): Option[HOLFormula]

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    Maps a function symbol to its corresponding formula in the end-sequent.

  29. def findESIndex(sym: Const): Option[SequentIndex]

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    Maps a function symbol to the index of its corresponding formula in the end-sequent.

  30. def formatted(fmtstr: String): String

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    Implicit information
    This member is added by an implicit conversion from InstanceTermEncoding to StringFormat[InstanceTermEncoding] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  31. final def getClass(): Class[_]

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  32. def hashCode(): Int

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  33. val instanceTermType: Ty

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  34. final def isInstanceOf[T0]: Boolean

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    Any
  35. val matrices: Sequent[HOLFormula]

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    The propositional matrices phi of the end-sequent.

  36. def mkSym(idx: SequentIndex): String

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    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.

    Attributes
    protected
  37. final def ne(arg0: AnyRef): Boolean

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    AnyRef
  38. final def notify(): Unit

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  39. final def notifyAll(): Unit

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    AnyRef
  40. val quantVars: Sequent[Seq[Var]]

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    The quantified variables of each formula in the end-sequent.

  41. val signedMatrices: Sequent[HOLFormula]

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    The propositional matrices of the end-sequent, where the formulas in the antecedent are negated.

  42. val symbols: Sequent[Const]

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    The function symbols used to encode the instances of each formula in the end-sequent.

  43. final def synchronized[T0](arg0: ⇒ T0): T0

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  44. def toString(): String

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  45. final def wait(): Unit

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    @throws( ... )
  46. final def wait(arg0: Long, arg1: Int): Unit

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    @throws( ... )
  47. final def wait(arg0: Long): Unit

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    @throws( ... )
  48. def [B](y: B): (InstanceTermEncoding, B)

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    Implicit information
    This member is added by an implicit conversion from InstanceTermEncoding to ArrowAssoc[InstanceTermEncoding] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd from InstanceTermEncoding to any2stringadd[InstanceTermEncoding]

Inherited by implicit conversion StringFormat from InstanceTermEncoding to StringFormat[InstanceTermEncoding]

Inherited by implicit conversion Ensuring from InstanceTermEncoding to Ensuring[InstanceTermEncoding]

Inherited by implicit conversion ArrowAssoc from InstanceTermEncoding to ArrowAssoc[InstanceTermEncoding]

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