Data.Singletons.Prelude

Mimics the Haskell Prelude, but with singleton types. Includes the basic singleton definitions. Note: This is currently very incomplete!

Because many of these definitions are produced by Template Haskell, it is not possible to create proper Haddock documentation. Also, please excuse the apparent repeated variable names. This is due to an interaction between Template Haskell and Haddock.

Basic singleton definitions

module Data.Singletons

data family Sing a

The singleton kind-indexed data family.

Instances

TestCoercion * (Sing *)

SDecide k (KProxy k) => TestEquality k (Sing k)

data Sing Bool where

• SFalse :: (~) Bool z False => Sing Bool z
• STrue :: (~) Bool z True => Sing Bool z

data Sing Ordering where

• SLT :: (~) Ordering z LT => Sing Ordering z
• SEQ :: (~) Ordering z EQ => Sing Ordering z
• SGT :: (~) Ordering z GT => Sing Ordering z

data Sing * where

• STypeRep :: Typeable * a => Sing * a

data Sing Nat where

• SNat :: KnownNat n => Sing Nat n

data Sing Symbol where

• SSym :: KnownSymbol n => Sing Symbol n

data Sing () where

• STuple0 :: (~) () z () => Sing () z

data Sing [a0] where

• SNil :: (~) [a] z ([] a) => Sing [a] z
• SCons :: (~) [a] z ((:) a n n) => Sing a n -> Sing [a] n -> Sing [a] z

data Sing (Maybe a0) where

• SNothing :: (~) (Maybe a) z (Nothing a) => Sing (Maybe a) z
• SJust :: (~) (Maybe a) z (Just a n) => Sing a n -> Sing (Maybe a) z

data Sing (TyFun k1 k2 -> *) = SLambda {

• applySing :: forall t. Sing k1 t -> Sing k2 ((@@) k2 k1 f t)

}

data Sing (Either a0 b0) where

• SLeft :: (~) (Either a b) z (Left a b n) => Sing a n -> Sing (Either a b) z
• SRight :: (~) (Either a b) z (Right a b n) => Sing b n -> Sing (Either a b) z

data Sing ((,) a0 b0) where

• STuple2 :: (~) ((,) a b) z ((,) a b n n) => Sing a n -> Sing b n -> Sing ((,) a b) z

data Sing ((,,) a0 b0 c0) where

• STuple3 :: (~) ((,,) a b c) z ((,,) a b c n n n) => Sing a n -> Sing b n -> Sing c n -> Sing ((,,) a b c) z

data Sing ((,,,) a0 b0 c0 d0) where

• STuple4 :: (~) ((,,,) a b c d) z ((,,,) a b c d n n n n) => Sing a n -> Sing b n -> Sing c n -> Sing d n -> Sing ((,,,) a b c d) z

data Sing ((,,,,) a0 b0 c0 d0 e0) where

• STuple5 :: (~) ((,,,,) a b c d e) z ((,,,,) a b c d e n n n n n) => Sing a n -> Sing b n -> Sing c n -> Sing d n -> Sing e n -> Sing ((,,,,) a b c d e) z

data Sing ((,,,,,) a0 b0 c0 d0 e0 f0) where

• STuple6 :: (~) ((,,,,,) a b c d e f) z ((,,,,,) a b c d e f n n n n n n) => Sing a n -> Sing b n -> Sing c n -> Sing d n -> Sing e n -> Sing f n -> Sing ((,,,,,) a b c d e f) z

data Sing ((,,,,,,) a0 b0 c0 d0 e0 f0 g0) where

• STuple7 :: (~) ((,,,,,,) a b c d e f g) z ((,,,,,,) a b c d e f g n n n n n n n) => Sing a n -> Sing b n -> Sing c n -> Sing d n -> Sing e n -> Sing f n -> Sing g n -> Sing ((,,,,,,) a b c d e f g) z

Though Haddock doesn't show it, the Sing instance above includes the following instances

data instance Sing (a :: Bool) where
  SFalse :: Sing False
  STrue  :: Sing True

data instance Sing (a :: [k]) where
  SNil  :: Sing '[]
  SCons :: Sing (h :: k) -> Sing (t :: [k]) -> Sing (h ': t)

data instance Sing (a :: Maybe k) where
  SNothing :: Sing Nothing
  SJust    :: Sing (a :: k) -> Sing (Just a)

data instance Sing (a :: Either x y) where
  SLeft  :: Sing (a :: x) -> Sing (Left a)
  SRight :: Sing (b :: y) -> Sing (Right b)

data instance Sing (a :: Ordering) where
  SLT :: Sing LT
  SEQ :: Sing EQ
  SGT :: Sing GT

data instance Sing (a :: ()) where
  STuple0 :: Sing '()

data instance Sing (z :: (a, b)) where
  STuple2 :: Sing a -> Sing b -> Sing '(a, b)

data instance Sing (z :: (a, b, c)) where
  STuple3 :: Sing a -> Sing b -> Sing c -> Sing '(a, b, c)

data instance Sing (z :: (a, b, c, d)) where
  STuple4 :: Sing a -> Sing b -> Sing c -> Sing d -> Sing '(a, b, c, d)

data instance Sing (z :: (a, b, c, d, e)) where
  STuple5 :: Sing a -> Sing b -> Sing c -> Sing d -> Sing e -> Sing '(a, b, c, d, e)

data instance Sing (z :: (a, b, c, d, e, f)) where
  STuple6 :: Sing a -> Sing b -> Sing c -> Sing d -> Sing e -> Sing f
          -> Sing '(a, b, c, d, e, f)

data instance Sing (z :: (a, b, c, d, e, f, g)) where
  STuple7 :: Sing a -> Sing b -> Sing c -> Sing d -> Sing e -> Sing f
          -> Sing g -> Sing '(a, b, c, d, e, f, g)

Singleton type synonyms

These synonyms are all kind-restricted synonyms of Sing. For example SBool requires an argument of kind Bool.

type SBool z = Sing z

type SList z = Sing z

type SMaybe z = Sing z

type SEither z = Sing z

type SOrdering z = Sing z

type STuple0 z = Sing z

type STuple2 z = Sing z

type STuple3 z = Sing z

type STuple4 z = Sing z

type STuple5 z = Sing z

type STuple6 z = Sing z

type STuple7 z = Sing z

Functions working with Bool

type family If cond tru fls :: k

Type-level If. If True a b ==> a; If False a b ==> b

Equations

If k True tru fls = tru

If k False tru fls = fls

sIf :: Sing a -> Sing b -> Sing c -> Sing (If a b c)

Conditional over singletons

type family Not a :: Bool

Equations

Not False = TrueSym0

Not True = FalseSym0

sNot :: forall t. Sing t -> Sing (Apply NotSym0 t)

type family a :&& a :: Bool

Equations

False :&& z = FalseSym0

True :&& x = x

type family a :|| a :: Bool

Equations

False :|| x = x

True :|| z = TrueSym0

(%:&&) :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply (:&&$) t) t)

(%:||) :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply (:||$) t) t)

type Otherwise = (TrueSym0 :: Bool)

sOtherwise :: Sing OtherwiseSym0

Error reporting

type family Error str :: k

The promotion of error

data ErrorSym0 t1

Instances

type Apply k Symbol (ErrorSym0 Symbol k) a = Error k a

sError :: Sing (str :: Symbol) -> a

The singleton for error

Singleton equality

module Data.Singletons.Prelude.Eq

Singleton comparisons

module Data.Singletons.Prelude.Ord

Miscellaneous functions

type family Id a :: a

Equations

Id x = x

sId :: forall t. Sing t -> Sing (Apply IdSym0 t)

type family Const a a :: a

Equations

Const x z = x

sConst :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply ConstSym0 t) t)

type family (a :. a) a :: c

Equations

(f :. g) a_1627849012 = Apply (Apply (Apply (Apply Lambda_1627849017Sym0 f) g) a_1627849012) a_1627849012

