Data.Singletons.Prelude.List

Defines functions and datatypes relating to the singleton for '[]', including a singletons version of a few of the definitions in Data.List.

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

The singleton for lists

data family Sing a

The singleton kind-indexed data family.

Instances

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 declares constructors

SNil  :: Sing '[]
SCons :: Sing (h :: k) -> Sing (t :: [k]) -> Sing (h ': t)

type SList = (Sing :: [a] -> *)

SList is a kind-restricted synonym for Sing: type SList (a :: [k]) = Sing a

Basic functions

type family a :++ a :: [a] infixr 5

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 :: [a]) infixr 5

type family Head a :: a

Equations

Head ((:) a _z_1627677281) = a

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

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

type family Last a :: a

Equations

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

Last `[x]` = x

Last ((:) _z_1627677271 ((:) x xs)) = Apply LastSym0 (Apply (Apply (:$) x) xs)

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

type family Tail a :: [a]

Equations

Tail ((:) _z_1627677262 t) = t

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

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

type family Init a :: [a]

Equations

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

Init ((:) x xs) = Apply (Apply (Let1627677231Init'Sym2 x xs) x) xs

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

type family Null a :: Bool

Equations

Null `[]` = TrueSym0

Null ((:) _z_1627677219 _z_1627677222) = FalseSym0

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

List transformations

type family Map a a :: [b]

Equations

Map _z_1627631698 `[]` = `[]`

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 :: [b])

type family Reverse a :: [a]

Equations

Reverse l = Apply (Apply (Let1627677185RevSym1 l) l) `[]`

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

type family Intersperse a a :: [a]

Equations

Intersperse _z_1627677163 `[]` = `[]`

Intersperse sep ((:) x xs) = Apply (Apply (:$) x) (Apply (Apply PrependToAllSym0 sep) xs)

sIntersperse :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply IntersperseSym0 t) t :: [a])

type family Intercalate a a :: [a]

Equations

Intercalate xs xss = Apply ConcatSym0 (Apply (Apply IntersperseSym0 xs) xss)

sIntercalate :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply IntercalateSym0 t) t :: [a])

type family Subsequences a :: [[a]]

Equations

Subsequences xs = Apply (Apply (:$) `[]`) (Apply NonEmptySubsequencesSym0 xs)

sSubsequences :: forall t. Sing t -> Sing (Apply SubsequencesSym0 t :: [[a]])

type family Permutations a :: [[a]]

Equations

Permutations xs0 = Apply (Apply (:$) xs0) (Apply (Apply (Let1627676738PermsSym1 xs0) xs0) `[]`)

sPermutations :: forall t. Sing t -> Sing (Apply PermutationsSym0 t :: [[a]])

Reducing lists (folds)

type family Foldl a a a :: b

Equations

Foldl f z0 xs0 = Apply (Apply (Let1627532338LgoSym3 f z0 xs0) z0) xs0

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

type family Foldl' a a a :: b

Equations

Foldl' f z0 xs0 = Apply (Apply (Let1627676652LgoSym3 f z0 xs0) z0) xs0

sFoldl' :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply Foldl'Sym0 t) t) t :: b)

type family Foldl1 a a :: a

Equations

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

Foldl1 _z_1627676457 `[]` = Apply ErrorSym0 "Data.Singletons.List.foldl1: empty list"

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

type family Foldl1' a a :: a

Equations

Foldl1' f ((:) x xs) = Apply (Apply (Apply Foldl'Sym0 f) x) xs

Foldl1' _z_1627676730 `[]` = Apply ErrorSym0 "Data.Singletons.List.foldl1': empty list"

sFoldl1' :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply Foldl1'Sym0 t) t :: a)

type family Foldr a a a :: b

Equations

Foldr k z a_1627631719 = Apply (Let1627631724GoSym3 k z a_1627631719) a_1627631719

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

type family Foldr1 a a :: a

Equations

Foldr1 _z_1627676415 `[x]` = x

Foldr1 f ((:) x ((:) wild_1627675043 wild_1627675045)) = Apply (Apply f x) (Apply (Apply Foldr1Sym0 f) (Let1627676423XsSym4 f x wild_1627675043 wild_1627675045))

Foldr1 _z_1627676442 `[]` = Apply ErrorSym0 "Data.Singletons.List.foldr1: empty list"

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

Special folds

type family Concat a :: [a]

Equations

Concat a_1627676399 = Apply (Apply (Apply FoldrSym0 (:++$)) `[]`) a_1627676399

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

type family ConcatMap a a :: [b]

