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 :: k -> Type infixr 5

The singleton kind-indexed data family.

Instances

SDecide k => TestCoercion (Sing :: k -> Type)

Defined in Data.Singletons.Decide

Methods

testCoercion :: Sing a -> Sing b -> Maybe (Coercion a b)

SDecide k => TestEquality (Sing :: k -> Type)

Defined in Data.Singletons.Decide

Methods

testEquality :: Sing a -> Sing b -> Maybe (a :~: b)

Show (SSymbol s)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> SSymbol s -> ShowS

show :: SSymbol s -> String

showList :: [SSymbol s] -> ShowS

Show (SNat n)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> SNat n -> ShowS

show :: SNat n -> String

showList :: [SNat n] -> ShowS

Eq (Sing a)

Defined in Data.Singletons.TypeRepTYPE

Methods

(==) :: Sing a -> Sing a -> Bool

(/=) :: Sing a -> Sing a -> Bool

Ord (Sing a)

Defined in Data.Singletons.TypeRepTYPE

Methods

compare :: Sing a -> Sing a -> Ordering

(<) :: Sing a -> Sing a -> Bool

(<=) :: Sing a -> Sing a -> Bool

(>) :: Sing a -> Sing a -> Bool

(>=) :: Sing a -> Sing a -> Bool

max :: Sing a -> Sing a -> Sing a

min :: Sing a -> Sing a -> Sing a

Show (Sing z)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

(ShowSing a, ShowSing [a]) => Show (Sing z)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

ShowSing a => Show (Sing z)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

Show (Sing z)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

(ShowSing a, ShowSing b) => Show (Sing z)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

Show (Sing a)

Defined in Data.Singletons.TypeRepTYPE

Methods

showsPrec :: Int -> Sing a -> ShowS

show :: Sing a -> String

showList :: [Sing a] -> ShowS

Show (Sing z)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

(ShowSing a, ShowSing b) => Show (Sing z)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

(ShowSing a, ShowSing b, ShowSing c) => Show (Sing z)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

(ShowSing a, ShowSing b, ShowSing c, ShowSing d) => Show (Sing z)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

(ShowSing a, ShowSing b, ShowSing c, ShowSing d, ShowSing e) => Show (Sing z)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

(ShowSing a, ShowSing b, ShowSing c, ShowSing d, ShowSing e, ShowSing f) => Show (Sing z)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

(ShowSing a, ShowSing b, ShowSing c, ShowSing d, ShowSing e, ShowSing f, ShowSing g) => Show (Sing z)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

Show (Sing z)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

ShowSing a => Show (Sing z)

Defined in Data.Singletons.Prelude.Semigroup

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

ShowSing a => Show (Sing z)

Defined in Data.Singletons.Prelude.Semigroup

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

(ShowSing a, ShowSing b) => Show (Sing z)

Defined in Data.Singletons.Prelude.Semigroup

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

ShowSing a => Show (Sing z)

Defined in Data.Singletons.Prelude.Semigroup

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

ShowSing a => Show (Sing z)

Defined in Data.Singletons.Prelude.Semigroup

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

ShowSing m => Show (Sing z)

Defined in Data.Singletons.Prelude.Semigroup

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

ShowSing (Maybe a) => Show (Sing z)

Defined in Data.Singletons.Prelude.Semigroup

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

ShowSing a => Show (Sing z)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

ShowSing (Maybe a) => Show (Sing z)

Defined in Data.Singletons.Prelude.Monoid

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

ShowSing (Maybe a) => Show (Sing z)

Defined in Data.Singletons.Prelude.Monoid

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

ShowSing a => Show (Sing z)

Defined in Data.Singletons.Prelude.Semigroup

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

ShowSing Bool => Show (Sing z)

Defined in Data.Singletons.Prelude.Semigroup

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

ShowSing Bool => Show (Sing z)

Defined in Data.Singletons.Prelude.Semigroup

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

ShowSing a => Show (Sing z)

Defined in Data.Singletons.Prelude.Semigroup

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

ShowSing a => Show (Sing z)

Defined in Data.Singletons.Prelude.Semigroup

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

(ShowSing a, ShowSing [a]) => Show (Sing z)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

data Sing (a :: Bool)

Defined in Data.Singletons.Prelude.Instances

data Sing (a :: Bool) where

• SFalse :: forall (a :: Bool). Sing False
• STrue :: forall (a :: Bool). Sing True

data Sing (a :: Ordering)

Defined in Data.Singletons.Prelude.Instances

data Sing (a :: Ordering) where

• SLT :: forall (a :: Ordering). Sing LT
• SEQ :: forall (a :: Ordering). Sing EQ
• SGT :: forall (a :: Ordering). Sing GT

data Sing (n :: Nat)

Defined in Data.Singletons.TypeLits.Internal

data Sing (n :: Nat) where

• SNat :: forall (n :: Nat). KnownNat n => Sing n

data Sing (n :: Symbol)

Defined in Data.Singletons.TypeLits.Internal

data Sing (n :: Symbol) where

• SSym :: forall (n :: Symbol). KnownSymbol n => Sing n

data Sing (a :: ())

Defined in Data.Singletons.Prelude.Instances

data Sing (a :: ()) where

• STuple0 :: forall (a :: ()). Sing ()

data Sing (a :: Void)

