Package

at.logic.gapt.expr

fol

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package fol

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Visibility
  1. Public
  2. All

Type Members

  1. class FOLPosition extends AnyRef

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    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.

  2. class FOLSubstitution extends Substitution

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  3. trait FinitaryUnification extends AnyRef

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    The interface for an unification algorithm of finitary type, i.e.

    The interface for an unification algorithm of finitary type, i.e. one where the complete set of most general unifiers is finite.

  4. trait UnificationAlgorithm extends FinitaryUnification

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  5. class UnificationException extends Exception

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  6. class reduceHolToFol extends AnyRef

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    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) by a constant. 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.

  7. class replaceAbstractions extends AnyRef

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    Replace lambda-abstractions by constants.

    Replace lambda-abstractions by constants.

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

  8. class undoReplaceAbstractions extends AnyRef

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

Value Members

  1. object BinaryConnective

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  2. object Delta

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    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

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    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

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    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 FOLMatchingAlgorithm

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  6. object FOLPosition

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  7. object FOLSubTerms

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

  8. object FOLSubstitution

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  9. object FOLUnificationAlgorithm extends UnificationAlgorithm

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    Created by sebastian on 2/9/15.

  10. object Pi

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

  11. object Sigma

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

  12. object Utils

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  13. object changeTypeIn

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    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.

  14. object getArityOfConstants

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  15. object isFOLFunction

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  16. object isFOLPrenexPi1

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  17. object isFOLPrenexSigma1

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  18. object reduceHolToFol extends reduceHolToFol

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  19. object replaceAbstractions extends replaceAbstractions

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  20. object toAbbreviatedString

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  21. object undoHol2Fol extends Logger

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

    This is implements some heuristics to convert a fol formula obtained by at.logic.gapt.language.fol.algorithms.replaceAbstractions and at.logic.gapt.language.fol.algorithms.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.

  22. object undoReplaceAbstractions extends undoReplaceAbstractions

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