Equations

ConcatMap f a_1627676395 = Apply (Apply (Apply FoldrSym0 (Apply (Apply (:.$) (:++$)) f)) `[]`) a_1627676395

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

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 :: Bool)

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 :: Bool)

type family Any_ a a :: Bool

Equations

Any_ _z_1627667533 `[]` = 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 :: Bool)

type family All a a :: Bool

Equations

All _z_1627676368 `[]` = 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 :: Bool)

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

Building lists

Scans

type family Scanl a a a :: [b]

Equations

Scanl f q ls = Apply (Apply (:$) q) (Case_1627676339 f q ls (Let1627676326Scrutinee_1627675047Sym3 f q ls))

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

type family Scanl1 a a :: [a]

Equations

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

Scanl1 _z_1627676356 `[]` = `[]`

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

type family Scanr a a a :: [b]

Equations

Scanr _z_1627676276 q0 `[]` = Apply (Apply (:$) q0) `[]`

Scanr f q0 ((:) x xs) = Case_1627676303 f q0 x xs (Let1627676284Scrutinee_1627675049Sym4 f q0 x xs)

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

type family Scanr1 a a :: [a]

Equations

Scanr1 _z_1627676207 `[]` = `[]`

Scanr1 _z_1627676210 `[x]` = Apply (Apply (:$) x) `[]`

Scanr1 f ((:) x ((:) wild_1627675053 wild_1627675055)) = Case_1627676256 f x wild_1627675053 wild_1627675055 (Let1627676237Scrutinee_1627675051Sym4 f x wild_1627675053 wild_1627675055)

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

Accumulating maps

type family MapAccumL a a a :: (acc, [y])

Equations

MapAccumL _z_1627676041 s `[]` = Apply (Apply Tuple2Sym0 s) `[]`

MapAccumL f s ((:) x xs) = Apply (Apply Tuple2Sym0 (Let1627676049S''Sym4 f s x xs)) (Apply (Apply (:$) (Let1627676049YSym4 f s x xs)) (Let1627676049YsSym4 f s x xs))

sMapAccumL :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply MapAccumLSym0 t) t) t :: (acc, [y]))

type family MapAccumR a a a :: (acc, [y])

Equations

MapAccumR _z_1627675869 s `[]` = Apply (Apply Tuple2Sym0 s) `[]`

MapAccumR f s ((:) x xs) = Apply (Apply Tuple2Sym0 (Let1627675877S''Sym4 f s x xs)) (Apply (Apply (:$) (Let1627675877YSym4 f s x xs)) (Let1627675877YsSym4 f s x xs))

sMapAccumR :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply MapAccumRSym0 t) t) t :: (acc, [y]))

Unfolding

type family Unfoldr a a :: [a]

Equations

Unfoldr f b = Case_1627675849 f b (Let1627675841Scrutinee_1627675057Sym2 f b)

sUnfoldr :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply UnfoldrSym0 t) t :: [a])

Sublists

Extracting sublists

type family Inits a :: [[a]]

Equations

Inits xs = Apply (Apply (:$) `[]`) (Case_1627675825 xs (Let1627675821Scrutinee_1627675059Sym1 xs))

sInits :: forall t. Sing t -> Sing (Apply InitsSym0 t :: [[a]])

type family Tails a :: [[a]]

Equations

Tails xs = Apply (Apply (:$) xs) (Case_1627675798 xs (Let1627675794Scrutinee_1627675061Sym1 xs))

sTails :: forall t. Sing t -> Sing (Apply TailsSym0 t :: [[a]])

Predicates

type family IsPrefixOf a a :: Bool

Equations

IsPrefixOf `[]` `[]` = TrueSym0

IsPrefixOf `[]` ((:) _z_1627675773 _z_1627675776) = TrueSym0

IsPrefixOf ((:) _z_1627675779 _z_1627675782) `[]` = FalseSym0

IsPrefixOf ((:) x xs) ((:) y ys) = Apply (Apply (:&&$) (Apply (Apply (:==$) x) y)) (Apply (Apply IsPrefixOfSym0 xs) ys)

sIsPrefixOf :: forall t t. SEq (KProxy :: KProxy a) => Sing t -> Sing t -> Sing (Apply (Apply IsPrefixOfSym0 t) t :: Bool)

