Data.Logic.ATP.Equate

ATOM with a distinguished Equate predicate.

Documentation

class HasApply atom => HasEquate atom where

Atoms that support equality must be an instance of HasEquate

Methods

equate :: TermOf atom -> TermOf atom -> atom

Create an equate predicate

foldEquate :: (TermOf atom -> TermOf atom -> r) -> (PredOf atom -> [TermOf atom] -> r) -> atom -> r

Analyze whether a predicate is an equate or a regular apply.

Instances

(IsPredicate predicate, IsTerm term) => HasEquate (FOL predicate term)

Defined in Data.Logic.ATP.Equate

Methods

equate :: TermOf (FOL predicate term) -> TermOf (FOL predicate term) -> FOL predicate term

foldEquate :: (TermOf (FOL predicate term) -> TermOf (FOL predicate term) -> r) -> (PredOf (FOL predicate term) -> [TermOf (FOL predicate term)] -> r) -> FOL predicate term -> r

(.=.) :: (IsFormula formula, HasEquate atom, atom ~ AtomOf formula) => TermOf atom -> TermOf atom -> formula infix 6

Combine equate and atomic to build a formula from two terms.

zipEquates :: (HasEquate atom1, HasEquate atom2, PredOf atom1 ~ PredOf atom2) => (TermOf atom1 -> TermOf atom1 -> TermOf atom2 -> TermOf atom2 -> Maybe r) -> (PredOf atom1 -> [(TermOf atom1, TermOf atom2)] -> Maybe r) -> atom1 -> atom2 -> Maybe r

Zip two atoms that support equality

prettyEquate :: IsTerm term => PrettyLevel -> Rational -> term -> term -> Doc

Format the infix equality predicate applied to two terms.

overtermsEq :: HasEquate atom => (TermOf atom -> r -> r) -> r -> atom -> r

Implementation of overterms for HasEquate types.

ontermsEq :: HasEquate atom => (TermOf atom -> TermOf atom) -> atom -> atom

Implementation of onterms for HasEquate types.

showApplyAndEquate :: (HasEquate atom, Show (TermOf atom)) => atom -> String

Implementation of Show for HasEquate types

showEquate :: Show term => term -> term -> String

convertEquate :: (HasEquate atom1, HasEquate atom2) => (PredOf atom1 -> PredOf atom2) -> (TermOf atom1 -> TermOf atom2) -> atom1 -> atom2

Convert between HasEquate atom types.

precedenceEquate :: HasEquate atom => atom -> Precedence

associativityEquate :: HasEquate atom => atom -> Associativity

data FOL predicate term

Instance of an atom type with a distinct equality predicate.

Constructors

R predicate [term]

Equals term term

Instances

IsFirstOrder EqFormula

Defined in Data.Logic.ATP.FOL

IsFirstOrder Formula

Defined in Data.Logic.ATP.Skolem

MonadFail m => Unify m (SkAtom, SkAtom)

Defined in Data.Logic.ATP.Unif

Associated Types

type UTermOf (SkAtom, SkAtom)

Methods

unify' :: (SkAtom, SkAtom) -> StateT (Map (TVarOf (UTermOf (SkAtom, SkAtom))) (UTermOf (SkAtom, SkAtom))) m ()

(IsPredicate predicate, IsTerm term) => HasApply (FOL predicate term)

Defined in Data.Logic.ATP.Equate

Associated Types

type PredOf (FOL predicate term)

type TermOf (FOL predicate term)

Methods

applyPredicate :: PredOf (FOL predicate term) -> [TermOf (FOL predicate term)] -> FOL predicate term

foldApply' :: (FOL predicate term -> r) -> (PredOf (FOL predicate term) -> [TermOf (FOL predicate term)] -> r) -> FOL predicate term -> r

overterms :: (TermOf (FOL predicate term) -> r -> r) -> r -> FOL predicate term -> r

onterms :: (TermOf (FOL predicate term) -> TermOf (FOL predicate term)) -> FOL predicate term -> FOL predicate term