(%:.) :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply (:.$) t) t) t)

type family f $ x :: b

Instances

type ($) k k1 f x = (@@) k k1 f x

(%$) :: forall f x. Sing f -> Sing x -> Sing ((($$) @@ f) @@ x)

type family f $! x :: b

Instances

type ($!) k k1 f x = (@@) k k1 f x

(%$!) :: forall f x. Sing f -> Sing x -> Sing ((($!$) @@ f) @@ x)

type family Flip a a a :: c

Equations

Flip f x y = Apply (Apply f y) x

sFlip :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply FlipSym0 t) t) t)

type family AsTypeOf a a :: a

Equations

AsTypeOf a_1627849051 a_1627849053 = Apply (Apply ConstSym0 a_1627849051) a_1627849053

sAsTypeOf :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply AsTypeOfSym0 t) t)

type family Seq a a :: b

Equations

Seq z x = x

sSeq :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply SeqSym0 t) t)

List operations

type family Map a a :: [] b

Equations

Map z [] = []

Map f ((:) x xs) = Apply (Apply (:$) (Apply f x)) (Apply (Apply MapSym0 f) xs)

sMap :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply MapSym0 t) t)

type family a :++ a :: [] a

Equations

[] :++ ys = ys

((:) x xs) :++ ys = Apply (Apply (:$) x) (Apply (Apply (:++$) xs) ys)

(%:++) :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply (:++$) t) t)

type family Head a :: a

Equations

Head ((:) a z) = a

Head [] = Apply ErrorSym0 "Data.Singletons.List.head: empty list"

sHead :: forall t. Sing t -> Sing (Apply HeadSym0 t)

type family Last a :: a

Equations

Last [] = Apply ErrorSym0 "Data.Singletons.List.last: empty list"

Last ((:) x xs) = Apply (Apply (Let_1627895699Last'Sym2 x xs) x) xs

sLast :: forall t. Sing t -> Sing (Apply LastSym0 t)

type family Tail a :: [] a

Equations

Tail ((:) z t) = t

Tail [] = Apply ErrorSym0 "Data.Singletons.List.tail: empty list"

sTail :: forall t. Sing t -> Sing (Apply TailSym0 t)

type family Init a :: [] a

Equations

Init [] = Apply ErrorSym0 "Data.Singletons.List.init: empty list"

Init ((:) x xs) = Apply (Apply (Let_1627895661Init'Sym2 x xs) x) xs

sInit :: forall t. Sing t -> Sing (Apply InitSym0 t)

type family Null a :: Bool

Equations

Null [] = TrueSym0

Null ((:) z z) = FalseSym0

sNull :: forall t. Sing t -> Sing (Apply NullSym0 t)

type family Reverse a :: [] a

Equations

Reverse l = Apply (Apply (Let_1627895618RevSym1 l) l) []

sReverse :: forall t. Sing t -> Sing (Apply ReverseSym0 t)

Reducing lists (folds)

type family Foldl a a a :: b

Equations

Foldl f z0 xs0 = Apply (Apply (Let_1627894911LgoSym3 f z0 xs0) z0) xs0

sFoldl :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply FoldlSym0 t) t) t)

type family Foldl1 a a :: a

Equations

Foldl1 f ((:) x xs) = Apply (Apply (Apply FoldlSym0 f) x) xs

Foldl1 z [] = Apply ErrorSym0 "Data.Singletons.List.foldl1: empty list"

sFoldl1 :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply Foldl1Sym0 t) t)

type family Foldr a a a :: b

Equations

Foldr k z a_1627849112 = Apply (Let_1627849117GoSym3 k z a_1627849112) a_1627849112

sFoldr :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply FoldrSym0 t) t) t)

type family Foldr1 a a :: a

Equations

Foldr1 z ((:) x []) = x

Foldr1 f ((:) x ((:) wild_1627893550 wild_1627893552)) = Apply (Apply f x) (Apply (Apply Foldr1Sym0 f) (Let_1627894773XsSym4 f x wild_1627893550 wild_1627893552))

Foldr1 z [] = Apply ErrorSym0 "Data.Singletons.List.foldr1: empty list"

sFoldr1 :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply Foldr1Sym0 t) t)

Special folds

type family And a :: Bool

Equations

And [] = TrueSym0

And ((:) x xs) = Apply (Apply (:&&$) x) (Apply AndSym0 xs)

sAnd :: forall t. Sing t -> Sing (Apply AndSym0 t)

type family Or a :: Bool

Equations

Or [] = FalseSym0

Or ((:) x xs) = Apply (Apply (:||$) x) (Apply OrSym0 xs)

sOr :: forall t. Sing t -> Sing (Apply OrSym0 t)

type family Any_ a a :: Bool

Equations

Any_ z [] = FalseSym0

Any_ p ((:) x xs) = Apply (Apply (:||$) (Apply p x)) (Apply (Apply Any_Sym0 p) xs)

sAny_ :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply Any_Sym0 t) t)

type family All a a :: Bool

Equations

All z [] = TrueSym0

All p ((:) x xs) = Apply (Apply (:&&$) (Apply p x)) (Apply (Apply AllSym0 p) xs)

sAll :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply AllSym0 t) t)

type family Concat a :: [] a

Equations

Concat a_1627894751 = Apply (Apply (Apply FoldrSym0 (:++$)) []) a_1627894751

sConcat :: forall t. Sing t -> Sing (Apply ConcatSym0 t)

type family ConcatMap a a :: [] b

Equations

ConcatMap f a_1627894747 = Apply (Apply (Apply FoldrSym0 (Apply (Apply (:.$) (:++$)) f)) []) a_1627894747

sConcatMap :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply ConcatMapSym0 t) t)

Scans

type family Scanl a a a :: [] b

Equations

Scanl f q ls = Apply (Apply (:$) q) (Case_1627894694 f q ls (Let_1627894680Scrutinee_1627893554Sym3 f q ls))

sScanl :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply ScanlSym0 t) t) t)

type family Scanl1 a a :: [] a

Equations

Scanl1 f ((:) x xs) = Apply (Apply (Apply ScanlSym0 f) x) xs

Scanl1 z [] = []

sScanl1 :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply Scanl1Sym0 t) t)

type family Scanr a a a :: [] b

Equations

Scanr z q0 [] = Apply (Apply (:$) q0) []

Scanr f q0 ((:) x xs) = Case_1627894656 f q0 x xs (Let_1627894636Scrutinee_1627893556Sym4 f q0 x xs)

sScanr :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply ScanrSym0 t) t) t)

type family Scanr1 a a :: [] a

Equations

Scanr1 z [] = []

Scanr1 z ((:) x []) = Apply (Apply (:$) x) []

Scanr1 f ((:) x ((:) wild_1627893560 wild_1627893562)) = Case_1627894609 f x wild_1627893560 wild_1627893562 (Let_1627894589Scrutinee_1627893558Sym4 f x wild_1627893560 wild_1627893562)

sScanr1 :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply Scanr1Sym0 t) t)

Searching lists

type family Elem a a :: Bool

Equations

Elem z [] = FalseSym0

Elem x ((:) y ys) = Apply (Apply (:||$) (Apply (Apply (:==$) x) y)) (Apply (Apply ElemSym0 x) ys)

sElem :: forall t t. SEq (KProxy :: KProxy a) => Sing t -> Sing t -> Sing (Apply (Apply ElemSym0 t) t)

type family NotElem a a :: Bool

Equations

NotElem z [] = TrueSym0

NotElem x ((:) y ys) = Apply (Apply (:&&$) (Apply (Apply (:/=$) x) y)) (Apply (Apply NotElemSym0 x) ys)

sNotElem :: forall t t. SEq (KProxy :: KProxy a) => Sing t -> Sing t -> Sing (Apply (Apply NotElemSym0 t) t)

Zipping and unzipping lists

type family Zip a a :: [] ((,) a b)

