package hol

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Type Members

  1. trait HOLAtomConst extends Const with HOLPartialAtom
  2. class HOLOrdering extends Ordering[Expr]
  3. trait HOLPartialAtom extends Expr
  4. case class HOLPosition(list: List[Int]) extends Product with Serializable

    Represents a position in a gapt.expr.Expr.

    Represents a position in a gapt.expr.Expr.

    Positions are represented by lists of Integers. The empty list denotes the expression itself. A nonempty list denotes a position in the left or right subexpression according to whether it starts with 1 or 2.

    The difference between this and gapt.expr.util.LambdaPosition lies in the handling of quantifiers and binary logical connectives. LambdaPositions treat e.g. conjunctions like any other function, while HOLPositions treat them naturally, i.e. 1 denotes the left conjunct and 2 the right conjunct.

    Note that this can cause unexpeted behavior: Say a variable of type o -> o -> o is substituted by ∧ in some expression. The LambdaPositions will stay the same, but the HOLPositions won't.

    list

    The list of integers describing the position.

  5. class TAOrdering extends Ordering[Ty]

Value Members

  1. object BinaryConnective
  2. object HOLAtomConst
  3. object HOLFunction
  4. object HOLOrdering extends HOLOrdering

    Ordering for HOL Formulas (also for FOL)

  5. object HOLPosition extends Serializable
  6. object TAOrdering extends TAOrdering

    Ordering on types.

  7. object atoms

    Return the list of all atoms in the given argument.

  8. object containsHOQuantifier
  9. object containsQuantifier

    True iff All or Ex matches any subterm of e.

  10. object containsQuantifierOnLogicalLevel

    True iff All or Ex is contained in the logical structure of the given Formula.

    True iff All or Ex is contained in the logical structure of the given Formula. For example, P( (all x:x) ) contains a quantifier, but it is inside of an atom.

  11. object containsStrongQuantifier
  12. object containsWeakQuantifier
  13. object dualize

    Dualize a formula in NNF by switching conjunctions with disjunctions, universal with existential quantifiers, top with bottom and positive literals with negative literals.

    Dualize a formula in NNF by switching conjunctions with disjunctions, universal with existential quantifiers, top with bottom and positive literals with negative literals. The formula dualize( A ) is logically equivalent to the negation of A.

  14. object existentialClosure
  15. object formulaToSequent

    Removes top-level connectives from a formula.

  16. object freeHOVariables
  17. object inductionPrinciple
  18. object instantiate

    Instantiates a formula with terms.

  19. object isAtom

    Returns true iff the given Formula is an atom (which does not include top nor bottom).

  20. object isExtendedAtom

    Returns true iff the given Formula is an extended atom, i.e.

    Returns true iff the given Formula is an extended atom, i.e. an atom or top or bottom.

  21. object isLogicalConstant

    Returns true iff the given Expr consists of a logical constant.

  22. object isNeg

    Returns true iff the given Formula starts with a negation.

  23. object isPrenex

    Returns true iff the given formula is prenex.

  24. object isReflexivity

    Returns true iff the given Formula is a reflexivity atom.

  25. object lcomp

    the logical complexity of this formula, i.e.

    the logical complexity of this formula, i.e. the number of logical connectives and atoms starting from the root of the formula. The inner structure of atoms is not counted.

  26. object normalizeFreeVariables
  27. object numOfAtoms

    Return the number of atoms in the given argument.

  28. object removeAllQuantifiers
  29. object removeNeg

    Remove the leading negation from a formula.

  30. object universalClosure

Ungrouped