Copyright	(C) 2013-2014 Richard Eisenberg, Jan Stolarek
License	BSD-style (see LICENSE)
Maintainer	Richard Eisenberg (eir@cis.upenn.edu)
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.Singletons.Prelude.List

Contents

The singleton for lists
Basic functions
List transformations
Reducing lists (folds)
- Special folds
Building lists
Sublists
- Extracting sublists
- Predicates
Searching lists
- Searching by equality
Zipping and unzipping lists
Special lists
- "Set" operations
- Ordered lists
Generalized functions
- The "By" operations
Defunctionalization symbols

Description

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.

Synopsis

The singleton for lists

data family Sing a Source

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 Source

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

Basic functions

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

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) Source

type family Head a :: a Source

Equations

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

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

type family Last a :: a Source

Equations

Last `[]` = Apply ErrorSym0 "Data.Singletons.List.last: empty list"
Last ((:) x xs) = Apply (Apply (Let1627597784Last'Sym2 x xs) x) xs

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

type family Tail a :: [a] Source

Equations

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

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

type family Init a :: [a] Source

Equations

Init `[]` = Apply ErrorSym0 "Data.Singletons.List.init: empty list"
Init ((:) x xs) = Apply (Apply (Let1627597747Init'Sym2 x xs) x) xs

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

type family Null a :: Bool Source

Equations

Null `[]` = TrueSym0
Null ((:) z z) = FalseSym0

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

List transformations

type family Map a a :: [b] Source

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) Source

type family Reverse a :: [a] Source

Equations

Reverse l = Apply (Apply (Let1627597705RevSym1 l) l) `[]`

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

type family Intersperse a a :: [a] Source

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) Source

type family Intercalate a a :: [a] Source

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) Source

type family Subsequences a :: [[a]] Source

Equations

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

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

type family Permutations a :: [[a]] Source

Equations

Permutations xs0 = Apply (Apply (:$) xs0) (Apply (Apply (Let1627597269PermsSym1 xs0) xs0) `[]`)

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

Reducing lists (folds)

type family Foldl a a a :: b Source

Equations

Foldl f z0 xs0 = Apply (Apply (Let1627597010LgoSym3 f z0 xs0) z0) xs0

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

type family Foldl' a a a :: b Source

Equations

Foldl' f z0 xs0 = Apply (Apply (Let1627596913LgoSym3 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) Source

type family Foldl1 a a :: a Source

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) Source

type family Foldl1' a a :: a Source

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) Source

type family Foldr a a a :: b Source

Equations

Foldr k z a_1627560700 = Apply (Let1627560705GoSym3 k z a_1627560700) a_1627560700

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

type family Foldr1 a a :: a Source

Equations

Foldr1 z `[x]` = x
Foldr1 f ((:) x ((:) wild_1627595664 wild_1627595666)) = Apply (Apply f x) (Apply (Apply Foldr1Sym0 f) (Let1627596875XsSym4 f x wild_1627595664 wild_1627595666))
Foldr1 z `[]` = Apply ErrorSym0 "Data.Singletons.List.foldr1: empty list"

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

Special folds

type family Concat a :: [a] Source

Equations

Concat a_1627596853 = Apply (Apply (Apply FoldrSym0 (:++$)) `[]`) a_1627596853

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

type family ConcatMap a a :: [b] Source

Equations

ConcatMap f a_1627596849 = Apply (Apply (Apply FoldrSym0 (Apply (Apply (:.$) (:++$)) f)) `[]`) a_1627596849

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

type family And a :: Bool Source

Equations

And `[]` = TrueSym0
And ((:) x xs) = Apply (Apply (:&&$) x) (Apply AndSym0 xs)

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

type family Or a :: Bool Source

Equations

Or `[]` = FalseSym0
Or ((:) x xs) = Apply (Apply (:\|\|$) x) (Apply OrSym0 xs)

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

type family Any_ a a :: Bool Source

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) Source

type family All a a :: Bool Source

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) Source

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

Building lists

Scans

type family Scanl a a a :: [b] Source

Equations

Scanl f q ls = Apply (Apply (:$) q) (Case_1627596796 f q ls (Let1627596783Scrutinee_1627595668Sym3 f q ls))

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

type family Scanl1 a a :: [a] Source

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) Source

type family Scanr a a a :: [b] Source

Equations

Scanr z q0 `[]` = Apply (Apply (:$) q0) `[]`
Scanr f q0 ((:) x xs) = Case_1627596759 f q0 x xs (Let1627596740Scrutinee_1627595670Sym4 f q0 x xs)