Equations

Zip ((:) x xs) ((:) y ys) = Apply (Apply (:$) (Apply (Apply Tuple2Sym0 x) y)) (Apply (Apply ZipSym0 xs) ys)

Zip [] [] = []

Zip ((:) z z) [] = []

Zip [] ((:) z z) = []

sZip :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply ZipSym0 t) t)

type family Zip3 a a a :: [] ((,,) a b c)

Equations

Zip3 ((:) a as) ((:) b bs) ((:) c cs) = Apply (Apply (:$) (Apply (Apply (Apply Tuple3Sym0 a) b) c)) (Apply (Apply (Apply Zip3Sym0 as) bs) cs)

Zip3 [] [] [] = []

Zip3 [] [] ((:) z z) = []

Zip3 [] ((:) z z) [] = []

Zip3 [] ((:) z z) ((:) z z) = []

Zip3 ((:) z z) [] [] = []

Zip3 ((:) z z) [] ((:) z z) = []

Zip3 ((:) z z) ((:) z z) [] = []

sZip3 :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply Zip3Sym0 t) t) t)

type family ZipWith a a a :: [] c

Equations

ZipWith f ((:) x xs) ((:) y ys) = Apply (Apply (:$) (Apply (Apply f x) y)) (Apply (Apply (Apply ZipWithSym0 f) xs) ys)

ZipWith z [] [] = []

ZipWith z ((:) z z) [] = []

ZipWith z [] ((:) z z) = []

sZipWith :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply ZipWithSym0 t) t) t)

type family ZipWith3 a a a a :: [] d

Equations

ZipWith3 z ((:) a as) ((:) b bs) ((:) c cs) = Apply (Apply (:$) (Apply (Apply (Apply z a) b) c)) (Apply (Apply (Apply (Apply ZipWith3Sym0 z) as) bs) cs)

ZipWith3 z [] [] [] = []

ZipWith3 z [] [] ((:) z z) = []

ZipWith3 z [] ((:) z z) [] = []

ZipWith3 z [] ((:) z z) ((:) z z) = []

ZipWith3 z ((:) z z) [] [] = []

ZipWith3 z ((:) z z) [] ((:) z z) = []

ZipWith3 z ((:) z z) ((:) z z) [] = []

sZipWith3 :: forall t t t t. Sing t -> Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply (Apply ZipWith3Sym0 t) t) t) t)

type family Unzip a :: (,) ([] a) ([] b)

Equations

Unzip xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627893943Sym0 xs)) (Apply (Apply Tuple2Sym0 []) [])) xs

sUnzip :: forall t. Sing t -> Sing (Apply UnzipSym0 t)

type family Unzip3 a :: (,,) ([] a) ([] b) ([] c)

Equations

Unzip3 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627893909Sym0 xs)) (Apply (Apply (Apply Tuple3Sym0 []) []) [])) xs

sUnzip3 :: forall t. Sing t -> Sing (Apply Unzip3Sym0 t)

Other datatypes

type family Maybe_ a a a :: b

Equations

Maybe_ n z Nothing = n

Maybe_ z f (Just x) = Apply f x

sMaybe_ :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply Maybe_Sym0 t) t) t)

type family Either_ a a a :: c

Equations

Either_ f z (Left x) = Apply f x

Either_ z g (Right y) = Apply g y

sEither_ :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply Either_Sym0 t) t) t)

type family Fst a :: a

Equations

Fst ((,) x z) = x

sFst :: forall t. Sing t -> Sing (Apply FstSym0 t)

type family Snd a :: b

Equations

Snd ((,) z y) = y

sSnd :: forall t. Sing t -> Sing (Apply SndSym0 t)

type family Curry a a a :: c

Equations

Curry f x y = Apply f (Apply (Apply Tuple2Sym0 x) y)

sCurry :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply CurrySym0 t) t) t)

type family Uncurry a a :: c

Equations

Uncurry f p = Apply (Apply f (Apply FstSym0 p)) (Apply SndSym0 p)

sUncurry :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply UncurrySym0 t) t)

data Symbol :: *

(Kind) This is the kind of type-level symbols.

Instances

KnownSymbol n => SingI Symbol n

SingKind Symbol (KProxy Symbol)

SDecide Symbol (KProxy Symbol)

PEq Symbol (KProxy Symbol)

SEq Symbol (KProxy Symbol)

POrd Symbol (KProxy Symbol)

data Sing Symbol where

• SSym :: KnownSymbol n => Sing Symbol n

type (==) Symbol a b = EqSymbol a b

type (:==) Symbol a b = (==) Symbol a b

type Compare Symbol a b = CmpSymbol a b

type Apply k Symbol (ErrorSym0 Symbol k) a = Error k a

type DemoteRep Symbol (KProxy Symbol) = String

Other functions

either_ :: forall a c b. (a -> c) -> (b -> c) -> Either a b -> c

maybe_ :: forall b a. b -> (a -> b) -> Maybe a -> b

bool_ :: forall a. a -> a -> Bool -> a

any_ :: forall a. (a -> Bool) -> [a] -> Bool

Defunctionalization symbols

type FalseSym0 = False

type TrueSym0 = True

data NotSym0 l

Instances

SuppressUnusedWarnings (TyFun Bool Bool -> *) NotSym0

type Apply Bool Bool NotSym0 l0 = NotSym1 l0

type NotSym1 t = Not t

data (:&&$) l

Instances

SuppressUnusedWarnings (TyFun Bool (TyFun Bool Bool -> *) -> *) (:&&$)

type Apply (TyFun Bool Bool -> *) Bool (:&&$) l0 = (:&&$$) l0

data l :&&$$ l

Instances

SuppressUnusedWarnings (Bool -> TyFun Bool Bool -> *) (:&&$$)

type Apply Bool Bool ((:&&$$) l1) l0 = (:&&$$$) l1 l0

type (:&&$$$) t t = (:&&) t t

data (:||$) l

Instances

SuppressUnusedWarnings (TyFun Bool (TyFun Bool Bool -> *) -> *) (:||$)

type Apply (TyFun Bool Bool -> *) Bool (:||$) l0 = (:||$$) l0

data l :||$$ l

Instances

SuppressUnusedWarnings (Bool -> TyFun Bool Bool -> *) (:||$$)

type Apply Bool Bool ((:||$$) l1) l0 = (:||$$$) l1 l0

type (:||$$$) t t = (:||) t t

type OtherwiseSym0 = Otherwise

type NothingSym0 = Nothing

data JustSym0 l

Instances

SuppressUnusedWarnings (TyFun k (Maybe k) -> *) (JustSym0 k)

type Apply (Maybe k) k (JustSym0 k) l0 = JustSym1 k l0

type JustSym1 t = Just t

data Maybe_Sym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun (TyFun k k -> *) (TyFun (Maybe k) k -> *) -> *) -> *) (Maybe_Sym0 k k)

type Apply (TyFun (TyFun k1 k -> *) (TyFun (Maybe k1) k -> *) -> *) k (Maybe_Sym0 k1 k) l0 = Maybe_Sym1 k k1 l0

data Maybe_Sym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun (TyFun k k -> *) (TyFun (Maybe k) k -> *) -> *) (Maybe_Sym1 k k)

type Apply (TyFun (Maybe k) k1 -> *) (TyFun k k1 -> *) (Maybe_Sym1 k1 k l1) l0 = Maybe_Sym2 k1 k l1 l0

data Maybe_Sym2 l l l

Instances

SuppressUnusedWarnings (k -> (TyFun k k -> *) -> TyFun (Maybe k) k -> *) (Maybe_Sym2 k k)

type Apply k (Maybe k1) (Maybe_Sym2 k k1 l1 l2) l0 = Maybe_Sym3 k k1 l1 l2 l0

type Maybe_Sym3 t t t = Maybe_ t t t

data LeftSym0 l

Instances

SuppressUnusedWarnings (TyFun k (Either k k) -> *) (LeftSym0 k k)