Defined in Data.Singletons.Prelude.Instances

data Sing (a :: Void)

data Sing (a :: All)

Defined in Data.Singletons.Prelude.Semigroup.Internal

data Sing (a :: All) where

• SAll :: forall (a :: All) (n :: Bool). {..} -> Sing (All n)

data Sing (a :: Any)

Defined in Data.Singletons.Prelude.Semigroup.Internal

data Sing (a :: Any) where

• SAny :: forall (a :: Any) (n :: Bool). {..} -> Sing (Any n)

data Sing (a :: PErrorMessage)

Defined in Data.Singletons.TypeError

data Sing (a :: PErrorMessage) where

• SText :: forall (a :: PErrorMessage) (t :: Symbol). Sing t -> Sing (Text t)
• SShowType :: forall (a :: PErrorMessage) t (ty :: t). Sing ty -> Sing (ShowType ty :: ErrorMessage' Symbol)
• (:%<>:) :: forall (a :: PErrorMessage) (e1 :: ErrorMessage' Symbol) (e2 :: ErrorMessage' Symbol). Sing e1 -> Sing e2 -> Sing (e1 :<>: e2)
• (:%$$:) :: forall (a :: PErrorMessage) (e1 :: ErrorMessage' Symbol) (e2 :: ErrorMessage' Symbol). Sing e1 -> Sing e2 -> Sing (e1 :$$: e2)

data Sing (b :: [a])

Defined in Data.Singletons.Prelude.Instances

data Sing (b :: [a]) where

• SNil :: forall k (b :: [k]). Sing ([] :: [k])
• SCons :: forall a (b :: [a]) (n :: a) (n :: [a]). Sing n -> Sing n -> Sing (n ': n)

data Sing (b :: Maybe a)

Defined in Data.Singletons.Prelude.Instances

data Sing (b :: Maybe a) where

• SNothing :: forall a (b :: Maybe a). Sing (Nothing :: Maybe a)
• SJust :: forall a (b :: Maybe a) (n :: a). Sing n -> Sing (Just n)

data Sing (a :: TYPE rep)

A choice of singleton for the kind TYPE rep (for some RuntimeRep rep), an instantiation of which is the famous kind Type.

Conceivably, one could generalize this instance to `Sing :: k -> Type` for any kind k, and remove all other Sing instances. We don't adopt this design, however, since it is far more convenient in practice to work with explicit singleton values than TypeReps (for instance, TypeReps are more difficult to pattern match on, and require extra runtime checks).

We cannot produce explicit singleton values for everything in TYPE rep, however, since it is an open kind, so we reach for TypeRep in this one particular case.

Defined in Data.Singletons.TypeRepTYPE

data Sing (a :: TYPE rep) = STypeRep (TypeRep a)

data Sing (b :: Min a)

Defined in Data.Singletons.Prelude.Semigroup.Internal

data Sing (b :: Min a) where

• SMin :: forall a (b :: Min a) (n :: a). {..} -> Sing (Min n)

data Sing (b :: Max a)

Defined in Data.Singletons.Prelude.Semigroup.Internal

data Sing (b :: Max a) where

• SMax :: forall a (b :: Max a) (n :: a). {..} -> Sing (Max n)

data Sing (b :: First a)

Defined in Data.Singletons.Prelude.Semigroup.Internal

data Sing (b :: First a) where

• SFirst :: forall a (b :: First a) (n :: a). {..} -> Sing (First n)

data Sing (b :: Last a)

Defined in Data.Singletons.Prelude.Semigroup.Internal

data Sing (b :: Last a) where

• SLast :: forall a (b :: Last a) (n :: a). {..} -> Sing (Last n)

data Sing (a :: WrappedMonoid m)

Defined in Data.Singletons.Prelude.Semigroup.Internal

data Sing (a :: WrappedMonoid m) where

• SWrapMonoid :: forall m (a :: WrappedMonoid m) (n :: m). {..} -> Sing (WrapMonoid n)

data Sing (b :: Option a)

Defined in Data.Singletons.Prelude.Semigroup.Internal

data Sing (b :: Option a) where

• SOption :: forall a (b :: Option a) (n :: Maybe a). {..} -> Sing (Option n)

data Sing (b :: Identity a)

Defined in Data.Singletons.Prelude.Instances

data Sing (b :: Identity a) where

• SIdentity :: forall a (b :: Identity a) (n :: a). {..} -> Sing (Identity n)

data Sing (b :: First a)

Defined in Data.Singletons.Prelude.Monoid

data Sing (b :: First a) where

• SFirst :: forall a (b :: First a) (n :: Maybe a). {..} -> Sing (First n)

data Sing (b :: Last a)

Defined in Data.Singletons.Prelude.Monoid

data Sing (b :: Last a) where

• SLast :: forall a (b :: Last a) (n :: Maybe a). {..} -> Sing (Last n)

data Sing (b :: Dual a)

Defined in Data.Singletons.Prelude.Semigroup.Internal

data Sing (b :: Dual a) where

• SDual :: forall a (b :: Dual a) (n :: a). {..} -> Sing (Dual n)

data Sing (b :: Sum a)

