Data.Eliminator

Dependently typed elimination functions using singletons.

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.

elimAll :: forall (p :: (~>) All Type) (s :: All). Sing s -> (forall (f0 :: Bool). Sing f0 -> Apply p ('All f0)) -> Apply p s

type family ElimAll p s p where ...

Equations

ElimAll p ('All s0) useThis = useThis s0

elimAny :: forall (p :: (~>) Any Type) (s :: Any). Sing s -> (forall (f0 :: Bool). Sing f0 -> Apply p ('Any f0)) -> Apply p s

type family ElimAny p s p where ...

Equations

ElimAny p ('Any s0) useThis = useThis s0

elimArg :: forall (a :: Type) (b :: Type) (p :: (~>) (Arg a b) Type) (s :: Arg a b). Sing s -> (forall (f0 :: a). Sing f0 -> forall (f1 :: b). Sing f1 -> Apply p ('Arg f0 f1)) -> Apply p s

type family ElimArg p s p where ...

Equations

ElimArg @a @b p ('Arg s0 s1) useThis = useThis s0 s1

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

type family ElimBool p s p p where ...

Equations

ElimBool p 'False useThis _p1 = useThis

ElimBool p 'True _p0 useThis = useThis

elimConst :: forall (a :: Type) (k :: Type) (b :: k) (p :: (~>) (Const a b) Type) (s :: Const a b). Sing s -> (forall (f0 :: a). Sing f0 -> Apply p ('Const f0)) -> Apply p s

type family ElimConst p s p where ...

Equations

ElimConst @a @k @b p ('Const s0) useThis = useThis s0

elimDown :: forall (a :: Type) (p :: (~>) (Down a) Type) (s :: Down a). Sing s -> (forall (f0 :: a). Sing f0 -> Apply p ('Down f0)) -> Apply p s

type family ElimDown p s p where ...

Equations

ElimDown @a p ('Down s0) useThis = useThis s0

elimDual :: forall (a :: Type) (p :: (~>) (Dual a) Type) (s :: Dual a). Sing s -> (forall (f0 :: a). Sing f0 -> Apply p ('Dual f0)) -> Apply p s

type family ElimDual p s p where ...

Equations

ElimDual @a p ('Dual s0) useThis = useThis s0

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

type family ElimEither p s p p where ...

Equations

ElimEither @a @b p ('Left s0) useThis _p1 = useThis s0

ElimEither @a @b p ('Right s0) _p0 useThis = useThis s0

elimFirst :: forall (a :: Type) (p :: (~>) (First a) Type) (s :: First a). Sing s -> (forall (f0 :: a). Sing f0 -> Apply p ('First f0)) -> Apply p s

type family ElimFirst p s p where ...

Equations

ElimFirst @a p ('First s0) useThis = useThis s0

elimIdentity :: forall (a :: Type) (p :: (~>) (Identity a) Type) (s :: Identity a). Sing s -> (forall (f0 :: a). Sing f0 -> Apply p ('Identity f0)) -> Apply p s

type family ElimIdentity p s p where ...

Equations

ElimIdentity @a p ('Identity s0) useThis = useThis s0

elimLast :: forall (a :: Type) (p :: (~>) (Last a) Type) (s :: Last a). Sing s -> (forall (f0 :: a). Sing f0 -> Apply p ('Last f0)) -> Apply p s

type family ElimLast p s p where ...

Equations

ElimLast @a p ('Last s0) useThis = useThis s0

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

type family ElimList p s p p where ...

Equations

ElimList @a p '[] useThis _p1 = useThis

ElimList @a p ('(:) s0 s1) _p0 useThis = Apply (useThis s0 s1) (ElimList @a p s1 _p0 useThis)

elimMax :: forall (a :: Type) (p :: (~>) (Max a) Type) (s :: Max a). Sing s -> (forall (f0 :: a). Sing f0 -> Apply p ('Max f0)) -> Apply p s

type family ElimMax p s p where ...

Equations

ElimMax @a p ('Max s0) useThis = useThis s0

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

type family ElimMaybe p s p p where ...

Equations

ElimMaybe @a p 'Nothing useThis _p1 = useThis

ElimMaybe @a p ('Just s0) _p0 useThis = useThis s0

elimMin :: forall (a :: Type) (p :: (~>) (Min a) Type) (s :: Min a). Sing s -> (forall (f0 :: a). Sing f0 -> Apply p ('Min f0)) -> Apply p s

type family ElimMin p s p where ...

Equations

ElimMin @a p ('Min s0) useThis = useThis s0

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

type family ElimNat p s p p where ...

Equations

ElimNat p 'Z useThis _p1 = useThis

ElimNat p ('S s0) _p0 useThis = Apply (useThis s0) (ElimNat p s0 _p0 useThis)

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

type family ElimNonEmpty p s p where ...

Equations

ElimNonEmpty @a p ('(:|) s0 s1) useThis = useThis s0 s1

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

type family ElimOrdering p s p p p where ...

Equations

ElimOrdering p 'LT useThis _p1 _p2 = useThis

ElimOrdering p 'EQ _p0 useThis _p2 = useThis

ElimOrdering p 'GT _p0 _p1 useThis = useThis

elimProduct :: forall (a :: Type) (p :: (~>) (Product a) Type) (s :: Product a). Sing s -> (forall (f0 :: a). Sing f0 -> Apply p ('Product f0)) -> Apply p s

type family ElimProduct p s p where ...

Equations

ElimProduct @a p ('Product s0) useThis = useThis s0

elimSum :: forall (a :: Type) (p :: (~>) (Sum a) Type) (s :: Sum a). Sing s -> (forall (f0 :: a). Sing f0 -> Apply p ('Sum f0)) -> Apply p s

type family ElimSum p s p where ...

Equations

ElimSum @a p ('Sum s0) useThis = useThis s0

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

type family ElimTuple0 p s p where ...

Equations

ElimTuple0 p '() useThis = useThis

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

type family ElimTuple2 p s p where ...

Equations

ElimTuple2 @a @b p ('(,) s0 s1) useThis = useThis s0 s1

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

type family ElimTuple3 p s p where ...

Equations

ElimTuple3 @a @b @c p ('(,,) s0 s1 s2) useThis = useThis s0 s1 s2

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

type family ElimTuple4 p s p where ...

Equations

ElimTuple4 @a @b @c @d p ('(,,,) s0 s1 s2 s3) useThis = useThis s0 s1 s2 s3

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

type family ElimTuple5 p s p where ...

Equations

ElimTuple5 @a @b @c @d @e p ('(,,,,) s0 s1 s2 s3 s4) useThis = useThis s0 s1 s2 s3 s4

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

type family ElimTuple6 p s p where ...

Equations

ElimTuple6 @a @b @c @d @e @f p ('(,,,,,) s0 s1 s2 s3 s4 s5) useThis = useThis s0 s1 s2 s3 s4 s5

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

type family ElimTuple7 p s p where ...

Equations

ElimTuple7 @a @b @c @d @e @f @g p ('(,,,,,,) s0 s1 s2 s3 s4 s5 s6) useThis = useThis s0 s1 s2 s3 s4 s5 s6

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

type family ElimVoid p s where ...

elimWrappedMonoid :: forall (m :: Type) (p :: (~>) (WrappedMonoid m) Type) (s :: WrappedMonoid m). Sing s -> (forall (f0 :: m). Sing f0 -> Apply p ('WrapMonoid f0)) -> Apply p s

type family ElimWrappedMonoid p s p where ...

Equations

ElimWrappedMonoid @m p ('WrapMonoid s0) useThis = useThis s0