(IsPredicate predicate, IsTerm term) => HasEquate (FOL predicate term)

Defined in Data.Logic.ATP.Equate

Methods

equate :: TermOf (FOL predicate term) -> TermOf (FOL predicate term) -> FOL predicate term

foldEquate :: (TermOf (FOL predicate term) -> TermOf (FOL predicate term) -> r) -> (PredOf (FOL predicate term) -> [TermOf (FOL predicate term)] -> r) -> FOL predicate term -> r

(IsPredicate predicate, IsTerm term) => IsAtom (FOL predicate term)

Defined in Data.Logic.ATP.Equate

(IsPredicate predicate, IsTerm term) => HasFixity (FOL predicate term)

Defined in Data.Logic.ATP.Equate

Methods

precedence :: FOL predicate term -> Precedence

associativity :: FOL predicate term -> Associativity

(Data predicate, Data term) => Data (FOL predicate term)

Defined in Data.Logic.ATP.Equate

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> FOL predicate term -> c (FOL predicate term)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (FOL predicate term)

toConstr :: FOL predicate term -> Constr

dataTypeOf :: FOL predicate term -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (FOL predicate term))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (FOL predicate term))

gmapT :: (forall b. Data b => b -> b) -> FOL predicate term -> FOL predicate term

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> FOL predicate term -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> FOL predicate term -> r

gmapQ :: (forall d. Data d => d -> u) -> FOL predicate term -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> FOL predicate term -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> FOL predicate term -> m (FOL predicate term)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> FOL predicate term -> m (FOL predicate term)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> FOL predicate term -> m (FOL predicate term)

(Read predicate, Read term) => Read (FOL predicate term)

Defined in Data.Logic.ATP.Equate

Methods

readsPrec :: Int -> ReadS (FOL predicate term)

readList :: ReadS [FOL predicate term]

readPrec :: ReadPrec (FOL predicate term)

readListPrec :: ReadPrec [FOL predicate term]

(IsPredicate predicate, IsTerm term, Show predicate, Show term) => Show (FOL predicate term)

Defined in Data.Logic.ATP.Equate

Methods

showsPrec :: Int -> FOL predicate term -> ShowS

show :: FOL predicate term -> String

showList :: [FOL predicate term] -> ShowS

(Eq predicate, Eq term) => Eq (FOL predicate term)

Defined in Data.Logic.ATP.Equate

Methods

(==) :: FOL predicate term -> FOL predicate term -> Bool

(/=) :: FOL predicate term -> FOL predicate term -> Bool

(Ord predicate, Ord term) => Ord (FOL predicate term)

Defined in Data.Logic.ATP.Equate

Methods

compare :: FOL predicate term -> FOL predicate term -> Ordering

(<) :: FOL predicate term -> FOL predicate term -> Bool

(<=) :: FOL predicate term -> FOL predicate term -> Bool

(>) :: FOL predicate term -> FOL predicate term -> Bool

(>=) :: FOL predicate term -> FOL predicate term -> Bool

max :: FOL predicate term -> FOL predicate term -> FOL predicate term

min :: FOL predicate term -> FOL predicate term -> FOL predicate term

(HasApply (FOL predicate term), HasEquate (FOL predicate term), IsTerm term) => Pretty (FOL predicate term)

Defined in Data.Logic.ATP.Equate

Methods

pPrintPrec :: PrettyLevel -> Rational -> FOL predicate term -> Doc

pPrint :: FOL predicate term -> Doc

pPrintList :: PrettyLevel -> [FOL predicate term] -> Doc

type PredOf (FOL predicate term)

Defined in Data.Logic.ATP.Equate

type PredOf (FOL predicate term) = predicate

type TermOf (FOL predicate term)

Defined in Data.Logic.ATP.Equate

type TermOf (FOL predicate term) = term

type UTermOf (SkAtom, SkAtom)

Defined in Data.Logic.ATP.Unif

type UTermOf (SkAtom, SkAtom) = TermOf SkAtom

type EqAtom = FOL Predicate FTerm

An atom type with equality predicate