Defined in Data.Singletons.Prelude.Semigroup.Internal

data Sing (b :: Sum a) where

• SSum :: forall a (b :: Sum a) (n :: a). {..} -> Sing (Sum n)

data Sing (b :: Product a)

Defined in Data.Singletons.Prelude.Semigroup.Internal

data Sing (b :: Product a) where

• SProduct :: forall a (b :: Product a) (n :: a). {..} -> Sing (Product n)

data Sing (b :: Down a)

Defined in Data.Singletons.Prelude.Ord

data Sing (b :: Down a) where

• SDown :: forall a (b :: Down a) (n :: a). Sing n -> Sing (Down n)

data Sing (b :: NonEmpty a)

Defined in Data.Singletons.Prelude.Instances

data Sing (b :: NonEmpty a) where

• (:%|) :: forall a (b :: NonEmpty a) (n :: a) (n :: [a]). Sing n -> Sing n -> Sing (n :| n)

data Sing (c :: Either a b)

Defined in Data.Singletons.Prelude.Instances

data Sing (c :: Either a b) where

• SLeft :: forall a b (c :: Either a b) (n :: a). Sing n -> Sing (Left n :: Either a b)
• SRight :: forall a b (c :: Either a b) (n :: b). Sing n -> Sing (Right n :: Either a b)

data Sing (c :: (a, b))

Defined in Data.Singletons.Prelude.Instances

data Sing (c :: (a, b)) where

• STuple2 :: forall a b (c :: (a, b)) (n :: a) (n :: b). Sing n -> Sing n -> Sing ((,) n n)

data Sing (c :: Arg a b)

Defined in Data.Singletons.Prelude.Semigroup

data Sing (c :: Arg a b) where

• SArg :: forall a b (c :: Arg a b) (n :: a) (n :: b). Sing n -> Sing n -> Sing (Arg n n)

data Sing (f :: k1 ~> k2)

Defined in Data.Singletons.Internal

data Sing (f :: k1 ~> k2) = SLambda {

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

}

data Sing (d :: (a, b, c))

Defined in Data.Singletons.Prelude.Instances

data Sing (d :: (a, b, c)) where

• STuple3 :: forall a b c (d :: (a, b, c)) (n :: a) (n :: b) (n :: c). Sing n -> Sing n -> Sing n -> Sing ((,,) n n n)

data Sing (c :: Const a b)

Defined in Data.Singletons.Prelude.Const

data Sing (c :: Const a b) where

• SConst :: forall k a (b :: k) (c :: Const a b) (a :: a). {..} -> Sing (Const a :: Const a b)

data Sing (e :: (a, b, c, d))

Defined in Data.Singletons.Prelude.Instances

data Sing (e :: (a, b, c, d)) where

• STuple4 :: forall a b c d (e :: (a, b, c, d)) (n :: a) (n :: b) (n :: c) (n :: d). Sing n -> Sing n -> Sing n -> Sing n -> Sing ((,,,) n n n n)

data Sing (f :: (a, b, c, d, e))

Defined in Data.Singletons.Prelude.Instances

data Sing (f :: (a, b, c, d, e)) where

• STuple5 :: forall a b c d e (f :: (a, b, c, d, e)) (n :: a) (n :: b) (n :: c) (n :: d) (n :: e). Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing ((,,,,) n n n n n)

data Sing (g :: (a, b, c, d, e, f))

Defined in Data.Singletons.Prelude.Instances

data Sing (g :: (a, b, c, d, e, f)) where

• STuple6 :: forall a b c d e f (g :: (a, b, c, d, e, f)) (n :: a) (n :: b) (n :: c) (n :: d) (n :: e) (n :: f). Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing ((,,,,,) n n n n n n)

data Sing (h :: (a, b, c, d, e, f, g))

Defined in Data.Singletons.Prelude.Instances

data Sing (h :: (a, b, c, d, e, f, g)) where

• STuple7 :: forall a b c d e f g (h :: (a, b, c, d, e, f, g)) (n :: a) (n :: b) (n :: c) (n :: d) (n :: e) (n :: f) (n :: g). Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing ((,,,,,,) n n n n n n n)

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] -> Type)

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

Basic functions

type family (a :: [a]) ++ (a :: [a]) :: [a] where ... infixr 5

Equations

'[] ++ ys = ys

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

(%++) :: forall a (t :: [a]) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply (++@#@$) t) t :: [a]) infixr 5

type family Head (a :: [a]) :: a where ...

Equations

Head ((:) a _) = a

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

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

type family Last (a :: [a]) :: a where ...

Equations

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

Last '[x] = x

Last ((:) _ ((:) x xs)) = Apply LastSym0 (Apply (Apply (:@#@$) x) xs)

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

type family Tail (a :: [a]) :: [a] where ...

Equations

Tail ((:) _ t) = t

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

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

type family Init (a :: [a]) :: [a] where ...

