Class

at.logic.gapt.proofs.expansionTrees

InstanceTermEncoding

Related Doc: package expansionTrees

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case class InstanceTermEncoding(endSequent: HOLSequent) extends Product with Serializable

Encodes instances of a prenex FOL Sigma_1 end-sequent as FOL terms.

In the case of cut-introduction, the end-sequent has no free variables 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 simple inductive proofs, the end-sequent contains one free variable (alpha). Here, we consider proofs of instance sequents, which are obtained by substituting a numeral for alpha. Hence the formulas occuring 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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Serializable, Serializable, Product, Equals, AnyRef, Any
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  1. InstanceTermEncoding
  2. Serializable
  3. Serializable
  4. Product
  5. Equals
  6. AnyRef
  7. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Instance Constructors

  1. new InstanceTermEncoding(endSequent: HOLSequent)

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Type Members

  1. type PolarizedFormula = (FOLFormula, Boolean)

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    Formula together with its polarity in a sequent, which is true if it is in the antecedent.

Value Members

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

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    Definition Classes
    AnyRef → Any
  2. final def ##(): Int

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    Definition Classes
    AnyRef → Any
  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.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any
  6. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any
  7. def clone(): AnyRef

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  8. def decode(terms: Iterable[FOLTerm]): Set[PolarizedFormula]

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  9. def decode(term: FOLTerm): PolarizedFormula

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  10. def decodeOption(term: FOLTerm): Option[PolarizedFormula]

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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.

  11. def decodeToExpansionSequent(terms: Iterable[FOLTerm]): ExpansionSequent

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  12. def decodeToFSequent(terms: Iterable[FOLTerm]): HOLSequent

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  13. def encode(instance: ExpansionSequent)(implicit dummyImplicit: DummyImplicit): Seq[FOLTerm]

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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.

  14. def encode(instance: HOLSequent): Seq[FOLTerm]

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    Encodes a sequent consisting of instances of an instance sequent.

  15. def encode(instance: PolarizedFormula): FOLTerm

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  16. def encodeOption(instance: PolarizedFormula): Option[FOLTerm]

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  17. val endSequent: HOLSequent

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  18. 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
  19. 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
  20. 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
  21. 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
  22. final def eq(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef
  23. def finalize(): Unit

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  24. def findESFormula(sym: String): Option[PolarizedFormula]

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

  25. 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()
  26. final def getClass(): Class[_]

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    Definition Classes
    AnyRef → Any
  27. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any
  28. def mkSym(esFormula: PolarizedFormula): String

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    Assigns each formula in the end-sequent a fresh function symbol used to encode its instances.

    Assigns each formula in the end-sequent a fresh function symbol used to encode its instances.

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

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    Definition Classes
    AnyRef
  30. final def notify(): Unit

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    Definition Classes
    AnyRef
  31. final def notifyAll(): Unit

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    Definition Classes
    AnyRef
  32. final def synchronized[T0](arg0: ⇒ T0): T0

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    Definition Classes
    AnyRef
  33. final def wait(): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  34. final def wait(arg0: Long, arg1: Int): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  35. final def wait(arg0: Long): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  36. 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 Serializable

Inherited from Serializable

Inherited from Product

Inherited from Equals

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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