type family IsSuffixOf a a :: Bool

Equations

IsSuffixOf x y = Apply (Apply IsPrefixOfSym0 (Apply ReverseSym0 x)) (Apply ReverseSym0 y)

sIsSuffixOf :: forall t t. SEq (KProxy :: KProxy a) => Sing t -> Sing t -> Sing (Apply (Apply IsSuffixOfSym0 t) t :: Bool)

type family IsInfixOf a a :: Bool

Equations

IsInfixOf needle haystack = Apply (Apply Any_Sym0 (Apply IsPrefixOfSym0 needle)) (Apply TailsSym0 haystack)

sIsInfixOf :: forall t t. SEq (KProxy :: KProxy a) => Sing t -> Sing t -> Sing (Apply (Apply IsInfixOfSym0 t) t :: Bool)

Searching lists

Searching by equality

type family Elem a a :: Bool

Equations

Elem _z_1627675758 `[]` = 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 :: Bool)

type family NotElem a a :: Bool

Equations

NotElem _z_1627675743 `[]` = 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 :: Bool)

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_1627675722 _z_1627675725) `[]` = `[]`

Zip `[]` ((:) _z_1627675728 _z_1627675731) = `[]`

sZip :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply ZipSym0 t) t :: [(a, b)])

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_1627675655 _z_1627675658) = `[]`

Zip3 `[]` ((:) _z_1627675661 _z_1627675664) `[]` = `[]`

Zip3 `[]` ((:) _z_1627675667 _z_1627675670) ((:) _z_1627675673 _z_1627675676) = `[]`

Zip3 ((:) _z_1627675679 _z_1627675682) `[]` `[]` = `[]`

Zip3 ((:) _z_1627675685 _z_1627675688) `[]` ((:) _z_1627675691 _z_1627675694) = `[]`

Zip3 ((:) _z_1627675697 _z_1627675700) ((:) _z_1627675703 _z_1627675706) `[]` = `[]`

sZip3 :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply Zip3Sym0 t) t) t :: [(a, b, c)])

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_1627675613 `[]` `[]` = `[]`

ZipWith _z_1627675616 ((:) _z_1627675619 _z_1627675622) `[]` = `[]`

ZipWith _z_1627675625 `[]` ((:) _z_1627675628 _z_1627675631) = `[]`

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

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_1627675518 `[]` `[]` `[]` = `[]`

ZipWith3 _z_1627675521 `[]` `[]` ((:) _z_1627675524 _z_1627675527) = `[]`

ZipWith3 _z_1627675530 `[]` ((:) _z_1627675533 _z_1627675536) `[]` = `[]`

ZipWith3 _z_1627675539 `[]` ((:) _z_1627675542 _z_1627675545) ((:) _z_1627675548 _z_1627675551) = `[]`

ZipWith3 _z_1627675554 ((:) _z_1627675557 _z_1627675560) `[]` `[]` = `[]`

ZipWith3 _z_1627675563 ((:) _z_1627675566 _z_1627675569) `[]` ((:) _z_1627675572 _z_1627675575) = `[]`

ZipWith3 _z_1627675578 ((:) _z_1627675581 _z_1627675584) ((:) _z_1627675587 _z_1627675590) `[]` = `[]`

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

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

Equations

Unzip xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627675464Sym0 xs)) (Apply (Apply Tuple2Sym0 `[]`) `[]`)) xs

sUnzip :: forall t. Sing t -> Sing (Apply UnzipSym0 t :: ([a], [b]))

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

Equations

Unzip3 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627675432Sym0 xs)) (Apply (Apply (Apply Tuple3Sym0 `[]`) `[]`) `[]`)) xs

sUnzip3 :: forall t. Sing t -> Sing (Apply Unzip3Sym0 t :: ([a], [b], [c]))

type family Unzip4 a :: ([a], [b], [c], [d])

Equations

Unzip4 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627675398Sym0 xs)) (Apply (Apply (Apply (Apply Tuple4Sym0 `[]`) `[]`) `[]`) `[]`)) xs

sUnzip4 :: forall t. Sing t -> Sing (Apply Unzip4Sym0 t :: ([a], [b], [c], [d]))

type family Unzip5 a :: ([a], [b], [c], [d], [e])

Equations

Unzip5 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627675362Sym0 xs)) (Apply (Apply (Apply (Apply (Apply Tuple5Sym0 `[]`) `[]`) `[]`) `[]`) `[]`)) xs

sUnzip5 :: forall t. Sing t -> Sing (Apply Unzip5Sym0 t :: ([a], [b], [c], [d], [e]))

type family Unzip6 a :: ([a], [b], [c], [d], [e], [f])