Equations

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

Init ((:) x xs) = Apply (Apply (Let6989586621679940044Init'Sym2 x xs) x) xs

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

type family Null (arg :: t a) :: Bool

Instances

type Null (a :: [a6989586621680438541])

Defined in Data.Singletons.Prelude.Foldable

type Null (a :: [a6989586621680438541])

type Null (arg :: Maybe a)

Defined in Data.Singletons.Prelude.Foldable

type Null (arg :: Maybe a)

type Null (arg :: Min a)

Defined in Data.Singletons.Prelude.Semigroup

type Null (arg :: Min a)

type Null (arg :: Max a)

Defined in Data.Singletons.Prelude.Semigroup

type Null (arg :: Max a)

type Null (arg :: First a)

Defined in Data.Singletons.Prelude.Semigroup

type Null (arg :: First a)

type Null (arg :: Last a)

Defined in Data.Singletons.Prelude.Semigroup

type Null (arg :: Last a)

type Null (arg :: Option a)

Defined in Data.Singletons.Prelude.Semigroup

type Null (arg :: Option a)

type Null (a :: Identity a6989586621680438541)

Defined in Data.Singletons.Prelude.Identity

type Null (a :: Identity a6989586621680438541)

type Null (arg :: First a)

Defined in Data.Singletons.Prelude.Foldable

type Null (arg :: First a)

type Null (arg :: Last a)

Defined in Data.Singletons.Prelude.Foldable

type Null (arg :: Last a)

type Null (a :: Dual a6989586621680438541)

Defined in Data.Singletons.Prelude.Foldable

type Null (a :: Dual a6989586621680438541)

type Null (a :: Sum a6989586621680438541)

Defined in Data.Singletons.Prelude.Foldable

type Null (a :: Sum a6989586621680438541)

type Null (a :: Product a6989586621680438541)

Defined in Data.Singletons.Prelude.Foldable

type Null (a :: Product a6989586621680438541)

type Null (arg :: NonEmpty a)

Defined in Data.Singletons.Prelude.Foldable

type Null (arg :: NonEmpty a)

type Null (a2 :: Either a1 a6989586621680438541)

Defined in Data.Singletons.Prelude.Foldable

type Null (a2 :: Either a1 a6989586621680438541)

type Null (arg :: (a1, a2))

Defined in Data.Singletons.Prelude.Foldable

type Null (arg :: (a1, a2))

type Null (arg :: Arg a1 a2)

Defined in Data.Singletons.Prelude.Semigroup

type Null (arg :: Arg a1 a2)

type Null (arg :: Const m a)

Defined in Data.Singletons.Prelude.Const

type Null (arg :: Const m a)

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

type family Length (arg :: t a) :: Nat

Instances

type Length (a :: [a6989586621680438542])

Defined in Data.Singletons.Prelude.Foldable

type Length (a :: [a6989586621680438542])

type Length (arg :: Maybe a)

Defined in Data.Singletons.Prelude.Foldable

type Length (arg :: Maybe a)

type Length (arg :: Min a)

Defined in Data.Singletons.Prelude.Semigroup

type Length (arg :: Min a)

type Length (arg :: Max a)

Defined in Data.Singletons.Prelude.Semigroup

type Length (arg :: Max a)

type Length (arg :: First a)

Defined in Data.Singletons.Prelude.Semigroup

type Length (arg :: First a)

type Length (arg :: Last a)

Defined in Data.Singletons.Prelude.Semigroup

type Length (arg :: Last a)

type Length (arg :: Option a)

Defined in Data.Singletons.Prelude.Semigroup

type Length (arg :: Option a)

type Length (a :: Identity a6989586621680438542)

Defined in Data.Singletons.Prelude.Identity

type Length (a :: Identity a6989586621680438542)

type Length (arg :: First a)

Defined in Data.Singletons.Prelude.Foldable

type Length (arg :: First a)

type Length (arg :: Last a)

Defined in Data.Singletons.Prelude.Foldable

type Length (arg :: Last a)

type Length (a :: Dual a6989586621680438542)

Defined in Data.Singletons.Prelude.Foldable

type Length (a :: Dual a6989586621680438542)

type Length (a :: Sum a6989586621680438542)

Defined in Data.Singletons.Prelude.Foldable

type Length (a :: Sum a6989586621680438542)

type Length (a :: Product a6989586621680438542)

Defined in Data.Singletons.Prelude.Foldable

type Length (a :: Product a6989586621680438542)

type Length (arg :: NonEmpty a)

Defined in Data.Singletons.Prelude.Foldable

type Length (arg :: NonEmpty a)

type Length (a2 :: Either a1 a6989586621680438542)

Defined in Data.Singletons.Prelude.Foldable

type Length (a2 :: Either a1 a6989586621680438542)

type Length (arg :: (a1, a2))

Defined in Data.Singletons.Prelude.Foldable

type Length (arg :: (a1, a2))

type Length (arg :: Arg a1 a2)

Defined in Data.Singletons.Prelude.Semigroup

type Length (arg :: Arg a1 a2)

type Length (arg :: Const m a)

Defined in Data.Singletons.Prelude.Const

type Length (arg :: Const m a)

sLength :: forall a (t :: t a). SFoldable t => Sing t -> Sing (Apply LengthSym0 t :: Nat)

List transformations

type family Map (a :: (~>) a b) (a :: [a]) :: [b] where ...

Equations

Map _ '[] = '[]

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

sMap :: forall a b (t :: (~>) a b) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply MapSym0 t) t :: [b])

type family Reverse (a :: [a]) :: [a] where ...