type Apply (Either k k1) k (LeftSym0 k1 k) l0 = LeftSym1 k k1 l0

type LeftSym1 t = Left t

data RightSym0 l

Instances

SuppressUnusedWarnings (TyFun k (Either k k) -> *) (RightSym0 k k)

type Apply (Either k k1) k1 (RightSym0 k k1) l0 = RightSym1 k k1 l0

type RightSym1 t = Right t

data Either_Sym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k k -> *) (TyFun (TyFun k k -> *) (TyFun (Either k k) k -> *) -> *) -> *) (Either_Sym0 k k k)

type Apply (TyFun (TyFun k2 k -> *) (TyFun (Either k1 k2) k -> *) -> *) (TyFun k1 k -> *) (Either_Sym0 k2 k k1) l0 = Either_Sym1 k k1 k2 l0

data Either_Sym1 l l

Instances

SuppressUnusedWarnings ((TyFun k k -> *) -> TyFun (TyFun k k -> *) (TyFun (Either k k) k -> *) -> *) (Either_Sym1 k k k)

type Apply (TyFun (Either k2 k) k1 -> *) (TyFun k k1 -> *) (Either_Sym1 k1 k2 k l1) l0 = Either_Sym2 k1 k2 k l1 l0

data Either_Sym2 l l l

Instances

SuppressUnusedWarnings ((TyFun k k -> *) -> (TyFun k k -> *) -> TyFun (Either k k) k -> *) (Either_Sym2 k k k)

type Apply k (Either k1 k2) (Either_Sym2 k k1 k2 l1 l2) l0 = Either_Sym3 k k1 k2 l1 l2 l0

type Either_Sym3 t t t = Either_ t t t

type Tuple0Sym0 = ()

data Tuple2Sym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun k ((,) k k) -> *) -> *) (Tuple2Sym0 k k)

type Apply (TyFun k1 ((,) k k1) -> *) k (Tuple2Sym0 k1 k) l0 = Tuple2Sym1 k k1 l0

data Tuple2Sym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun k ((,) k k) -> *) (Tuple2Sym1 k k)

type Apply ((,) k1 k) k (Tuple2Sym1 k1 k l1) l0 = Tuple2Sym2 k1 k l1 l0

type Tuple2Sym2 t t = (,) t t

data Tuple3Sym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun k (TyFun k ((,,) k k k) -> *) -> *) -> *) (Tuple3Sym0 k k k)

type Apply (TyFun k2 (TyFun k ((,,) k1 k2 k) -> *) -> *) k1 (Tuple3Sym0 k2 k k1) l0 = Tuple3Sym1 k k1 k2 l0

data Tuple3Sym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun k (TyFun k ((,,) k k k) -> *) -> *) (Tuple3Sym1 k k k)

type Apply (TyFun k1 ((,,) k2 k k1) -> *) k (Tuple3Sym1 k1 k2 k l1) l0 = Tuple3Sym2 k2 k k1 l1 l0

data Tuple3Sym2 l l l

Instances

SuppressUnusedWarnings (k -> k -> TyFun k ((,,) k k k) -> *) (Tuple3Sym2 k k k)

type Apply ((,,) k1 k2 k) k (Tuple3Sym2 k1 k2 k l1 l2) l0 = Tuple3Sym3 k1 k2 k l1 l2 l0

type Tuple3Sym3 t t t = (,,) t t t

data Tuple4Sym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun k (TyFun k (TyFun k ((,,,) k k k k) -> *) -> *) -> *) -> *) (Tuple4Sym0 k k k k)

type Apply (TyFun k3 (TyFun k (TyFun k1 ((,,,) k2 k3 k k1) -> *) -> *) -> *) k2 (Tuple4Sym0 k3 k k1 k2) l0 = Tuple4Sym1 k k1 k2 k3 l0

data Tuple4Sym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun k (TyFun k (TyFun k ((,,,) k k k k) -> *) -> *) -> *) (Tuple4Sym1 k k k k)

type Apply (TyFun k2 (TyFun k ((,,,) k3 k1 k2 k) -> *) -> *) k1 (Tuple4Sym1 k2 k k3 k1 l1) l0 = Tuple4Sym2 k k3 k1 k2 l1 l0

data Tuple4Sym2 l l l

Instances

SuppressUnusedWarnings (k -> k -> TyFun k (TyFun k ((,,,) k k k k) -> *) -> *) (Tuple4Sym2 k k k k)

type Apply (TyFun k1 ((,,,) k2 k3 k k1) -> *) k (Tuple4Sym2 k1 k2 k3 k l1 l2) l0 = Tuple4Sym3 k2 k3 k k1 l1 l2 l0

data Tuple4Sym3 l l l l

Instances

SuppressUnusedWarnings (k -> k -> k -> TyFun k ((,,,) k k k k) -> *) (Tuple4Sym3 k k k k)

type Apply ((,,,) k1 k2 k3 k) k (Tuple4Sym3 k1 k2 k3 k l1 l2 l3) l0 = Tuple4Sym4 k1 k2 k3 k l1 l2 l3 l0

type Tuple4Sym4 t t t t = (,,,) t t t t

data Tuple5Sym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun k (TyFun k (TyFun k (TyFun k ((,,,,) k k k k k) -> *) -> *) -> *) -> *) -> *) (Tuple5Sym0 k k k k k)

type Apply (TyFun k4 (TyFun k (TyFun k1 (TyFun k2 ((,,,,) k3 k4 k k1 k2) -> *) -> *) -> *) -> *) k3 (Tuple5Sym0 k4 k k1 k2 k3) l0 = Tuple5Sym1 k k1 k2 k3 k4 l0

data Tuple5Sym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun k (TyFun k (TyFun k (TyFun k ((,,,,) k k k k k) -> *) -> *) -> *) -> *) (Tuple5Sym1 k k k k k)

type Apply (TyFun k3 (TyFun k (TyFun k1 ((,,,,) k4 k2 k3 k k1) -> *) -> *) -> *) k2 (Tuple5Sym1 k3 k k1 k4 k2 l1) l0 = Tuple5Sym2 k k1 k4 k2 k3 l1 l0

data Tuple5Sym2 l l l

Instances

SuppressUnusedWarnings (k -> k -> TyFun k (TyFun k (TyFun k ((,,,,) k k k k k) -> *) -> *) -> *) (Tuple5Sym2 k k k k k)

type Apply (TyFun k2 (TyFun k ((,,,,) k3 k4 k1 k2 k) -> *) -> *) k1 (Tuple5Sym2 k2 k k3 k4 k1 l1 l2) l0 = Tuple5Sym3 k k3 k4 k1 k2 l1 l2 l0

data Tuple5Sym3 l l l l

Instances

SuppressUnusedWarnings (k -> k -> k -> TyFun k (TyFun k ((,,,,) k k k k k) -> *) -> *) (Tuple5Sym3 k k k k k)

type Apply (TyFun k1 ((,,,,) k2 k3 k4 k k1) -> *) k (Tuple5Sym3 k1 k2 k3 k4 k l1 l2 l3) l0 = Tuple5Sym4 k2 k3 k4 k k1 l1 l2 l3 l0

data Tuple5Sym4 l l l l l

Instances

SuppressUnusedWarnings (k -> k -> k -> k -> TyFun k ((,,,,) k k k k k) -> *) (Tuple5Sym4 k k k k k)

type Apply ((,,,,) k1 k2 k3 k4 k) k (Tuple5Sym4 k1 k2 k3 k4 k l1 l2 l3 l4) l0 = Tuple5Sym5 k1 k2 k3 k4 k l1 l2 l3 l4 l0

type Tuple5Sym5 t t t t t = (,,,,) t t t t t

data Tuple6Sym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun k (TyFun k (TyFun k (TyFun k (TyFun k ((,,,,,) k k k k k k) -> *) -> *) -> *) -> *) -> *) -> *) (Tuple6Sym0 k k k k k k)