Equations

Unzip6 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627675324Sym0 xs)) (Apply (Apply (Apply (Apply (Apply (Apply Tuple6Sym0 `[]`) `[]`) `[]`) `[]`) `[]`) `[]`)) xs

sUnzip6 :: forall t. Sing t -> Sing (Apply Unzip6Sym0 t :: ([a], [b], [c], [d], [e], [f]))

type family Unzip7 a :: ([a], [b], [c], [d], [e], [f], [g])

Equations

Unzip7 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627675284Sym0 xs)) (Apply (Apply (Apply (Apply (Apply (Apply (Apply Tuple7Sym0 `[]`) `[]`) `[]`) `[]`) `[]`) `[]`) `[]`)) xs

sUnzip7 :: forall t. Sing t -> Sing (Apply Unzip7Sym0 t :: ([a], [b], [c], [d], [e], [f], [g]))

Special lists

"Set" operations

type family Delete a a :: [a]

Equations

Delete a_1627675249 a_1627675251 = Apply (Apply (Apply DeleteBySym0 (:==$)) a_1627675249) a_1627675251

sDelete :: forall t t. SEq (KProxy :: KProxy a) => Sing t -> Sing t -> Sing (Apply (Apply DeleteSym0 t) t :: [a])

type family a :\\ a :: [a] infix 5

Equations

a_1627675264 :\\ a_1627675266 = Apply (Apply (Apply FoldlSym0 (Apply FlipSym0 DeleteSym0)) a_1627675264) a_1627675266

(%:\\) :: forall t t. SEq (KProxy :: KProxy a) => Sing t -> Sing t -> Sing (Apply (Apply (:\\$) t) t :: [a]) infix 5

Ordered lists

Generalized functions

The "By" operations

type family DeleteBy a a a :: [a]

Equations

DeleteBy _z_1627675195 _z_1627675198 `[]` = `[]`

DeleteBy eq x ((:) y ys) = Case_1627675224 eq x y ys (Let1627675205Scrutinee_1627675087Sym4 eq x y ys)

sDeleteBy :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply DeleteBySym0 t) t) t :: [a])

type family DeleteFirstsBy a a a :: [a]

Equations

DeleteFirstsBy eq a_1627675242 a_1627675244 = Apply (Apply (Apply FoldlSym0 (Apply FlipSym0 (Apply DeleteBySym0 eq))) a_1627675242) a_1627675244

sDeleteFirstsBy :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply DeleteFirstsBySym0 t) t) t :: [a])

type family SortBy a a :: [a]

Equations

SortBy cmp a_1627675176 = Apply (Apply (Apply FoldrSym0 (Apply InsertBySym0 cmp)) `[]`) a_1627675176

sSortBy :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply SortBySym0 t) t :: [a])

type family InsertBy a a a :: [a]

Equations

InsertBy _z_1627675118 x `[]` = Apply (Apply (:$) x) `[]`

InsertBy cmp x ((:) y ys') = Case_1627675164 cmp x y ys' (Let1627675145Scrutinee_1627675089Sym4 cmp x y ys')

sInsertBy :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply InsertBySym0 t) t) t :: [a])

type family MaximumBy a a :: a

Equations

MaximumBy _z_1627676469 `[]` = Apply ErrorSym0 "Data.Singletons.List.maximumBy: empty list"

MaximumBy cmp ((:) wild_1627675093 wild_1627675095) = Apply (Apply Foldl1Sym0 (Let1627676488MaxBySym3 cmp wild_1627675093 wild_1627675095)) (Let1627676475XsSym3 cmp wild_1627675093 wild_1627675095)

sMaximumBy :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply MaximumBySym0 t) t :: a)

type family MinimumBy a a :: a

Equations

MinimumBy _z_1627676556 `[]` = Apply ErrorSym0 "Data.Singletons.List.minimumBy: empty list"

MinimumBy cmp ((:) wild_1627675099 wild_1627675101) = Apply (Apply Foldl1Sym0 (Let1627676575MinBySym3 cmp wild_1627675099 wild_1627675101)) (Let1627676562XsSym3 cmp wild_1627675099 wild_1627675101)

sMinimumBy :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply MinimumBySym0 t) t :: a)