Equations

Reverse l = Apply (Apply (Let6989586621679939996RevSym1 l) l) '[]

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

type family Intersperse (a :: a) (a :: [a]) :: [a] where ...

Equations

Intersperse _ '[] = '[]

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

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

type family Intercalate (a :: [a]) (a :: [[a]]) :: [a] where ...

Equations

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

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

type family Transpose (a :: [[a]]) :: [[a]] where ...

Equations

Transpose '[] = '[]

Transpose ((:) '[] xss) = Apply TransposeSym0 xss

Transpose ((:) ((:) x xs) xss) = Apply (Apply (:@#@$) (Apply (Apply (:@#@$) x) (Apply (Apply MapSym0 HeadSym0) xss))) (Apply TransposeSym0 (Apply (Apply (:@#@$) xs) (Apply (Apply MapSym0 TailSym0) xss)))

sTranspose :: forall a (t :: [[a]]). Sing t -> Sing (Apply TransposeSym0 t :: [[a]])

type family Subsequences (a :: [a]) :: [[a]] where ...

Equations

Subsequences xs = Apply (Apply (:@#@$) '[]) (Apply NonEmptySubsequencesSym0 xs)

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

type family Permutations (a :: [a]) :: [[a]] where ...

Equations

Permutations xs0 = Apply (Apply (:@#@$) xs0) (Apply (Apply (Let6989586621679939862PermsSym1 xs0) xs0) '[])

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

Reducing lists (folds)

type family Foldl (arg :: (~>) b ((~>) a b)) (arg :: b) (arg :: t a) :: b

Instances

type Foldl (a1 :: k2 ~> (a6989586621680438535 ~> k2)) (a2 :: k2) (a3 :: [a6989586621680438535])

Defined in Data.Singletons.Prelude.Foldable

type Foldl (a1 :: k2 ~> (a6989586621680438535 ~> k2)) (a2 :: k2) (a3 :: [a6989586621680438535])

type Foldl (a1 :: k2 ~> (a6989586621680438535 ~> k2)) (a2 :: k2) (a3 :: Maybe a6989586621680438535)

Defined in Data.Singletons.Prelude.Foldable

type Foldl (a1 :: k2 ~> (a6989586621680438535 ~> k2)) (a2 :: k2) (a3 :: Maybe a6989586621680438535)

type Foldl (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Min a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Min a)

type Foldl (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Max a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Max a)

type Foldl (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: First a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: First a)

type Foldl (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Last a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Last a)

type Foldl (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Option a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Option a)

type Foldl (a1 :: k2 ~> (a6989586621680438535 ~> k2)) (a2 :: k2) (a3 :: Identity a6989586621680438535)

Defined in Data.Singletons.Prelude.Identity

type Foldl (a1 :: k2 ~> (a6989586621680438535 ~> k2)) (a2 :: k2) (a3 :: Identity a6989586621680438535)

type Foldl (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: First a)

Defined in Data.Singletons.Prelude.Foldable

type Foldl (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: First a)

type Foldl (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Last a)

Defined in Data.Singletons.Prelude.Foldable

type Foldl (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Last a)

type Foldl (a1 :: k2 ~> (a6989586621680438535 ~> k2)) (a2 :: k2) (a3 :: Dual a6989586621680438535)

Defined in Data.Singletons.Prelude.Foldable

type Foldl (a1 :: k2 ~> (a6989586621680438535 ~> k2)) (a2 :: k2) (a3 :: Dual a6989586621680438535)

type Foldl (a1 :: k2 ~> (a6989586621680438535 ~> k2)) (a2 :: k2) (a3 :: Sum a6989586621680438535)

Defined in Data.Singletons.Prelude.Foldable

type Foldl (a1 :: k2 ~> (a6989586621680438535 ~> k2)) (a2 :: k2) (a3 :: Sum a6989586621680438535)

type Foldl (a1 :: k2 ~> (a6989586621680438535 ~> k2)) (a2 :: k2) (a3 :: Product a6989586621680438535)

Defined in Data.Singletons.Prelude.Foldable

type Foldl (a1 :: k2 ~> (a6989586621680438535 ~> k2)) (a2 :: k2) (a3 :: Product a6989586621680438535)

type Foldl (a1 :: k2 ~> (a6989586621680438535 ~> k2)) (a2 :: k2) (a3 :: NonEmpty a6989586621680438535)

Defined in Data.Singletons.Prelude.Foldable

type Foldl (a1 :: k2 ~> (a6989586621680438535 ~> k2)) (a2 :: k2) (a3 :: NonEmpty a6989586621680438535)

type Foldl (arg1 :: b ~> (a1 ~> b)) (arg2 :: b) (arg3 :: Either a2 a1)

Defined in Data.Singletons.Prelude.Foldable

type Foldl (arg1 :: b ~> (a1 ~> b)) (arg2 :: b) (arg3 :: Either a2 a1)

type Foldl (arg1 :: b ~> (a1 ~> b)) (arg2 :: b) (arg3 :: (a2, a1))

Defined in Data.Singletons.Prelude.Foldable

type Foldl (arg1 :: b ~> (a1 ~> b)) (arg2 :: b) (arg3 :: (a2, a1))

type Foldl (arg1 :: b ~> (a1 ~> b)) (arg2 :: b) (arg3 :: Arg a2 a1)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl (arg1 :: b ~> (a1 ~> b)) (arg2 :: b) (arg3 :: Arg a2 a1)

type Foldl (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Const m a)