type Apply (TyFun k5 (TyFun k (TyFun k1 (TyFun k2 (TyFun k3 ((,,,,,) k4 k5 k k1 k2 k3) -> *) -> *) -> *) -> *) -> *) k4 (Tuple6Sym0 k5 k k1 k2 k3 k4) l0 = Tuple6Sym1 k k1 k2 k3 k4 k5 l0

data Tuple6Sym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun k (TyFun k (TyFun k (TyFun k (TyFun k ((,,,,,) k k k k k k) -> *) -> *) -> *) -> *) -> *) (Tuple6Sym1 k k k k k k)

type Apply (TyFun k4 (TyFun k (TyFun k1 (TyFun k2 ((,,,,,) k5 k3 k4 k k1 k2) -> *) -> *) -> *) -> *) k3 (Tuple6Sym1 k4 k k1 k2 k5 k3 l1) l0 = Tuple6Sym2 k k1 k2 k5 k3 k4 l1 l0

data Tuple6Sym2 l l l

Instances

SuppressUnusedWarnings (k -> k -> TyFun k (TyFun k (TyFun k (TyFun k ((,,,,,) k k k k k k) -> *) -> *) -> *) -> *) (Tuple6Sym2 k k k k k k)

type Apply (TyFun k3 (TyFun k (TyFun k1 ((,,,,,) k4 k5 k2 k3 k k1) -> *) -> *) -> *) k2 (Tuple6Sym2 k3 k k1 k4 k5 k2 l1 l2) l0 = Tuple6Sym3 k k1 k4 k5 k2 k3 l1 l2 l0

data Tuple6Sym3 l l l l

Instances

SuppressUnusedWarnings (k -> k -> k -> TyFun k (TyFun k (TyFun k ((,,,,,) k k k k k k) -> *) -> *) -> *) (Tuple6Sym3 k k k k k k)

type Apply (TyFun k2 (TyFun k ((,,,,,) k3 k4 k5 k1 k2 k) -> *) -> *) k1 (Tuple6Sym3 k2 k k3 k4 k5 k1 l1 l2 l3) l0 = Tuple6Sym4 k k3 k4 k5 k1 k2 l1 l2 l3 l0

data Tuple6Sym4 l l l l l

Instances

SuppressUnusedWarnings (k -> k -> k -> k -> TyFun k (TyFun k ((,,,,,) k k k k k k) -> *) -> *) (Tuple6Sym4 k k k k k k)

type Apply (TyFun k1 ((,,,,,) k2 k3 k4 k5 k k1) -> *) k (Tuple6Sym4 k1 k2 k3 k4 k5 k l1 l2 l3 l4) l0 = Tuple6Sym5 k2 k3 k4 k5 k k1 l1 l2 l3 l4 l0

data Tuple6Sym5 l l l l l l

Instances

SuppressUnusedWarnings (k -> k -> k -> k -> k -> TyFun k ((,,,,,) k k k k k k) -> *) (Tuple6Sym5 k k k k k k)

type Apply ((,,,,,) k1 k2 k3 k4 k5 k) k (Tuple6Sym5 k1 k2 k3 k4 k5 k l1 l2 l3 l4 l5) l0 = Tuple6Sym6 k1 k2 k3 k4 k5 k l1 l2 l3 l4 l5 l0

type Tuple6Sym6 t t t t t t = (,,,,,) t t t t t t

data Tuple7Sym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun k (TyFun k (TyFun k (TyFun k (TyFun k (TyFun k ((,,,,,,) k k k k k k k) -> *) -> *) -> *) -> *) -> *) -> *) -> *) (Tuple7Sym0 k k k k k k k)

type Apply (TyFun k6 (TyFun k (TyFun k1 (TyFun k2 (TyFun k3 (TyFun k4 ((,,,,,,) k5 k6 k k1 k2 k3 k4) -> *) -> *) -> *) -> *) -> *) -> *) k5 (Tuple7Sym0 k6 k k1 k2 k3 k4 k5) l0 = Tuple7Sym1 k k1 k2 k3 k4 k5 k6 l0

data Tuple7Sym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun k (TyFun k (TyFun k (TyFun k (TyFun k (TyFun k ((,,,,,,) k k k k k k k) -> *) -> *) -> *) -> *) -> *) -> *) (Tuple7Sym1 k k k k k k k)

type Apply (TyFun k5 (TyFun k (TyFun k1 (TyFun k2 (TyFun k3 ((,,,,,,) k6 k4 k5 k k1 k2 k3) -> *) -> *) -> *) -> *) -> *) k4 (Tuple7Sym1 k5 k k1 k2 k3 k6 k4 l1) l0 = Tuple7Sym2 k k1 k2 k3 k6 k4 k5 l1 l0

data Tuple7Sym2 l l l

Instances

SuppressUnusedWarnings (k -> k -> TyFun k (TyFun k (TyFun k (TyFun k (TyFun k ((,,,,,,) k k k k k k k) -> *) -> *) -> *) -> *) -> *) (Tuple7Sym2 k k k k k k k)

type Apply (TyFun k4 (TyFun k (TyFun k1 (TyFun k2 ((,,,,,,) k5 k6 k3 k4 k k1 k2) -> *) -> *) -> *) -> *) k3 (Tuple7Sym2 k4 k k1 k2 k5 k6 k3 l1 l2) l0 = Tuple7Sym3 k k1 k2 k5 k6 k3 k4 l1 l2 l0

data Tuple7Sym3 l l l l

Instances

SuppressUnusedWarnings (k -> k -> k -> TyFun k (TyFun k (TyFun k (TyFun k ((,,,,,,) k k k k k k k) -> *) -> *) -> *) -> *) (Tuple7Sym3 k k k k k k k)

type Apply (TyFun k3 (TyFun k (TyFun k1 ((,,,,,,) k4 k5 k6 k2 k3 k k1) -> *) -> *) -> *) k2 (Tuple7Sym3 k3 k k1 k4 k5 k6 k2 l1 l2 l3) l0 = Tuple7Sym4 k k1 k4 k5 k6 k2 k3 l1 l2 l3 l0

data Tuple7Sym4 l l l l l

Instances

SuppressUnusedWarnings (k -> k -> k -> k -> TyFun k (TyFun k (TyFun k ((,,,,,,) k k k k k k k) -> *) -> *) -> *) (Tuple7Sym4 k k k k k k k)

type Apply (TyFun k2 (TyFun k ((,,,,,,) k3 k4 k5 k6 k1 k2 k) -> *) -> *) k1 (Tuple7Sym4 k2 k k3 k4 k5 k6 k1 l1 l2 l3 l4) l0 = Tuple7Sym5 k k3 k4 k5 k6 k1 k2 l1 l2 l3 l4 l0

data Tuple7Sym5 l l l l l l

Instances

SuppressUnusedWarnings (k -> k -> k -> k -> k -> TyFun k (TyFun k ((,,,,,,) k k k k k k k) -> *) -> *) (Tuple7Sym5 k k k k k k k)

type Apply (TyFun k1 ((,,,,,,) k2 k3 k4 k5 k6 k k1) -> *) k (Tuple7Sym5 k1 k2 k3 k4 k5 k6 k l1 l2 l3 l4 l5) l0 = Tuple7Sym6 k2 k3 k4 k5 k6 k k1 l1 l2 l3 l4 l5 l0

data Tuple7Sym6 l l l l l l l

Instances

SuppressUnusedWarnings (k -> k -> k -> k -> k -> k -> TyFun k ((,,,,,,) k k k k k k k) -> *) (Tuple7Sym6 k k k k k k k)

type Apply ((,,,,,,) k1 k2 k3 k4 k5 k6 k) k (Tuple7Sym6 k1 k2 k3 k4 k5 k6 k l1 l2 l3 l4 l5 l6) l0 = Tuple7Sym7 k1 k2 k3 k4 k5 k6 k l1 l2 l3 l4 l5 l6 l0

type Tuple7Sym7 t t t t t t t = (,,,,,,) t t t t t t t

data FstSym0 l

Instances

SuppressUnusedWarnings (TyFun ((,) k k) k -> *) (FstSym0 k k)