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

type family Scanr1 a a :: [a] Source

Equations

Scanr1 z `[]` = `[]`
Scanr1 z `[x]` = Apply (Apply (:$) x) `[]`
Scanr1 f ((:) x ((:) wild_1627595674 wild_1627595676)) = Case_1627596713 f x wild_1627595674 wild_1627595676 (Let1627596694Scrutinee_1627595672Sym4 f x wild_1627595674 wild_1627595676)

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

Accumulating maps

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

Equations

MapAccumL z s `[]` = Apply (Apply Tuple2Sym0 s) `[]`
MapAccumL f s ((:) x xs) = Apply (Apply Tuple2Sym0 (Let1627596514S''Sym4 f s x xs)) (Apply (Apply (:$) (Let1627596514YSym4 f s x xs)) (Let1627596514YsSym4 f s x xs))

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

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

Equations

MapAccumR z s `[]` = Apply (Apply Tuple2Sym0 s) `[]`
MapAccumR f s ((:) x xs) = Apply (Apply Tuple2Sym0 (Let1627596348S''Sym4 f s x xs)) (Apply (Apply (:$) (Let1627596348YSym4 f s x xs)) (Let1627596348YsSym4 f s x xs))

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

Unfolding

type family Unfoldr a a :: [a] Source

Equations

Unfoldr f b = Case_1627596321 f b (Let1627596313Scrutinee_1627595678Sym2 f b)

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

Sublists

Extracting sublists

type family Inits a :: [[a]] Source

Equations

Inits xs = Apply (Apply (:$) `[]`) (Case_1627596296 xs (Let1627596292Scrutinee_1627595680Sym1 xs))

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

type family Tails a :: [[a]] Source

Equations

Tails xs = Apply (Apply (:$) xs) (Case_1627596270 xs (Let1627596266Scrutinee_1627595682Sym1 xs))

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

Predicates

type family IsPrefixOf a a :: Bool Source

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) Source

type family IsSuffixOf a a :: Bool Source

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) Source

type family IsInfixOf a a :: Bool Source

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) Source

Searching lists

Searching by equality

type family Elem a a :: Bool Source

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) Source

type family NotElem a a :: Bool Source

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) Source

Zipping and unzipping lists

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

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) Source

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

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) Source

type family ZipWith a a a :: [c] Source

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) Source

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

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) Source

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

Equations

Unzip xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627596054Sym0 xs)) (Apply (Apply Tuple2Sym0 `[]`) `[]`)) xs

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

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

Equations

Unzip3 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627596020Sym0 xs)) (Apply (Apply (Apply Tuple3Sym0 `[]`) `[]`) `[]`)) xs

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

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

Equations

Unzip4 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627595984Sym0 xs)) (Apply (Apply (Apply (Apply Tuple4Sym0 `[]`) `[]`) `[]`) `[]`)) xs

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

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

Equations

Unzip5 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627595946Sym0 xs)) (Apply (Apply (Apply (Apply (Apply Tuple5Sym0 `[]`) `[]`) `[]`) `[]`) `[]`)) xs

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

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

Equations

Unzip6 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627595906Sym0 xs)) (Apply (Apply (Apply (Apply (Apply (Apply Tuple6Sym0 `[]`) `[]`) `[]`) `[]`) `[]`) `[]`)) xs

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

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

Equations

Unzip7 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_1627595864Sym0 xs)) (Apply (Apply (Apply (Apply (Apply (Apply (Apply Tuple7Sym0 `[]`) `[]`) `[]`) `[]`) `[]`) `[]`) `[]`)) xs

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

Special lists

"Set" operations

type family Delete a a :: [a] Source

Equations

Delete a_1627595844 a_1627595846 = Apply (Apply (Apply DeleteBySym0 (:==$)) a_1627595844) a_1627595846

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

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

Equations

a_1627597227 :\\ a_1627597229 = Apply (Apply (Apply FoldlSym0 (Apply FlipSym0 DeleteSym0)) a_1627597227) a_1627597229

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

Ordered lists

Generalized functions

The "`By`" operations

type family DeleteBy a a a :: [a] Source

Equations

DeleteBy z z `[]` = `[]`
DeleteBy eq x ((:) y ys) = Case_1627595840 eq x y ys (Let1627595821Scrutinee_1627595708Sym4 eq x y ys)