Defunctionalization symbols

type NilSym0 = `[]`

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 (:++$$$) t t = (:++) t t

data l :++$$ l

Instances

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

type Apply [k] [k] ((:++$$) k l1) l0 = (:++$$$) 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 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 IntersperseSym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun [k] [k] -> *) -> *) (IntersperseSym0 k)

type Apply (TyFun [k] [k] -> *) k (IntersperseSym0 k) l0 = IntersperseSym1 k l0

data IntersperseSym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun [k] [k] -> *) (IntersperseSym1 k)

type Apply [k] [k] (IntersperseSym1 k l1) l0 = IntersperseSym2 k l1 l0

type IntersperseSym2 t t = Intersperse t t

data IntercalateSym0 l

Instances

SuppressUnusedWarnings (TyFun [k] (TyFun [[k]] [k] -> *) -> *) (IntercalateSym0 k)

type Apply (TyFun [[k]] [k] -> *) [k] (IntercalateSym0 k) l0 = IntercalateSym1 k l0

data IntercalateSym1 l l

Instances

SuppressUnusedWarnings ([k] -> TyFun [[k]] [k] -> *) (IntercalateSym1 k)

type Apply [k] [[k]] (IntercalateSym1 k l1) l0 = IntercalateSym2 k l1 l0

type IntercalateSym2 t t = Intercalate t t

data SubsequencesSym0 l

Instances

SuppressUnusedWarnings (TyFun [k] [[k]] -> *) (SubsequencesSym0 k)

type Apply [[k]] [k] (SubsequencesSym0 k) l0 = SubsequencesSym1 k l0

type SubsequencesSym1 t = Subsequences t

data PermutationsSym0 l

Instances

SuppressUnusedWarnings (TyFun [k] [[k]] -> *) (PermutationsSym0 k)

type Apply [[k]] [k] (PermutationsSym0 k) l0 = PermutationsSym1 k l0

type PermutationsSym1 t = Permutations t

data FoldlSym0 l

Instances

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

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

data FoldlSym2 l l l

Instances

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

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

type FoldlSym3 t t t = Foldl t t t

data Foldl'Sym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k k -> *) -> *) (TyFun k (TyFun [k] k -> *) -> *) -> *) (Foldl'Sym0 k k)

type Apply (TyFun k1 (TyFun [k] k1 -> *) -> *) (TyFun k1 (TyFun k k1 -> *) -> *) (Foldl'Sym0 k k1) l0 = Foldl'Sym1 k k1 l0

data Foldl'Sym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> TyFun k (TyFun [k] k -> *) -> *) (Foldl'Sym1 k k)

type Apply (TyFun [k1] k -> *) k (Foldl'Sym1 k1 k l1) l0 = Foldl'Sym2 k1 k l1 l0

data Foldl'Sym2 l l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> k -> TyFun [k] k -> *) (Foldl'Sym2 k k)

type Apply k1 [k] (Foldl'Sym2 k k1 l1 l2) l0 = Foldl'Sym3 k1 k l1 l2 l0

type Foldl'Sym3 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 Foldl1'Sym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k k -> *) -> *) (TyFun [k] k -> *) -> *) (Foldl1'Sym0 k)

type Apply (TyFun [k] k -> *) (TyFun k (TyFun k k -> *) -> *) (Foldl1'Sym0 k) l0 = Foldl1'Sym1 k l0

data Foldl1'Sym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> *) -> *) -> TyFun [k] k -> *) (Foldl1'Sym1 k)

type Apply k [k] (Foldl1'Sym1 k l1) l0 = Foldl1'Sym2 k l1 l0

type Foldl1'Sym2 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 k1 (TyFun [k] k1 -> *) -> *) (TyFun k (TyFun k1 k1 -> *) -> *) (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 k1 k l1) l0 = FoldrSym2 k1 k l1 l0

data FoldrSym2 l l l

Instances

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

type Apply k1 [k] (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 MapAccumLSym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k ((,) k k) -> *) -> *) (TyFun k (TyFun [k] ((,) k [k]) -> *) -> *) -> *) (MapAccumLSym0 k k k)

type Apply (TyFun k (TyFun [k1] ((,) k [k2]) -> *) -> *) (TyFun k (TyFun k1 ((,) k k2) -> *) -> *) (MapAccumLSym0 k k1 k2) l0 = MapAccumLSym1 k k1 k2 l0

data MapAccumLSym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k ((,) k k) -> *) -> *) -> TyFun k (TyFun [k] ((,) k [k]) -> *) -> *) (MapAccumLSym1 k k k)