type Apply k ((,) k k1) (FstSym0 k k1) l0 = FstSym1 k k1 l0

type FstSym1 t = Fst t

data SndSym0 l

Instances

SuppressUnusedWarnings (TyFun ((,) k k) k -> *) (SndSym0 k k)

type Apply k ((,) k1 k) (SndSym0 k k1) l0 = SndSym1 k k1 l0

type SndSym1 t = Snd t

data CurrySym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun ((,) k k) k -> *) (TyFun k (TyFun k k -> *) -> *) -> *) (CurrySym0 k k k)

type Apply (TyFun k1 (TyFun k2 k -> *) -> *) (TyFun ((,) k1 k2) k -> *) (CurrySym0 k k1 k2) l0 = CurrySym1 k k1 k2 l0

data CurrySym1 l l

Instances

SuppressUnusedWarnings ((TyFun ((,) k k) k -> *) -> TyFun k (TyFun k k -> *) -> *) (CurrySym1 k k k)

type Apply (TyFun k2 k1 -> *) k (CurrySym1 k1 k k2 l1) l0 = CurrySym2 k1 k k2 l1 l0

data CurrySym2 l l l

Instances

SuppressUnusedWarnings ((TyFun ((,) k k) k -> *) -> k -> TyFun k k -> *) (CurrySym2 k k k)

type Apply k1 k (CurrySym2 k1 k2 k l1 l2) l0 = CurrySym3 k1 k2 k l1 l2 l0

type CurrySym3 t t t = Curry t t t

data UncurrySym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k k -> *) -> *) (TyFun ((,) k k) k -> *) -> *) (UncurrySym0 k k k)

type Apply (TyFun ((,) k1 k2) k -> *) (TyFun k1 (TyFun k2 k -> *) -> *) (UncurrySym0 k k1 k2) l0 = UncurrySym1 k k1 k2 l0

data UncurrySym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> TyFun ((,) k k) k -> *) (UncurrySym1 k k k)

type Apply k ((,) k1 k2) (UncurrySym1 k k1 k2 l1) l0 = UncurrySym2 k k1 k2 l1 l0

type UncurrySym2 t t = Uncurry t t

data IdSym0 l

Instances

SuppressUnusedWarnings (TyFun k k -> *) (IdSym0 k)

type Apply k k (IdSym0 k) l0 = IdSym1 k l0

type IdSym1 t = Id t

data ConstSym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun k k -> *) -> *) (ConstSym0 k k)

type Apply (TyFun k1 k -> *) k (ConstSym0 k1 k) l0 = ConstSym1 k k1 l0

data ConstSym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun k k -> *) (ConstSym1 k k)

type Apply k1 k (ConstSym1 k1 k l1) l0 = ConstSym2 k1 k l1 l0

type ConstSym2 t t = Const t t

data (:.$) l

Instances

SuppressUnusedWarnings (TyFun (TyFun k k -> *) (TyFun (TyFun k k -> *) (TyFun k k -> *) -> *) -> *) ((:.$) k k k)

type Apply (TyFun (TyFun k2 k1 -> *) (TyFun k2 k -> *) -> *) (TyFun k1 k -> *) ((:.$) k2 k k1) l0 = (:.$$) k k1 k2 l0

data l :.$$ l

Instances

SuppressUnusedWarnings ((TyFun k k -> *) -> TyFun (TyFun k k -> *) (TyFun k k -> *) -> *) ((:.$$) k k k)

type Apply (TyFun k k1 -> *) (TyFun k k2 -> *) ((:.$$) k1 k2 k l1) l0 = (:.$$$) k1 k2 k l1 l0

data (l :.$$$ l) l

Instances

SuppressUnusedWarnings ((TyFun k k -> *) -> (TyFun k k -> *) -> TyFun k k -> *) ((:.$$$) k k k)

type Apply k1 k ((:.$$$) k1 k2 k l1 l2) l0

data ($$) :: TyFun (TyFun a b -> *) (TyFun a b -> *) -> *

Instances

type Apply (TyFun k k1 -> *) (TyFun k k1 -> *) (($$) k k1) arg = ($$$) k k1 arg

data ($$$) :: (TyFun a b -> *) -> TyFun a b -> *

Instances

type Apply k1 k (($$$) k k1 f) arg = ($$$$) k1 k f arg

type ($$$$) a b = ($) a b

data ($!$) :: TyFun (TyFun a b -> *) (TyFun a b -> *) -> *

Instances

type Apply (TyFun k k1 -> *) (TyFun k k1 -> *) (($!$) k k1) arg = ($!$$) k k1 arg

data ($!$$) :: (TyFun a b -> *) -> TyFun a b -> *

Instances

type Apply k1 k (($!$$) k k1 f) arg = ($!$$$) k1 k f arg

type ($!$$$) a b = ($!) a b

data FlipSym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k k -> *) -> *) (TyFun k (TyFun k k -> *) -> *) -> *) (FlipSym0 k k k)

type Apply (TyFun k2 (TyFun k1 k -> *) -> *) (TyFun k1 (TyFun k2 k -> *) -> *) (FlipSym0 k k1 k2) l0 = FlipSym1 k k1 k2 l0

data FlipSym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> TyFun k (TyFun k k -> *) -> *) (FlipSym1 k k k)

type Apply (TyFun k2 k1 -> *) k (FlipSym1 k1 k2 k l1) l0 = FlipSym2 k1 k2 k l1 l0

data FlipSym2 l l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> k -> TyFun k k -> *) (FlipSym2 k k k)

type Apply k1 k (FlipSym2 k1 k k2 l1 l2) l0

data AsTypeOfSym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun k k -> *) -> *) (AsTypeOfSym0 k)

type Apply (TyFun k k -> *) k (AsTypeOfSym0 k) l0 = AsTypeOfSym1 k l0

data AsTypeOfSym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun k k -> *) (AsTypeOfSym1 k)

type Apply k k (AsTypeOfSym1 k l1) l0 = AsTypeOfSym2 k l1 l0

type AsTypeOfSym2 t t = AsTypeOf t t

data SeqSym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun k k -> *) -> *) (SeqSym0 k k)

type Apply (TyFun k1 k1 -> *) k (SeqSym0 k1 k) l0 = SeqSym1 k1 k l0

data SeqSym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun k k -> *) (SeqSym1 k k)

type Apply k k (SeqSym1 k k1 l1) l0 = SeqSym2 k k1 l1 l0

type SeqSym2 t t = Seq t t

data (:$) l

Instances

SuppressUnusedWarnings (TyFun k (TyFun [k] [k] -> *) -> *) ((:$) k)

type Apply (TyFun [k] [k] -> *) k ((:$) k) l0 = (:$$) k l0

data l :$$ l

Instances

SuppressUnusedWarnings (k -> TyFun [k] [k] -> *) ((:$$) k)

type Apply [k] [k] ((:$$) k l1) l0 = (:$$$) k l1 l0

type (:$$$) t t = (:) t t

type NilSym0 = []

type ConsSym0 = (:$)

type ConsSym1 = (:$$)

type ConsSym2 a b = (:$$$) a b

data MapSym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k k -> *) (TyFun [k] [k] -> *) -> *) (MapSym0 k k)

type Apply (TyFun [k] [k1] -> *) (TyFun k k1 -> *) (MapSym0 k k1) l0 = MapSym1 k k1 l0

data MapSym1 l l

Instances

SuppressUnusedWarnings ((TyFun k k -> *) -> TyFun [k] [k] -> *) (MapSym1 k k)

type Apply [k1] [k] (MapSym1 k k1 l1) l0 = MapSym2 k k1 l1 l0

type MapSym2 t t = Map t t

data ReverseSym0 l

Instances

SuppressUnusedWarnings (TyFun [k] [k] -> *) (ReverseSym0 k)

type Apply [k] [k] (ReverseSym0 k) l0 = ReverseSym1 k l0

type ReverseSym1 t = Reverse t

data l :++$$ l

Instances

SuppressUnusedWarnings ([k] -> TyFun [k] [k] -> *) ((:++$$) k)

