package hol
- Alphabetic
- Public
- Protected
Type Members
- trait HOLAtomConst extends Const with HOLPartialAtom
- class HOLOrdering extends Ordering[Expr]
- trait HOLPartialAtom extends Expr
- 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.
- class TAOrdering extends Ordering[Ty]
Value Members
- object BinaryConnective
- object HOLAtomConst
- object HOLFunction
- object HOLOrdering extends HOLOrdering
Ordering for HOL Formulas (also for FOL)
- object HOLPosition extends Serializable
- object TAOrdering extends TAOrdering
Ordering on types.
- object atoms
Return the list of all atoms in the given argument.
- object containsHOQuantifier
- object containsQuantifier
True iff All or Ex matches any subterm of e.
- 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.
- object containsStrongQuantifier
- object containsWeakQuantifier
- 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.
- object existentialClosure
- object formulaToSequent
Removes top-level connectives from a formula.
- object freeHOVariables
- object inductionPrinciple
- object instantiate
Instantiates a formula with terms.
- object isAtom
Returns true iff the given Formula is an atom (which does not include top nor bottom).
- 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.
- object isLogicalConstant
Returns true iff the given Expr consists of a logical constant.
- object isNeg
Returns true iff the given Formula starts with a negation.
- object isPrenex
Returns true iff the given formula is prenex.
- object isReflexivity
Returns true iff the given Formula is a reflexivity atom.
- 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.
- object normalizeFreeVariables
- object numOfAtoms
Return the number of atoms in the given argument.
- object removeAllQuantifiers
- object removeNeg
Remove the leading negation from a formula.
- object universalClosure
This is the API documentation for GAPT.
The main package is gapt.