type Apply (TyFun [k1] ((,) k [k2]) -> *) k (MapAccumLSym1 k k1 k2 l1) l0 = MapAccumLSym2 k k1 k2 l1 l0

data MapAccumLSym2 l l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k ((,) k k) -> *) -> *) -> k -> TyFun [k] ((,) k [k]) -> *) (MapAccumLSym2 k k k)

type Apply ((,) k [k2]) [k1] (MapAccumLSym2 k k1 k2 l1 l2) l0 = MapAccumLSym3 k k1 k2 l1 l2 l0

type MapAccumLSym3 t t t = MapAccumL t t t

data MapAccumRSym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k ((,) k k) -> *) -> *) (TyFun k (TyFun [k] ((,) k [k]) -> *) -> *) -> *) (MapAccumRSym0 k k k)

type Apply (TyFun k (TyFun [k1] ((,) k [k2]) -> *) -> *) (TyFun k (TyFun k1 ((,) k k2) -> *) -> *) (MapAccumRSym0 k k1 k2) l0 = MapAccumRSym1 k k1 k2 l0

data MapAccumRSym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k ((,) k k) -> *) -> *) -> TyFun k (TyFun [k] ((,) k [k]) -> *) -> *) (MapAccumRSym1 k k k)

type Apply (TyFun [k1] ((,) k [k2]) -> *) k (MapAccumRSym1 k k1 k2 l1) l0 = MapAccumRSym2 k k1 k2 l1 l0

data MapAccumRSym2 l l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k ((,) k k) -> *) -> *) -> k -> TyFun [k] ((,) k [k]) -> *) (MapAccumRSym2 k k k)

type Apply ((,) k [k2]) [k1] (MapAccumRSym2 k k1 k2 l1 l2) l0 = MapAccumRSym3 k k1 k2 l1 l2 l0

type MapAccumRSym3 t t t = MapAccumR t t t

data UnfoldrSym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (Maybe ((,) k k)) -> *) (TyFun k [k] -> *) -> *) (UnfoldrSym0 k k)

type Apply (TyFun k [k1] -> *) (TyFun k (Maybe ((,) k1 k)) -> *) (UnfoldrSym0 k k1) l0 = UnfoldrSym1 k k1 l0

data UnfoldrSym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (Maybe ((,) k k)) -> *) -> TyFun k [k] -> *) (UnfoldrSym1 k k)

type Apply [k1] k (UnfoldrSym1 k k1 l1) l0 = UnfoldrSym2 k k1 l1 l0

type UnfoldrSym2 t t = Unfoldr t t

data InitsSym0 l

Instances

SuppressUnusedWarnings (TyFun [k] [[k]] -> *) (InitsSym0 k)

type Apply [[k]] [k] (InitsSym0 k) l0 = InitsSym1 k l0

type InitsSym1 t = Inits t

data TailsSym0 l

Instances

SuppressUnusedWarnings (TyFun [k] [[k]] -> *) (TailsSym0 k)

type Apply [[k]] [k] (TailsSym0 k) l0 = TailsSym1 k l0

type TailsSym1 t = Tails t

data IsPrefixOfSym0 l

Instances

SuppressUnusedWarnings (TyFun [k] (TyFun [k] Bool -> *) -> *) (IsPrefixOfSym0 k)

type Apply (TyFun [k] Bool -> *) [k] (IsPrefixOfSym0 k) l0 = IsPrefixOfSym1 k l0

data IsPrefixOfSym1 l l

Instances

SuppressUnusedWarnings ([k] -> TyFun [k] Bool -> *) (IsPrefixOfSym1 k)

type Apply Bool [k] (IsPrefixOfSym1 k l1) l0 = IsPrefixOfSym2 k l1 l0

type IsPrefixOfSym2 t t = IsPrefixOf t t

data IsSuffixOfSym0 l

Instances

SuppressUnusedWarnings (TyFun [k] (TyFun [k] Bool -> *) -> *) (IsSuffixOfSym0 k)

type Apply (TyFun [k] Bool -> *) [k] (IsSuffixOfSym0 k) l0 = IsSuffixOfSym1 k l0

data IsSuffixOfSym1 l l

Instances

SuppressUnusedWarnings ([k] -> TyFun [k] Bool -> *) (IsSuffixOfSym1 k)

type Apply Bool [k] (IsSuffixOfSym1 k l1) l0 = IsSuffixOfSym2 k l1 l0

type IsSuffixOfSym2 t t = IsSuffixOf t t

data IsInfixOfSym0 l

Instances

SuppressUnusedWarnings (TyFun [k] (TyFun [k] Bool -> *) -> *) (IsInfixOfSym0 k)