type Apply [k] [k] ((:++$$) k l1) l0

data (:++$) l

Instances

SuppressUnusedWarnings (TyFun [k] (TyFun [k] [k] -> *) -> *) ((:++$) k)

type Apply (TyFun [k] [k] -> *) [k] ((:++$) k) l0 = (:++$$) k l0

data HeadSym0 l

Instances

SuppressUnusedWarnings (TyFun [k] k -> *) (HeadSym0 k)

type Apply k [k] (HeadSym0 k) l0 = HeadSym1 k l0

type HeadSym1 t = Head t

data LastSym0 l

Instances

SuppressUnusedWarnings (TyFun [k] k -> *) (LastSym0 k)

type Apply k [k] (LastSym0 k) l0 = LastSym1 k l0

type LastSym1 t = Last t

data TailSym0 l

Instances

SuppressUnusedWarnings (TyFun [k] [k] -> *) (TailSym0 k)

type Apply [k] [k] (TailSym0 k) l0 = TailSym1 k l0

type TailSym1 t = Tail t

data InitSym0 l

Instances

SuppressUnusedWarnings (TyFun [k] [k] -> *) (InitSym0 k)

type Apply [k] [k] (InitSym0 k) l0 = InitSym1 k l0

type InitSym1 t = Init t

data NullSym0 l

Instances

SuppressUnusedWarnings (TyFun [k] Bool -> *) (NullSym0 k)

type Apply Bool [k] (NullSym0 k) l0 = NullSym1 k l0

type NullSym1 t = Null t

data FoldlSym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k k -> *) -> *) (TyFun k (TyFun [k] k -> *) -> *) -> *) (FoldlSym0 k k)

type Apply (TyFun k (TyFun [k1] k -> *) -> *) (TyFun k (TyFun k1 k -> *) -> *) (FoldlSym0 k k1) l0 = FoldlSym1 k k1 l0

data FoldlSym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> TyFun k (TyFun [k] k -> *) -> *) (FoldlSym1 k k)

type Apply (TyFun [k1] k -> *) k (FoldlSym1 k k1 l1) l0 = FoldlSym2 k k1 l1 l0

data FoldlSym2 l l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> k -> TyFun [k] k -> *) (FoldlSym2 k k)

type Apply k [k1] (FoldlSym2 k k1 l1 l2) l0 = FoldlSym3 k k1 l1 l2 l0

type FoldlSym3 t t t = Foldl t t t

data Foldl1Sym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k k -> *) -> *) (TyFun [k] k -> *) -> *) (Foldl1Sym0 k)

type Apply (TyFun [k] k -> *) (TyFun k (TyFun k k -> *) -> *) (Foldl1Sym0 k) l0 = Foldl1Sym1 k l0

data Foldl1Sym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> TyFun [k] k -> *) (Foldl1Sym1 k)

type Apply k [k] (Foldl1Sym1 k l1) l0 = Foldl1Sym2 k l1 l0

type Foldl1Sym2 t t = Foldl1 t t

data FoldrSym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k k -> *) -> *) (TyFun k (TyFun [k] k -> *) -> *) -> *) (FoldrSym0 k k)

type Apply (TyFun k (TyFun [k1] k -> *) -> *) (TyFun k1 (TyFun k k -> *) -> *) (FoldrSym0 k k1) l0 = FoldrSym1 k k1 l0

data FoldrSym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> TyFun k (TyFun [k] k -> *) -> *) (FoldrSym1 k k)

type Apply (TyFun [k1] k -> *) k (FoldrSym1 k k1 l1) l0 = FoldrSym2 k k1 l1 l0

data FoldrSym2 l l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> k -> TyFun [k] k -> *) (FoldrSym2 k k)

type Apply k [k1] (FoldrSym2 k k1 l1 l2) l0 = FoldrSym3 k k1 l1 l2 l0

type FoldrSym3 t t t = Foldr t t t

data Foldr1Sym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k k -> *) -> *) (TyFun [k] k -> *) -> *) (Foldr1Sym0 k)

type Apply (TyFun [k] k -> *) (TyFun k (TyFun k k -> *) -> *) (Foldr1Sym0 k) l0 = Foldr1Sym1 k l0

data Foldr1Sym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> TyFun [k] k -> *) (Foldr1Sym1 k)

type Apply k [k] (Foldr1Sym1 k l1) l0 = Foldr1Sym2 k l1 l0

type Foldr1Sym2 t t = Foldr1 t t

data ConcatSym0 l

Instances

SuppressUnusedWarnings (TyFun [[k]] [k] -> *) (ConcatSym0 k)

type Apply [k] [[k]] (ConcatSym0 k) l0 = ConcatSym1 k l0

type ConcatSym1 t = Concat t

data ConcatMapSym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k [k] -> *) (TyFun [k] [k] -> *) -> *) (ConcatMapSym0 k k)

type Apply (TyFun [k] [k1] -> *) (TyFun k [k1] -> *) (ConcatMapSym0 k k1) l0 = ConcatMapSym1 k k1 l0

data ConcatMapSym1 l l

Instances

SuppressUnusedWarnings ((TyFun k [k] -> *) -> TyFun [k] [k] -> *) (ConcatMapSym1 k k)

type Apply [k1] [k] (ConcatMapSym1 k k1 l1) l0 = ConcatMapSym2 k k1 l1 l0

type ConcatMapSym2 t t = ConcatMap t t

data AndSym0 l

Instances

SuppressUnusedWarnings (TyFun [Bool] Bool -> *) AndSym0

type Apply Bool [Bool] AndSym0 l0 = AndSym1 l0

type AndSym1 t = And t

data OrSym0 l

Instances

SuppressUnusedWarnings (TyFun [Bool] Bool -> *) OrSym0

type Apply Bool [Bool] OrSym0 l0 = OrSym1 l0

type OrSym1 t = Or t

data Any_Sym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k Bool -> *) (TyFun [k] Bool -> *) -> *) (Any_Sym0 k)

type Apply (TyFun [k] Bool -> *) (TyFun k Bool -> *) (Any_Sym0 k) l0 = Any_Sym1 k l0

data Any_Sym1 l l

Instances

SuppressUnusedWarnings ((TyFun k Bool -> *) -> TyFun [k] Bool -> *) (Any_Sym1 k)

type Apply Bool [k] (Any_Sym1 k l1) l0 = Any_Sym2 k l1 l0

type Any_Sym2 t t = Any_ t t

data AllSym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k Bool -> *) (TyFun [k] Bool -> *) -> *) (AllSym0 k)

type Apply (TyFun [k] Bool -> *) (TyFun k Bool -> *) (AllSym0 k) l0 = AllSym1 k l0

data AllSym1 l l

Instances

SuppressUnusedWarnings ((TyFun k Bool -> *) -> TyFun [k] Bool -> *) (AllSym1 k)

type Apply Bool [k] (AllSym1 k l1) l0 = AllSym2 k l1 l0

type AllSym2 t t = All t t

data ScanlSym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k k -> *) -> *) (TyFun k (TyFun [k] [k] -> *) -> *) -> *) (ScanlSym0 k k)

type Apply (TyFun k (TyFun [k1] [k] -> *) -> *) (TyFun k (TyFun k1 k -> *) -> *) (ScanlSym0 k k1) l0 = ScanlSym1 k k1 l0

data ScanlSym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> TyFun k (TyFun [k] [k] -> *) -> *) (ScanlSym1 k k)

type Apply (TyFun [k1] [k] -> *) k (ScanlSym1 k k1 l1) l0 = ScanlSym2 k k1 l1 l0

data ScanlSym2 l l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> k -> TyFun [k] [k] -> *) (ScanlSym2 k k)

type Apply [k] [k1] (ScanlSym2 k k1 l1 l2) l0 = ScanlSym3 k k1 l1 l2 l0

type ScanlSym3 t t t = Scanl t t t

data Scanl1Sym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k k -> *) -> *) (TyFun [k] [k] -> *) -> *) (Scanl1Sym0 k)