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

type family DeleteFirstsBy a a a :: [a] Source

Equations

DeleteFirstsBy eq a_1627597257 a_1627597259 = Apply (Apply (Apply FoldlSym0 (Apply FlipSym0 (Apply DeleteBySym0 eq))) a_1627597257) a_1627597259

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

type family SortBy a a :: [a] Source

Equations

SortBy cmp a_1627595796 = Apply (Apply (Apply FoldrSym0 (Apply InsertBySym0 cmp)) `[]`) a_1627595796

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

type family InsertBy a a a :: [a] Source

Equations

InsertBy z x `[]` = Apply (Apply (:$) x) `[]`
InsertBy cmp x ((:) y ys') = Case_1627595783 cmp x y ys' (Let1627595764Scrutinee_1627595710Sym4 cmp x y ys')

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

type family MaximumBy a a :: a Source

Equations

MaximumBy z `[]` = Apply ErrorSym0 "Data.Singletons.List.maximumBy: empty list"
MaximumBy cmp ((:) wild_1627595714 wild_1627595716) = Apply (Apply Foldl1Sym0 (Let1627597081MaxBySym3 cmp wild_1627595714 wild_1627595716)) (Let1627597068XsSym3 cmp wild_1627595714 wild_1627595716)

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

type family MinimumBy a a :: a Source

Equations

MinimumBy z `[]` = Apply ErrorSym0 "Data.Singletons.List.minimumBy: empty list"
MinimumBy cmp ((:) wild_1627595720 wild_1627595722) = Apply (Apply Foldl1Sym0 (Let1627597167MinBySym3 cmp wild_1627595720 wild_1627595722)) (Let1627597154XsSym3 cmp wild_1627595720 wild_1627595722)

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

Defunctionalization symbols

type NilSym0 = `[]` Source

data (:$) l Source

Instances

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

data l :$$ l Source

Instances

SuppressUnusedWarnings (k -> TyFun [k] [k] -> *) ((:$$) k)
type Apply [k] [k] ((:$$) k l1) l0 = (:$$$) k l1 l0

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

data l :++$$ l Source

Instances

SuppressUnusedWarnings ([k] -> TyFun [k] [k] -> *) ((:++$$) k)
type Apply [k] [k] ((:++$$) k l1) l0

data (:++$) l Source

Instances

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

data HeadSym0 l Source

Instances

SuppressUnusedWarnings (TyFun [k] k -> *) (HeadSym0 k)
type Apply k [k] (HeadSym0 k) l0 = HeadSym1 k l0

type HeadSym1 t = Head t Source

data LastSym0 l Source

Instances

SuppressUnusedWarnings (TyFun [k] k -> *) (LastSym0 k)
type Apply k [k] (LastSym0 k) l0 = LastSym1 k l0

type LastSym1 t = Last t Source

data TailSym0 l Source

Instances

SuppressUnusedWarnings (TyFun [k] [k] -> *) (TailSym0 k)
type Apply [k] [k] (TailSym0 k) l0 = TailSym1 k l0

type TailSym1 t = Tail t Source

data InitSym0 l Source

Instances

SuppressUnusedWarnings (TyFun [k] [k] -> *) (InitSym0 k)
type Apply [k] [k] (InitSym0 k) l0 = InitSym1 k l0

type InitSym1 t = Init t Source

data NullSym0 l Source

Instances

SuppressUnusedWarnings (TyFun [k] Bool -> *) (NullSym0 k)
type Apply Bool [k] (NullSym0 k) l0 = NullSym1 k l0

type NullSym1 t = Null t Source

data MapSym0 l Source

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 Source

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 Source

data ReverseSym0 l Source

Instances

SuppressUnusedWarnings (TyFun [k] [k] -> *) (ReverseSym0 k)
type Apply [k] [k] (ReverseSym0 k) l0 = ReverseSym1 k l0

type ReverseSym1 t = Reverse t Source

data IntersperseSym0 l Source

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 Source

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 Source

data IntercalateSym0 l Source

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 Source

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 Source

data SubsequencesSym0 l Source

Instances

SuppressUnusedWarnings (TyFun [k] [[k]] -> *) (SubsequencesSym0 k)
type Apply [[k]] [k] (SubsequencesSym0 k) l0 = SubsequencesSym1 k l0

type SubsequencesSym1 t = Subsequences t Source

data PermutationsSym0 l Source

Instances

SuppressUnusedWarnings (TyFun [k] [[k]] -> *) (PermutationsSym0 k)
type Apply [[k]] [k] (PermutationsSym0 k) l0 = PermutationsSym1 k l0

