logic-classes-1.4.7: Framework for propositional and first order logic, theorem proving

Data.Logic.Classes.Literal

Synopsis

# Documentation

class (Negatable lit, Constants lit, HasFixity atom, Formula lit atom, Ord lit) => Literal lit atom | lit -> atom whereSource

Literals are the building blocks of the clause and implicative normal |forms. They support negation and must include True and False elements.

Methods

foldLiteral :: (lit -> r) -> (Bool -> r) -> (atom -> r) -> lit -> rSource

Instances

 (Negatable (Formula atom), Constants (Formula atom), Formula (Formula atom) atom, Ord (Formula atom), Pretty atom, HasFixity atom, Ord atom) => Literal (Formula atom) atom (Negatable (Formula atom), Constants (Formula atom), Formula (Formula atom) atom, Ord (Formula atom), HasFixity atom, Pretty atom, Ord atom) => Literal (Formula atom) atom (Negatable (Formula FOLEQ), Constants (Formula FOLEQ), HasFixity FOLEQ, Ord (Formula FOLEQ), Formula (Formula FOLEQ) FOLEQ) => Literal (Formula FOLEQ) FOLEQ (Negatable (Formula v p f), Constants (Formula v p f), HasFixity (Predicate p (PTerm v f)), Ord (Formula v p f), Constants p, Ord v, Ord p, Ord f, Constants (Predicate p (PTerm v f)), Formula (Formula v p f) (Predicate p (PTerm v f))) => Literal (Formula v p f) (Predicate p (PTerm v f))

zipLiterals :: Literal lit atom => (lit -> lit -> Maybe r) -> (Bool -> Bool -> Maybe r) -> (atom -> atom -> Maybe r) -> lit -> lit -> Maybe rSource

fromFirstOrder :: forall formula atom v lit atom2. (Formula lit atom2, FirstOrderFormula formula atom v, Literal lit atom2) => (atom -> atom2) -> formula -> Failing litSource

Just like Logic.FirstOrder.convertFOF except it rejects anything with a construct unsupported in a normal logic formula, i.e. quantifiers and formula combinators other than negation.

fromLiteral :: forall lit atom v fof atom2. (Literal lit atom, FirstOrderFormula fof atom2 v) => (atom -> atom2) -> lit -> fofSource

toPropositional :: forall lit atom pf atom2. (Literal lit atom, PropositionalFormula pf atom2) => (atom -> atom2) -> lit -> pfSource

prettyLit :: forall lit atom v. Literal lit atom => (Int -> atom -> Doc) -> (v -> Doc) -> Int -> lit -> DocSource

foldAtomsLiteral :: Literal lit atom => (r -> atom -> r) -> r -> lit -> rSource