type Apply (TyFun [k] [k] -> *) (TyFun k (TyFun k k -> *) -> *) (Scanl1Sym0 k) l0 = Scanl1Sym1 k l0

data Scanl1Sym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> TyFun [k] [k] -> *) (Scanl1Sym1 k)

type Apply [k] [k] (Scanl1Sym1 k l1) l0 = Scanl1Sym2 k l1 l0

type Scanl1Sym2 t t = Scanl1 t t

data ScanrSym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k k -> *) -> *) (TyFun k (TyFun [k] [k] -> *) -> *) -> *) (ScanrSym0 k k)

type Apply (TyFun k1 (TyFun [k] [k1] -> *) -> *) (TyFun k (TyFun k1 k1 -> *) -> *) (ScanrSym0 k k1) l0 = ScanrSym1 k k1 l0

data ScanrSym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> TyFun k (TyFun [k] [k] -> *) -> *) (ScanrSym1 k k)

type Apply (TyFun [k1] [k] -> *) k (ScanrSym1 k1 k l1) l0 = ScanrSym2 k1 k l1 l0

data ScanrSym2 l l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> k -> TyFun [k] [k] -> *) (ScanrSym2 k k)

type Apply [k1] [k] (ScanrSym2 k k1 l1 l2) l0 = ScanrSym3 k k1 l1 l2 l0

type ScanrSym3 t t t = Scanr t t t

data Scanr1Sym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k k -> *) -> *) (TyFun [k] [k] -> *) -> *) (Scanr1Sym0 k)

type Apply (TyFun [k] [k] -> *) (TyFun k (TyFun k k -> *) -> *) (Scanr1Sym0 k) l0 = Scanr1Sym1 k l0

data Scanr1Sym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> TyFun [k] [k] -> *) (Scanr1Sym1 k)

type Apply [k] [k] (Scanr1Sym1 k l1) l0 = Scanr1Sym2 k l1 l0

type Scanr1Sym2 t t = Scanr1 t t

data ElemSym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun [k] Bool -> *) -> *) (ElemSym0 k)

type Apply (TyFun [k] Bool -> *) k (ElemSym0 k) l0 = ElemSym1 k l0

data ElemSym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun [k] Bool -> *) (ElemSym1 k)

type Apply Bool [k] (ElemSym1 k l1) l0 = ElemSym2 k l1 l0

type ElemSym2 t t = Elem t t

data NotElemSym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun [k] Bool -> *) -> *) (NotElemSym0 k)

type Apply (TyFun [k] Bool -> *) k (NotElemSym0 k) l0 = NotElemSym1 k l0

data NotElemSym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun [k] Bool -> *) (NotElemSym1 k)

type Apply Bool [k] (NotElemSym1 k l1) l0 = NotElemSym2 k l1 l0

type NotElemSym2 t t = NotElem t t

data ZipSym0 l

Instances

SuppressUnusedWarnings (TyFun [k] (TyFun [k] [(,) k k] -> *) -> *) (ZipSym0 k k)

type Apply (TyFun [k1] [(,) k k1] -> *) [k] (ZipSym0 k k1) l0 = ZipSym1 k k1 l0

data ZipSym1 l l

Instances

SuppressUnusedWarnings ([k] -> TyFun [k] [(,) k k] -> *) (ZipSym1 k k)

type Apply [(,) k1 k] [k] (ZipSym1 k1 k l1) l0 = ZipSym2 k1 k l1 l0

type ZipSym2 t t = Zip t t

data Zip3Sym0 l

Instances

SuppressUnusedWarnings (TyFun [k] (TyFun [k] (TyFun [k] [(,,) k k k] -> *) -> *) -> *) (Zip3Sym0 k k k)

type Apply (TyFun [k1] (TyFun [k2] [(,,) k k1 k2] -> *) -> *) [k] (Zip3Sym0 k k1 k2) l0 = Zip3Sym1 k k1 k2 l0

data Zip3Sym1 l l

Instances

SuppressUnusedWarnings ([k] -> TyFun [k] (TyFun [k] [(,,) k k k] -> *) -> *) (Zip3Sym1 k k k)

type Apply (TyFun [k1] [(,,) k2 k k1] -> *) [k] (Zip3Sym1 k2 k k1 l1) l0 = Zip3Sym2 k2 k k1 l1 l0

data Zip3Sym2 l l l

Instances

SuppressUnusedWarnings ([k] -> [k] -> TyFun [k] [(,,) k k k] -> *) (Zip3Sym2 k k k)

type Apply [(,,) k1 k2 k] [k] (Zip3Sym2 k1 k2 k l1 l2) l0 = Zip3Sym3 k1 k2 k l1 l2 l0

type Zip3Sym3 t t t = Zip3 t t t

data ZipWithSym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k k -> *) -> *) (TyFun [k] (TyFun [k] [k] -> *) -> *) -> *) (ZipWithSym0 k k k)

type Apply (TyFun [k] (TyFun [k1] [k2] -> *) -> *) (TyFun k (TyFun k1 k2 -> *) -> *) (ZipWithSym0 k k1 k2) l0 = ZipWithSym1 k k1 k2 l0

data ZipWithSym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> TyFun [k] (TyFun [k] [k] -> *) -> *) (ZipWithSym1 k k k)

type Apply (TyFun [k1] [k2] -> *) [k] (ZipWithSym1 k k1 k2 l1) l0 = ZipWithSym2 k k1 k2 l1 l0

data ZipWithSym2 l l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> [k] -> TyFun [k] [k] -> *) (ZipWithSym2 k k k)

type Apply [k2] [k1] (ZipWithSym2 k k1 k2 l1 l2) l0 = ZipWithSym3 k k1 k2 l1 l2 l0

type ZipWithSym3 t t t = ZipWith t t t

data ZipWith3Sym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k (TyFun k k -> *) -> *) -> *) (TyFun [k] (TyFun [k] (TyFun [k] [k] -> *) -> *) -> *) -> *) (ZipWith3Sym0 k k k k)

type Apply (TyFun [k] (TyFun [k1] (TyFun [k2] [k3] -> *) -> *) -> *) (TyFun k (TyFun k1 (TyFun k2 k3 -> *) -> *) -> *) (ZipWith3Sym0 k k1 k2 k3) l0 = ZipWith3Sym1 k k1 k2 k3 l0

data ZipWith3Sym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k (TyFun k k -> *) -> *) -> *) -> TyFun [k] (TyFun [k] (TyFun [k] [k] -> *) -> *) -> *) (ZipWith3Sym1 k k k k)

type Apply (TyFun [k1] (TyFun [k2] [k3] -> *) -> *) [k] (ZipWith3Sym1 k k1 k2 k3 l1) l0 = ZipWith3Sym2 k k1 k2 k3 l1 l0

data ZipWith3Sym2 l l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k (TyFun k k -> *) -> *) -> *) -> [k] -> TyFun [k] (TyFun [k] [k] -> *) -> *) (ZipWith3Sym2 k k k k)

type Apply (TyFun [k2] [k3] -> *) [k1] (ZipWith3Sym2 k k1 k2 k3 l1 l2) l0 = ZipWith3Sym3 k k1 k2 k3 l1 l2 l0

data ZipWith3Sym3 l l l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k (TyFun k k -> *) -> *) -> *) -> [k] -> [k] -> TyFun [k] [k] -> *) (ZipWith3Sym3 k k k k)

type Apply [k3] [k2] (ZipWith3Sym3 k k1 k2 k3 l1 l2 l3) l0

data UnzipSym0 l

Instances

SuppressUnusedWarnings (TyFun [(,) k k] ((,) [k] [k]) -> *) (UnzipSym0 k k)

type Apply ((,) [k] [k1]) [(,) k k1] (UnzipSym0 k k1) l0 = UnzipSym1 k k1 l0

type UnzipSym1 t = Unzip t