type PermutationsSym1 t = Permutations t Source

data FoldlSym0 l Source

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 Source

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 Source

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 Source

data Foldl'Sym0 l Source

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 Source

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 Source

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 Source

data Foldl1Sym0 l Source

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 Source

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 Source

data Foldl1'Sym0 l Source

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 Source

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 Source

data FoldrSym0 l Source

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 Source

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 Source

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 Source

data Foldr1Sym0 l Source

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 Source

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 Source

data ConcatSym0 l Source

Instances

SuppressUnusedWarnings (TyFun [[k]] [k] -> *) (ConcatSym0 k)
type Apply [k] [[k]] (ConcatSym0 k) l0 = ConcatSym1 k l0

type ConcatSym1 t = Concat t Source

data ConcatMapSym0 l Source

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 Source

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 Source

data AndSym0 l Source

Instances

SuppressUnusedWarnings (TyFun [Bool] Bool -> *) AndSym0
type Apply Bool [Bool] AndSym0 l0 = AndSym1 l0

type AndSym1 t = And t Source

data OrSym0 l Source

Instances

SuppressUnusedWarnings (TyFun [Bool] Bool -> *) OrSym0
type Apply Bool [Bool] OrSym0 l0 = OrSym1 l0

type OrSym1 t = Or t Source

data Any_Sym0 l Source

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 Source

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 Source

data AllSym0 l Source

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 Source

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 Source

data ScanlSym0 l Source

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 Source

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 Source

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 Source

data Scanl1Sym0 l Source

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 Source

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 Source

data ScanrSym0 l Source

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 Source

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 Source

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 Source

data Scanr1Sym0 l Source

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 Source

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 Source

data MapAccumLSym0 l Source

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 Source

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 Source

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 Source

data MapAccumRSym0 l Source

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 Source

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 Source

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 Source

data UnfoldrSym0 l Source

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 Source

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 Source

data InitsSym0 l Source

Instances

SuppressUnusedWarnings (TyFun [k] [[k]] -> *) (InitsSym0 k)
type Apply [[k]] [k] (InitsSym0 k) l0 = InitsSym1 k l0

type InitsSym1 t = Inits t Source

data TailsSym0 l Source

Instances

SuppressUnusedWarnings (TyFun [k] [[k]] -> *) (TailsSym0 k)
type Apply [[k]] [k] (TailsSym0 k) l0 = TailsSym1 k l0

type TailsSym1 t = Tails t Source

data IsPrefixOfSym0 l Source

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 Source

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 Source

data IsSuffixOfSym0 l Source

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 Source

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 Source

data IsInfixOfSym0 l Source

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 Source

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 Source

data ElemSym0 l Source

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 Source

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 Source

data NotElemSym0 l Source

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 Source

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 Source

data ZipSym0 l Source

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 Source

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 Source

data Zip3Sym0 l Source

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 Source

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 Source

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 Source

data ZipWithSym0 l Source

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 Source

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 Source

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 Source

data ZipWith3Sym0 l Source

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 Source

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 Source

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 Source

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 Source

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 Source

data Unzip3Sym0 l Source

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 Source

data Unzip4Sym0 l Source

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 Source

data Unzip5Sym0 l Source

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 Source

data Unzip6Sym0 l Source

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 Source

data Unzip7Sym0 l Source

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 Source

data DeleteSym0 l Source

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 Source

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 Source

data (:\\$) l Source

Instances

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

data l :\\$$ l Source

Instances

SuppressUnusedWarnings ([k] -> TyFun [k] [k] -> *) ((:\\$$) k)
type Apply [k] [k] ((:\\$$) k l1) l0 = (:\\$$$) k l1 l0

type (:\\$$$) t t = (:\\) t t Source

data DeleteBySym0 l Source

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 Source

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 Source

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 Source

data DeleteFirstsBySym0 l Source

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 Source

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 Source

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 Source

data SortBySym0 l Source

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 Source

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 Source

data InsertBySym0 l Source

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 Source

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 Source

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 Source

data MaximumBySym0 l Source

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 Source

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 Source

data MinimumBySym0 l Source

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 Source

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 Source

The singleton for lists

Basic functions

List transformations

Reducing lists (folds)

Special folds

Building lists

Scans

Accumulating maps

Unfolding

Sublists

Extracting sublists

Predicates

Searching lists

Searching by equality

Zipping and unzipping lists

Special lists

"Set" operations

Ordered lists

Generalized functions

The "By" operations

Defunctionalization symbols

The "`By`" operations