type Apply (TyFun [k] Bool -> *) [k] (IsInfixOfSym0 k) l0 = IsInfixOfSym1 k l0

data IsInfixOfSym1 l l

Instances

SuppressUnusedWarnings ([k] -> TyFun [k] Bool -> *) (IsInfixOfSym1 k)

type Apply Bool [k] (IsInfixOfSym1 k l1) l0 = IsInfixOfSym2 k l1 l0

type IsInfixOfSym2 t t = IsInfixOf 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 = ZipWith3Sym4 k k1 k2 k3 l1 l2 l3 l0

type ZipWith3Sym4 t t t t = ZipWith3 t t t t

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

data Unzip3Sym0 l

Instances

SuppressUnusedWarnings (TyFun [(,,) k k k] ((,,) [k] [k] [k]) -> *) (Unzip3Sym0 k k k)

type Apply ((,,) [k] [k1] [k2]) [(,,) k k1 k2] (Unzip3Sym0 k k1 k2) l0 = Unzip3Sym1 k k1 k2 l0

type Unzip3Sym1 t = Unzip3 t

data Unzip4Sym0 l

Instances

SuppressUnusedWarnings (TyFun [(,,,) k k k k] ((,,,) [k] [k] [k] [k]) -> *) (Unzip4Sym0 k k k k)

type Apply ((,,,) [k] [k1] [k2] [k3]) [(,,,) k k1 k2 k3] (Unzip4Sym0 k k1 k2 k3) l0 = Unzip4Sym1 k k1 k2 k3 l0

type Unzip4Sym1 t = Unzip4 t

data Unzip5Sym0 l

Instances

SuppressUnusedWarnings (TyFun [(,,,,) k k k k k] ((,,,,) [k] [k] [k] [k] [k]) -> *) (Unzip5Sym0 k k k k k)

type Apply ((,,,,) [k] [k1] [k2] [k3] [k4]) [(,,,,) k k1 k2 k3 k4] (Unzip5Sym0 k k1 k2 k3 k4) l0 = Unzip5Sym1 k k1 k2 k3 k4 l0

type Unzip5Sym1 t = Unzip5 t

data Unzip6Sym0 l

Instances

SuppressUnusedWarnings (TyFun [(,,,,,) k k k k k k] ((,,,,,) [k] [k] [k] [k] [k] [k]) -> *) (Unzip6Sym0 k k k k k k)

type Apply ((,,,,,) [k] [k1] [k2] [k3] [k4] [k5]) [(,,,,,) k k1 k2 k3 k4 k5] (Unzip6Sym0 k k1 k2 k3 k4 k5) l0 = Unzip6Sym1 k k1 k2 k3 k4 k5 l0

type Unzip6Sym1 t = Unzip6 t

data Unzip7Sym0 l

Instances

SuppressUnusedWarnings (TyFun [(,,,,,,) k k k k k k k] ((,,,,,,) [k] [k] [k] [k] [k] [k] [k]) -> *) (Unzip7Sym0 k k k k k k k)

type Apply ((,,,,,,) [k] [k1] [k2] [k3] [k4] [k5] [k6]) [(,,,,,,) k k1 k2 k3 k4 k5 k6] (Unzip7Sym0 k k1 k2 k3 k4 k5 k6) l0 = Unzip7Sym1 k k1 k2 k3 k4 k5 k6 l0

type Unzip7Sym1 t = Unzip7 t

data DeleteSym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun [k] [k] -> *) -> *) (DeleteSym0 k)

type Apply (TyFun [k] [k] -> *) k (DeleteSym0 k) l0 = DeleteSym1 k l0

data DeleteSym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun [k] [k] -> *) (DeleteSym1 k)

type Apply [k] [k] (DeleteSym1 k l1) l0 = DeleteSym2 k l1 l0

type DeleteSym2 t t = Delete 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

data DeleteBySym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k Bool -> *) -> *) (TyFun k (TyFun [k] [k] -> *) -> *) -> *) (DeleteBySym0 k)

type Apply (TyFun k (TyFun [k] [k] -> *) -> *) (TyFun k (TyFun k Bool -> *) -> *) (DeleteBySym0 k) l0 = DeleteBySym1 k l0

data DeleteBySym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k Bool -> *) -> *) -> TyFun k (TyFun [k] [k] -> *) -> *) (DeleteBySym1 k)