Defined in Data.Singletons.Prelude.Const

type Foldl (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Const m a)

sFoldl :: forall b a (t :: (~>) b ((~>) a b)) (t :: b) (t :: t a). SFoldable t => Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply FoldlSym0 t) t) t :: b)

type family Foldl' (arg :: (~>) b ((~>) a b)) (arg :: b) (arg :: t a) :: b

Instances

type Foldl' (a1 :: k2 ~> (a6989586621680438537 ~> k2)) (a2 :: k2) (a3 :: [a6989586621680438537])

Defined in Data.Singletons.Prelude.Foldable

type Foldl' (a1 :: k2 ~> (a6989586621680438537 ~> k2)) (a2 :: k2) (a3 :: [a6989586621680438537])

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Maybe a)

Defined in Data.Singletons.Prelude.Foldable

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Maybe a)

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Min a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Min a)

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Max a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Max a)

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: First a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: First a)

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Last a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Last a)

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Option a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Option a)

type Foldl' (a1 :: k2 ~> (a6989586621680438537 ~> k2)) (a2 :: k2) (a3 :: Identity a6989586621680438537)

Defined in Data.Singletons.Prelude.Identity

type Foldl' (a1 :: k2 ~> (a6989586621680438537 ~> k2)) (a2 :: k2) (a3 :: Identity a6989586621680438537)

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: First a)

Defined in Data.Singletons.Prelude.Foldable

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: First a)

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Last a)

Defined in Data.Singletons.Prelude.Foldable

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Last a)

type Foldl' (a1 :: k2 ~> (a6989586621680438537 ~> k2)) (a2 :: k2) (a3 :: Dual a6989586621680438537)

Defined in Data.Singletons.Prelude.Foldable

type Foldl' (a1 :: k2 ~> (a6989586621680438537 ~> k2)) (a2 :: k2) (a3 :: Dual a6989586621680438537)

type Foldl' (a1 :: k2 ~> (a6989586621680438537 ~> k2)) (a2 :: k2) (a3 :: Sum a6989586621680438537)

Defined in Data.Singletons.Prelude.Foldable

type Foldl' (a1 :: k2 ~> (a6989586621680438537 ~> k2)) (a2 :: k2) (a3 :: Sum a6989586621680438537)

type Foldl' (a1 :: k2 ~> (a6989586621680438537 ~> k2)) (a2 :: k2) (a3 :: Product a6989586621680438537)

Defined in Data.Singletons.Prelude.Foldable

type Foldl' (a1 :: k2 ~> (a6989586621680438537 ~> k2)) (a2 :: k2) (a3 :: Product a6989586621680438537)

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: NonEmpty a)

Defined in Data.Singletons.Prelude.Foldable

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: NonEmpty a)

type Foldl' (arg1 :: b ~> (a1 ~> b)) (arg2 :: b) (arg3 :: Either a2 a1)

Defined in Data.Singletons.Prelude.Foldable

type Foldl' (arg1 :: b ~> (a1 ~> b)) (arg2 :: b) (arg3 :: Either a2 a1)

type Foldl' (arg1 :: b ~> (a1 ~> b)) (arg2 :: b) (arg3 :: (a2, a1))

Defined in Data.Singletons.Prelude.Foldable

type Foldl' (arg1 :: b ~> (a1 ~> b)) (arg2 :: b) (arg3 :: (a2, a1))

type Foldl' (arg1 :: b ~> (a1 ~> b)) (arg2 :: b) (arg3 :: Arg a2 a1)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl' (arg1 :: b ~> (a1 ~> b)) (arg2 :: b) (arg3 :: Arg a2 a1)

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Const m a)

Defined in Data.Singletons.Prelude.Const

type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Const m a)

sFoldl' :: forall b a (t :: (~>) b ((~>) a b)) (t :: b) (t :: t a). SFoldable t => Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply Foldl'Sym0 t) t) t :: b)

type family Foldl1 (arg :: (~>) a ((~>) a a)) (arg :: t a) :: a

Instances

type Foldl1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: [k2])

Defined in Data.Singletons.Prelude.Foldable

type Foldl1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: [k2])

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: Maybe a)

Defined in Data.Singletons.Prelude.Foldable

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: Maybe a)

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: Min a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: Min a)

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: Max a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: Max a)

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: First a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: First a)

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: Last a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: Last a)

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: Option a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: Option a)

type Foldl1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: Identity k2)

Defined in Data.Singletons.Prelude.Identity

type Foldl1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: Identity k2)

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: First a)

Defined in Data.Singletons.Prelude.Foldable

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: First a)

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: Last a)

Defined in Data.Singletons.Prelude.Foldable

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: Last a)

type Foldl1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: Dual k2)

Defined in Data.Singletons.Prelude.Foldable

type Foldl1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: Dual k2)

type Foldl1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: Sum k2)

Defined in Data.Singletons.Prelude.Foldable

type Foldl1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: Sum k2)

type Foldl1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: Product k2)

Defined in Data.Singletons.Prelude.Foldable

type Foldl1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: Product k2)

type Foldl1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: NonEmpty k2)

