object moveQuantifiers
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- moveQuantifiers.scala
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- moveQuantifiers
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- 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
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- 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
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This is the API documentation for GAPT.
The main package is gapt.