type Apply (TyFun [k] [k] -> *) k (DeleteBySym1 k l1) l0 = DeleteBySym2 k l1 l0

data DeleteBySym2 l l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k Bool -> *) -> *) -> k -> TyFun [k] [k] -> *) (DeleteBySym2 k)

type Apply [k] [k] (DeleteBySym2 k l1 l2) l0 = DeleteBySym3 k l1 l2 l0

type DeleteBySym3 t t t = DeleteBy t t t

data DeleteFirstsBySym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k Bool -> *) -> *) (TyFun [k] (TyFun [k] [k] -> *) -> *) -> *) (DeleteFirstsBySym0 k)

type Apply (TyFun [k] (TyFun [k] [k] -> *) -> *) (TyFun k (TyFun k Bool -> *) -> *) (DeleteFirstsBySym0 k) l0 = DeleteFirstsBySym1 k l0

data DeleteFirstsBySym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k Bool -> *) -> *) -> TyFun [k] (TyFun [k] [k] -> *) -> *) (DeleteFirstsBySym1 k)

type Apply (TyFun [k] [k] -> *) [k] (DeleteFirstsBySym1 k l1) l0 = DeleteFirstsBySym2 k l1 l0

data DeleteFirstsBySym2 l l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k Bool -> *) -> *) -> [k] -> TyFun [k] [k] -> *) (DeleteFirstsBySym2 k)

type Apply [k] [k] (DeleteFirstsBySym2 k l1 l2) l0 = DeleteFirstsBySym3 k l1 l2 l0

type DeleteFirstsBySym3 t t t = DeleteFirstsBy t t t

data SortBySym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k Ordering -> *) -> *) (TyFun [k] [k] -> *) -> *) (SortBySym0 k)

type Apply (TyFun [k] [k] -> *) (TyFun k (TyFun k Ordering -> *) -> *) (SortBySym0 k) l0 = SortBySym1 k l0

data SortBySym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k Ordering -> *) -> *) -> TyFun [k] [k] -> *) (SortBySym1 k)

type Apply [k] [k] (SortBySym1 k l1) l0 = SortBySym2 k l1 l0

type SortBySym2 t t = SortBy t t

data InsertBySym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k Ordering -> *) -> *) (TyFun k (TyFun [k] [k] -> *) -> *) -> *) (InsertBySym0 k)

type Apply (TyFun k (TyFun [k] [k] -> *) -> *) (TyFun k (TyFun k Ordering -> *) -> *) (InsertBySym0 k) l0 = InsertBySym1 k l0

data InsertBySym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k Ordering -> *) -> *) -> TyFun k (TyFun [k] [k] -> *) -> *) (InsertBySym1 k)

type Apply (TyFun [k] [k] -> *) k (InsertBySym1 k l1) l0 = InsertBySym2 k l1 l0

data InsertBySym2 l l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k Ordering -> *) -> *) -> k -> TyFun [k] [k] -> *) (InsertBySym2 k)

type Apply [k] [k] (InsertBySym2 k l1 l2) l0 = InsertBySym3 k l1 l2 l0

type InsertBySym3 t t t = InsertBy t t t

data MaximumBySym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k Ordering -> *) -> *) (TyFun [k] k -> *) -> *) (MaximumBySym0 k)

type Apply (TyFun [k] k -> *) (TyFun k (TyFun k Ordering -> *) -> *) (MaximumBySym0 k) l0 = MaximumBySym1 k l0

data MaximumBySym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k Ordering -> *) -> *) -> TyFun [k] k -> *) (MaximumBySym1 k)

type Apply k [k] (MaximumBySym1 k l1) l0 = MaximumBySym2 k l1 l0

type MaximumBySym2 t t = MaximumBy t t

data MinimumBySym0 l

Instances

SuppressUnusedWarnings (TyFun (TyFun k (TyFun k Ordering -> *) -> *) (TyFun [k] k -> *) -> *) (MinimumBySym0 k)

type Apply (TyFun [k] k -> *) (TyFun k (TyFun k Ordering -> *) -> *) (MinimumBySym0 k) l0 = MinimumBySym1 k l0

data MinimumBySym1 l l

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k Ordering -> *) -> *) -> TyFun [k] k -> *) (MinimumBySym1 k)

type Apply k [k] (MinimumBySym1 k l1) l0 = MinimumBySym2 k l1 l0

type MinimumBySym2 t t = MinimumBy t t