Defined in Data.Singletons.Prelude.Foldable

type Foldl1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: NonEmpty k2)

type Foldl1 (arg1 :: a1 ~> (a1 ~> a1)) (arg2 :: Either a2 a1)

Defined in Data.Singletons.Prelude.Foldable

type Foldl1 (arg1 :: a1 ~> (a1 ~> a1)) (arg2 :: Either a2 a1)

type Foldl1 (arg1 :: a1 ~> (a1 ~> a1)) (arg2 :: (a2, a1))

Defined in Data.Singletons.Prelude.Foldable

type Foldl1 (arg1 :: a1 ~> (a1 ~> a1)) (arg2 :: (a2, a1))

type Foldl1 (arg1 :: a1 ~> (a1 ~> a1)) (arg2 :: Arg a2 a1)

Defined in Data.Singletons.Prelude.Semigroup

type Foldl1 (arg1 :: a1 ~> (a1 ~> a1)) (arg2 :: Arg a2 a1)

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: Const m a)

Defined in Data.Singletons.Prelude.Const

type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: Const m a)

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

type family Foldl1' (a :: (~>) a ((~>) a a)) (a :: [a]) :: a where ...

Equations

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

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

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

type family Foldr (arg :: (~>) a ((~>) b b)) (arg :: b) (arg :: t a) :: b

Instances

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: [a6989586621680438530])

Defined in Data.Singletons.Prelude.Foldable

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: [a6989586621680438530])

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Maybe a6989586621680438530)

Defined in Data.Singletons.Prelude.Foldable

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Maybe a6989586621680438530)

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Min a6989586621680438530)

Defined in Data.Singletons.Prelude.Semigroup

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Min a6989586621680438530)

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Max a6989586621680438530)

Defined in Data.Singletons.Prelude.Semigroup

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Max a6989586621680438530)

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: First a6989586621680438530)

Defined in Data.Singletons.Prelude.Semigroup

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: First a6989586621680438530)

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Last a6989586621680438530)

Defined in Data.Singletons.Prelude.Semigroup

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Last a6989586621680438530)

type Foldr (arg1 :: a ~> (b ~> b)) (arg2 :: b) (arg3 :: Option a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldr (arg1 :: a ~> (b ~> b)) (arg2 :: b) (arg3 :: Option a)

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Identity a6989586621680438530)

Defined in Data.Singletons.Prelude.Identity

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Identity a6989586621680438530)

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: First a6989586621680438530)

Defined in Data.Singletons.Prelude.Foldable

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: First a6989586621680438530)

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Last a6989586621680438530)

Defined in Data.Singletons.Prelude.Foldable

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Last a6989586621680438530)

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Dual a6989586621680438530)

Defined in Data.Singletons.Prelude.Foldable

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Dual a6989586621680438530)

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Sum a6989586621680438530)

Defined in Data.Singletons.Prelude.Foldable

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Sum a6989586621680438530)

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Product a6989586621680438530)

Defined in Data.Singletons.Prelude.Foldable

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Product a6989586621680438530)

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: NonEmpty a6989586621680438530)

Defined in Data.Singletons.Prelude.Foldable

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: NonEmpty a6989586621680438530)

type Foldr (a2 :: a6989586621680438530 ~> (k2 ~> k2)) (a3 :: k2) (a4 :: Either a1 a6989586621680438530)

Defined in Data.Singletons.Prelude.Foldable

type Foldr (a2 :: a6989586621680438530 ~> (k2 ~> k2)) (a3 :: k2) (a4 :: Either a1 a6989586621680438530)

type Foldr (a2 :: a6989586621680438530 ~> (k2 ~> k2)) (a3 :: k2) (a4 :: (a1, a6989586621680438530))

Defined in Data.Singletons.Prelude.Foldable

type Foldr (a2 :: a6989586621680438530 ~> (k2 ~> k2)) (a3 :: k2) (a4 :: (a1, a6989586621680438530))

type Foldr (a2 :: a6989586621680438530 ~> (k2 ~> k2)) (a3 :: k2) (a4 :: Arg a1 a6989586621680438530)

Defined in Data.Singletons.Prelude.Semigroup

type Foldr (a2 :: a6989586621680438530 ~> (k2 ~> k2)) (a3 :: k2) (a4 :: Arg a1 a6989586621680438530)

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Const m a6989586621680438530)

Defined in Data.Singletons.Prelude.Const

type Foldr (a1 :: a6989586621680438530 ~> (k2 ~> k2)) (a2 :: k2) (a3 :: Const m a6989586621680438530)

sFoldr :: forall a b (t :: (~>) a ((~>) b b)) (t :: b) (t :: t a). SFoldable t => Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply FoldrSym0 t) t) t :: b)

type family Foldr1 (arg :: (~>) a ((~>) a a)) (arg :: t a) :: a

Instances

type Foldr1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: [k2])

Defined in Data.Singletons.Prelude.Foldable

type Foldr1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: [k2])

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: Maybe a)

Defined in Data.Singletons.Prelude.Foldable

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: Maybe a)

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: Min a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: Min a)

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: Max a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: Max a)

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: First a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: First a)

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: Last a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: Last a)

