eliminators-0.5: Dependently typed elimination functions using singletons

Data.Eliminator

Contents

Description

Dependently typed elimination functions using singletons.

Synopsis

# Eliminator functions

These eliminators are defined with propositions of kind <Datatype> ~> Type (that is, using the (~>) kind). These eliminators are designed for defunctionalized (i.e., "partially applied") types as predicates, and as a result, the predicates must be applied manually with Apply.

The naming conventions are:

• If the datatype has an alphanumeric name, its eliminator will have that name with elim prepended.
• If the datatype has a symbolic name, its eliminator will have that name with ~> prepended.

elimBool :: forall (p :: (~>) Bool Type) (s :: Bool). Sing s -> Apply p False -> Apply p True -> Apply p s Source #

elimEither :: forall (a :: Type) (b :: Type) (p :: (~>) (Either a b) Type) (s :: Either a b). Sing s -> (forall (f0 :: a). Sing f0 -> Apply p (Left f0)) -> (forall (f0 :: b). Sing f0 -> Apply p (Right f0)) -> Apply p s Source #

elimList :: forall (a :: Type) (p :: (~>) ([] a) Type) (s :: [] a). Sing s -> Apply p [] -> (forall (f0 :: a). Sing f0 -> forall (f1 :: [a]). Sing f1 -> Apply p f1 -> Apply p ((:) f0 f1)) -> Apply p s Source #

elimMaybe :: forall (a :: Type) (p :: (~>) (Maybe a) Type) (s :: Maybe a). Sing s -> Apply p Nothing -> (forall (f0 :: a). Sing f0 -> Apply p (Just f0)) -> Apply p s Source #

elimNat :: forall (p :: (~>) Nat Type) (s :: Nat). Sing s -> Apply p Z -> (forall (f0 :: Nat). Sing f0 -> Apply p f0 -> Apply p (S f0)) -> Apply p s Source #

elimNonEmpty :: forall (a :: Type) (p :: (~>) (NonEmpty a) Type) (s :: NonEmpty a). Sing s -> (forall (f0 :: a). Sing f0 -> forall (f1 :: [a]). Sing f1 -> Apply p ((:|) f0 f1)) -> Apply p s Source #

elimOrdering :: forall (p :: (~>) Ordering Type) (s :: Ordering). Sing s -> Apply p LT -> Apply p EQ -> Apply p GT -> Apply p s Source #

elimTuple0 :: forall (p :: (~>) () Type) (s :: ()). Sing s -> Apply p () -> Apply p s Source #

elimTuple2 :: forall (a :: Type) (b :: Type) (p :: (~>) ((,) a b) Type) (s :: (,) a b). Sing s -> (forall (f0 :: a). Sing f0 -> forall (f1 :: b). Sing f1 -> Apply p ((,) f0 f1)) -> Apply p s Source #

elimTuple3 :: forall (a :: Type) (b :: Type) (c :: Type) (p :: (~>) ((,,) a b c) Type) (s :: (,,) a b c). Sing s -> (forall (f0 :: a). Sing f0 -> forall (f1 :: b). Sing f1 -> forall (f2 :: c). Sing f2 -> Apply p ((,,) f0 f1 f2)) -> Apply p s Source #

elimTuple4 :: forall (a :: Type) (b :: Type) (c :: Type) (d :: Type) (p :: (~>) ((,,,) a b c d) Type) (s :: (,,,) a b c d). Sing s -> (forall (f0 :: a). Sing f0 -> forall (f1 :: b). Sing f1 -> forall (f2 :: c). Sing f2 -> forall (f3 :: d). Sing f3 -> Apply p ((,,,) f0 f1 f2 f3)) -> Apply p s Source #

elimTuple5 :: forall (a :: Type) (b :: Type) (c :: Type) (d :: Type) (e :: Type) (p :: (~>) ((,,,,) a b c d e) Type) (s :: (,,,,) a b c d e). Sing s -> (forall (f0 :: a). Sing f0 -> forall (f1 :: b). Sing f1 -> forall (f2 :: c). Sing f2 -> forall (f3 :: d). Sing f3 -> forall (f4 :: e). Sing f4 -> Apply p ((,,,,) f0 f1 f2 f3 f4)) -> Apply p s Source #

elimTuple6 :: forall (a :: Type) (b :: Type) (c :: Type) (d :: Type) (e :: Type) (f :: Type) (p :: (~>) ((,,,,,) a b c d e f) Type) (s :: (,,,,,) a b c d e f). Sing s -> (forall (f0 :: a). Sing f0 -> forall (f1 :: b). Sing f1 -> forall (f2 :: c). Sing f2 -> forall (f3 :: d). Sing f3 -> forall (f4 :: e). Sing f4 -> forall (f5 :: f). Sing f5 -> Apply p ((,,,,,) f0 f1 f2 f3 f4 f5)) -> Apply p s Source #

elimTuple7 :: forall (a :: Type) (b :: Type) (c :: Type) (d :: Type) (e :: Type) (f :: Type) (g :: Type) (p :: (~>) ((,,,,,,) a b c d e f g) Type) (s :: (,,,,,,) a b c d e f g). Sing s -> (forall (f0 :: a). Sing f0 -> forall (f1 :: b). Sing f1 -> forall (f2 :: c). Sing f2 -> forall (f3 :: d). Sing f3 -> forall (f4 :: e). Sing f4 -> forall (f5 :: f). Sing f5 -> forall (f6 :: g). Sing f6 -> Apply p ((,,,,,,) f0 f1 f2 f3 f4 f5 f6)) -> Apply p s Source #

elimVoid :: forall (p :: (~>) Void Type) (s :: Void). Sing s -> Apply p s Source #