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

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 declares constructors

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

type SList z = Sing z

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

Basic functions

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_1627596970Last'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_1627596932Init'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)

List transformations

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 Reverse a :: [a]

Equations

Reverse l = Apply (Apply (Let_1627596889RevSym1 l) l) `[]`

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

type family Intersperse a a :: [a]

Equations

Intersperse z `[]` = `[]`

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)

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)

type family Subsequences a :: [[a]]

Equations

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

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

type family Permutations a :: [[a]]

Equations

Permutations xs0 = Apply (Apply (:$) xs0) (Apply (Apply (Let_1627596448PermsSym1 xs0) xs0) `[]`)

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

Reducing lists (folds)

type family Foldl a a a :: b

Equations

Foldl f z0 xs0 = Apply (Apply (Let_1627596182LgoSym3 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 Foldl' a a a :: b

Equations

Foldl' f z0 xs0 = Apply (Apply (Let_1627596083LgoSym3 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)

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 Foldl1' a a :: a

Equations

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

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

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

type family Foldr a a a :: b

Equations

Foldr k z a_1627559854 = Apply (Let_1627559859GoSym3 k z a_1627559854) a_1627559854

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_1627594821 wild_1627594823)) = Apply (Apply f x) (Apply (Apply Foldr1Sym0 f) (Let_1627596044XsSym4 f x wild_1627594821 wild_1627594823))

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 Concat a :: [a]

Equations

Concat a_1627596022 = Apply (Apply (Apply FoldrSym0 (:++$)) `[]`) a_1627596022

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

type family ConcatMap a a :: [b]

Equations

ConcatMap f a_1627596018 = Apply (Apply (Apply FoldrSym0 (Apply (Apply (:.$) (:++$)) f)) `[]`) a_1627596018

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

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)

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_1627595965 f q ls (Let_1627595951Scrutinee_1627594825Sym3 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_1627595927 f q0 x xs (Let_1627595907Scrutinee_1627594827Sym4 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_1627594831 wild_1627594833)) = Case_1627595880 f x wild_1627594831 wild_1627594833 (Let_1627595860Scrutinee_1627594829Sym4 f x wild_1627594831 wild_1627594833)

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

Accumulating maps

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

Equations

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

MapAccumL f s ((:) x xs) = Apply (Apply Tuple2Sym0 (Let_1627595678S''Sym4 f s x xs)) (Apply (Apply (:$) (Let_1627595678YSym4 f s x xs)) (Let_1627595678YsSym4 f s x xs))

sMapAccumL :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply MapAccumLSym0 t) t) t)

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

Equations

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

MapAccumR f s ((:) x xs) = Apply (Apply Tuple2Sym0 (Let_1627595511S''Sym4 f s x xs)) (Apply (Apply (:$) (Let_1627595511YSym4 f s x xs)) (Let_1627595511YsSym4 f s x xs))

sMapAccumR :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply MapAccumRSym0 t) t) t)

Unfolding

type family Unfoldr a a :: [a]

Equations

Unfoldr f b = Case_1627595484 f b (Let_1627595475Scrutinee_1627594835Sym2 f b)

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

Sublists

Extracting sublists

type family Inits a :: [[a]]

Equations

Inits xs = Apply (Apply (:$) `[]`) (Case_1627595458 xs (Let_1627595453Scrutinee_1627594837Sym1 xs))

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

type family Tails a :: [[a]]

Equations

Tails xs = Apply (Apply (:$) xs) (Case_1627595431 xs (Let_1627595426Scrutinee_1627594839Sym1 xs))

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

Predicates

type family IsPrefixOf a a :: Bool

Equations

IsPrefixOf `[]` `[]` = TrueSym0

IsPrefixOf `[]` ((:) z z) = TrueSym0

IsPrefixOf ((:) z z) `[]` = 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)

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)

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)

Searching lists

Searching by equality

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_1627595214Sym0 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_1627595180Sym0 xs)) (Apply (Apply (Apply Tuple3Sym0 `[]`) `[]`) `[]`)) xs

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

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

Equations

Unzip4 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627595144Sym0 xs)) (Apply (Apply (Apply (Apply Tuple4Sym0 `[]`) `[]`) `[]`) `[]`)) xs

sUnzip4 :: forall t. Sing t -> Sing (Apply Unzip4Sym0 t)

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

Equations

Unzip5 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627595106Sym0 xs)) (Apply (Apply (Apply (Apply (Apply Tuple5Sym0 `[]`) `[]`) `[]`) `[]`) `[]`)) xs

sUnzip5 :: forall t. Sing t -> Sing (Apply Unzip5Sym0 t)

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

Equations

Unzip6 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627595066Sym0 xs)) (Apply (Apply (Apply (Apply (Apply (Apply Tuple6Sym0 `[]`) `[]`) `[]`) `[]`) `[]`) `[]`)) xs

sUnzip6 :: forall t. Sing t -> Sing (Apply Unzip6Sym0 t)

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

Equations

Unzip7 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627595024Sym0 xs)) (Apply (Apply (Apply (Apply (Apply (Apply (Apply Tuple7Sym0 `[]`) `[]`) `[]`) `[]`) `[]`) `[]`) `[]`)) xs

sUnzip7 :: forall t. Sing t -> Sing (Apply Unzip7Sym0 t)

Special lists

"Set" operations

type family Delete a a :: [a]

Equations

Delete a_1627595004 a_1627595006 = Apply (Apply (Apply DeleteBySym0 (:==$)) a_1627595004) a_1627595006

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

type family a :\\ a :: [a]

Equations

a_1627596406 :\\ a_1627596408 = Apply (Apply (Apply FoldlSym0 (Apply FlipSym0 DeleteSym0)) a_1627596406) a_1627596408

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

Ordered lists

Generalized functions

The "By" operations

type family DeleteBy a a a :: [a]

Equations

DeleteBy z z `[]` = `[]`

DeleteBy eq x ((:) y ys) = Case_1627595000 eq x y ys (Let_1627594980Scrutinee_1627594865Sym4 eq x y ys)

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

type family DeleteFirstsBy a a a :: [a]

Equations

DeleteFirstsBy eq a_1627596436 a_1627596438 = Apply (Apply (Apply FoldlSym0 (Apply FlipSym0 (Apply DeleteBySym0 eq))) a_1627596436) a_1627596438

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

type family SortBy a a :: [a]

Equations

SortBy cmp a_1627594955 = Apply (Apply (Apply FoldrSym0 (Apply InsertBySym0 cmp)) `[]`) a_1627594955

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

type family InsertBy a a a :: [a]

Equations

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

InsertBy cmp x ((:) y ys') = Case_1627594942 cmp x y ys' (Let_1627594922Scrutinee_1627594867Sym4 cmp x y ys')

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

type family MaximumBy a a :: a

Equations

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

MaximumBy cmp ((:) wild_1627594871 wild_1627594873) = Apply (Apply Foldl1Sym0 (Let_1627596255MaxBySym3 cmp wild_1627594871 wild_1627594873)) (Let_1627596241XsSym3 cmp wild_1627594871 wild_1627594873)

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

type family MinimumBy a a :: a

Equations

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

MinimumBy cmp ((:) wild_1627594877 wild_1627594879) = Apply (Apply Foldl1Sym0 (Let_1627596344MinBySym3 cmp wild_1627594877 wild_1627594879)) (Let_1627596330XsSym3 cmp wild_1627594877 wild_1627594879)

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

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

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 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 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 Foldl'Sym0 l

Instances

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

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

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