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gapt.logic.hol

moveQuantifiers

object moveQuantifiers

Source
moveQuantifiers.scala
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  1. final def !=(arg0: Any): Boolean
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  6. def down(quantifier: QuantifierHelper, formula: Formula): Formula

    Moves all quantifiers of the given type down (decreases the scope) as far as possible by applying the following equivalences in the left to right direction:

    Moves all quantifiers of the given type down (decreases the scope) as far as possible by applying the following equivalences in the left to right direction:

    - ∃x (α ∨ β) <-> (∃x α) ∨ (∃x β), - ∀x (α ∧ β) <-> (∀x α) ∧ (∀x β), - Qx (α C β) <-> (Qx α) C β where Q is a quantifier, C ∈ {∧, ∨} and x does not occur in β, - Qx (β C α) <-> β C (Qx α) where Q is a quantifier, C ∈ {∧, ∨} and x does not occur in β.

    Moving stops when function encounters

    quantifier

    the type of quantifier to move down

    formula

    formula in which to move the quantifier down

    returns

    result of applying the above equivalences in the left to right direction as often as possible to the input formula

  7. final def eq(arg0: AnyRef): Boolean
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  17. def up(quantifier: QuantifierHelper, formula: Formula): Formula

    Moves all quantifiers of the given type (increases the scope) as far as possible by applying the following equivalences in the right to left direction:

    Moves all quantifiers of the given type (increases the scope) as far as possible by applying the following equivalences in the right to left direction:

    - ∃z (α[z/x] ∨ β[z/y]) <-> (∃x α) ∨ (∃y β) where z neither occurs in α nor in β, - ∀z (α[z/x] ∧ β[z/y]) <-> (∀x α) ∧ (∀y β) where z neither occurs in α nor in β, - Qx (α C β) <-> (Qx α) C β where Q is a quantifier, C ∈ {∧,∨} and x does not occur in β, - Qx (β C α) <-> β C (Qx α) where Q is a quantifier, C ∈ {∧,∨} and x does not occur in β.

    quantifier

    the type of quantifier to move up

    formula

    formula in which to move the quantifier up

    returns

    result of applying the above equivalences in the right to left equivalences as often as possible to the input formula

  18. final def wait(arg0: Long, arg1: Int): Unit
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  1. def finalize(): Unit
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    Deprecated

    (Since version ) see corresponding Javadoc for more information.

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