Packages

package fol

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Type Members

  1. class Counter extends AnyRef
  2. trait CountingFormulas extends AnyRef
  3. case class FOLPosition(list: List[Int]) extends Product with Serializable

    Positions are given as lists of Integers.

    Positions are given as lists of Integers. The empty list denotes the current expression itself. A list starting with k denotes a subexpression in the kth argument of the current expression.

    list

    The list describing the position.

  4. class TseitinCNF extends AnyRef
  5. class reduceHolToFol extends AnyRef

    Creates a FOL formula from a HOL formula, but applies transformations which do _not_ preserve validity! Transformations applied:

    Creates a FOL formula from a HOL formula, but applies transformations which do _not_ preserve validity! Transformations applied:

    • Replace all subterms (\x.t[v]) by a function q_n(v). The scope parameter is needed to pass existing term-constant mappings.
    • Change the type of constants and variables s.t. they are first order (i.e. Const("c", To->Ti) is mapped to FOLConst("c",Ti)
    • Logical operators inside the term structure are replaced by first order terms
    Note

    Make sure you need all of these tricks. To only replace abstraction subterms, use replaceAbstractions.

  6. class replaceAbstractions extends AnyRef

    Replace lambda-abstractions by constants.

    Replace lambda-abstractions by constants.

    Each abstraction in an at.logic.gapt.proofs.HOLSequent is replaced by a separate constant symbol; the used constants are returned in a Map.

  7. class undoReplaceAbstractions extends AnyRef

    Replaces the constants introduced by replaceAbstractions with the original lambda-abstractions.

Value Members

  1. object BinaryConnective
  2. object Delta

    Matcher for Deltan A FOLFormula f will match Delta(k) if it is both Sigmak and Pik, but not Sigmak-1 or Pik-1.

  3. object FOLFunctionArgs

    Unsafely extracts the function arguments from a term.

    Unsafely extracts the function arguments from a term. Fails if the term is not a function.

  4. object FOLFunctionName

    Unsafely extracts the function name from a term.

    Unsafely extracts the function name from a term. Fails if the term is not a function.

  5. object FOLPosition extends Serializable
  6. object Numeral
  7. object Pi

    Matcher for Pin A FOLFormula f will match Pi(k) if f is Pik, but not Pik-1.

  8. object Sigma

    Matcher for Sigman A FOLFormula f will match Sigma(k) if f is Sigmak, but not Sigmak-1.

  9. object TseitinCNF
  10. object Utils
  11. object changeTypeIn

    Introducing abstractions and converting to fol changes more complex types to fol compatible ones.

    Introducing abstractions and converting to fol changes more complex types to fol compatible ones. With changeTypeIn you can change them back.

  12. object folSubTerms

    Generation of first-order subterms (note that this notion differs from lambda subterms).

  13. object folTermSize
  14. object getArityOfConstants
  15. object isFOLFunction
  16. object isFOLPrenexPi1
  17. object isFOLPrenexSigma1
  18. object naive extends CountingFormulas
  19. object natMaker
  20. object reduceHolToFol extends reduceHolToFol
  21. object replaceAbstractions extends replaceAbstractions
  22. object thresholds extends CountingFormulas
  23. object undoHol2Fol

    This is implements some heuristics to convert a fol formula obtained by at.logic.gapt.expr.fol.replaceAbstractions and at.logic.gapt.expr.fol.reduceHolToFol back to its original signature.

    This is implements some heuristics to convert a fol formula obtained by at.logic.gapt.expr.fol.replaceAbstractions and at.logic.gapt.expr.fol.reduceHolToFol back to its original signature. Sometimes, types have to be guessed and the code is poorly tested, so it is unclear how general it is. It works (and is necessary) during the acnf creation of the n-tape proof.

    To extract a signature, use the undoHol2Fol.getSignature, to to the back translation use undoHol2Fol.backtranslate.

  24. object undoReplaceAbstractions extends undoReplaceAbstractions

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