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: Option a)

Defined in Data.Singletons.Prelude.Semigroup

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: Option a)

type Foldr1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: Identity k2)

Defined in Data.Singletons.Prelude.Identity

type Foldr1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: Identity k2)

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: First a)

Defined in Data.Singletons.Prelude.Foldable

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: First a)

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: Last a)

Defined in Data.Singletons.Prelude.Foldable

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: Last a)

type Foldr1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: Dual k2)

Defined in Data.Singletons.Prelude.Foldable

type Foldr1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: Dual k2)

type Foldr1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: Sum k2)

Defined in Data.Singletons.Prelude.Foldable

type Foldr1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: Sum k2)

type Foldr1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: Product k2)

Defined in Data.Singletons.Prelude.Foldable

type Foldr1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: Product k2)

type Foldr1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: NonEmpty k2)

Defined in Data.Singletons.Prelude.Foldable

type Foldr1 (a1 :: k2 ~> (k2 ~> k2)) (a2 :: NonEmpty k2)

type Foldr1 (arg1 :: a1 ~> (a1 ~> a1)) (arg2 :: Either a2 a1)

Defined in Data.Singletons.Prelude.Foldable

type Foldr1 (arg1 :: a1 ~> (a1 ~> a1)) (arg2 :: Either a2 a1)

type Foldr1 (arg1 :: a1 ~> (a1 ~> a1)) (arg2 :: (a2, a1))

Defined in Data.Singletons.Prelude.Foldable

type Foldr1 (arg1 :: a1 ~> (a1 ~> a1)) (arg2 :: (a2, a1))

type Foldr1 (arg1 :: a1 ~> (a1 ~> a1)) (arg2 :: Arg a2 a1)

Defined in Data.Singletons.Prelude.Semigroup

type Foldr1 (arg1 :: a1 ~> (a1 ~> a1)) (arg2 :: Arg a2 a1)

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: Const m a)

Defined in Data.Singletons.Prelude.Const

type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: Const m a)

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

Special folds

type family Concat (a :: t [a]) :: [a] where ...

Equations

Concat xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_6989586621680439040Sym0 xs)) '[]) xs

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

type family ConcatMap (a :: (~>) a [b]) (a :: t a) :: [b] where ...

Equations

ConcatMap f xs = Apply (Apply (Apply FoldrSym0 (Apply (Apply Lambda_6989586621680439027Sym0 f) xs)) '[]) xs

sConcatMap :: forall t a b (t :: (~>) a [b]) (t :: t a). SFoldable t => Sing t -> Sing t -> Sing (Apply (Apply ConcatMapSym0 t) t :: [b])

type family And (a :: t Bool) :: Bool where ...

Equations

And x = Case_6989586621680439017 x (Let6989586621680439015Scrutinee_6989586621680438773Sym1 x)

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

type family Or (a :: t Bool) :: Bool where ...

Equations

Or x = Case_6989586621680439008 x (Let6989586621680439006Scrutinee_6989586621680438775Sym1 x)

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

type family Any (a :: (~>) a Bool) (a :: t a) :: Bool where ...

Equations

Any p x = Case_6989586621680438999 p x (Let6989586621680438996Scrutinee_6989586621680438777Sym2 p x)

sAny :: forall t a (t :: (~>) a Bool) (t :: t a). SFoldable t => Sing t -> Sing t -> Sing (Apply (Apply AnySym0 t) t :: Bool)

type family All (a :: (~>) a Bool) (a :: t a) :: Bool where ...

Equations

All p x = Case_6989586621680438986 p x (Let6989586621680438983Scrutinee_6989586621680438779Sym2 p x)

sAll :: forall t a (t :: (~>) a Bool) (t :: t a). SFoldable t => Sing t -> Sing t -> Sing (Apply (Apply AllSym0 t) t :: Bool)

type family Sum (arg :: t a) :: a

Instances

type Sum (a :: [k2])

Defined in Data.Singletons.Prelude.Foldable

type Sum (a :: [k2])

type Sum (arg :: Maybe a)

Defined in Data.Singletons.Prelude.Foldable

type Sum (arg :: Maybe a)

type Sum (arg :: Min a)

Defined in Data.Singletons.Prelude.Semigroup

type Sum (arg :: Min a)

type Sum (arg :: Max a)

Defined in Data.Singletons.Prelude.Semigroup

type Sum (arg :: Max a)

type Sum (arg :: First a)

Defined in Data.Singletons.Prelude.Semigroup

type Sum (arg :: First a)

type Sum (arg :: Last a)

Defined in Data.Singletons.Prelude.Semigroup

type Sum (arg :: Last a)

type Sum (arg :: Option a)

Defined in Data.Singletons.Prelude.Semigroup

type Sum (arg :: Option a)

type Sum (a :: Identity k2)

Defined in Data.Singletons.Prelude.Identity

type Sum (a :: Identity k2)

type Sum (arg :: First a)

Defined in Data.Singletons.Prelude.Foldable

type Sum (arg :: First a)

type Sum (arg :: Last a)

Defined in Data.Singletons.Prelude.Foldable

type Sum (arg :: Last a)

type Sum (a :: Dual k2)

Defined in Data.Singletons.Prelude.Foldable

type Sum (a :: Dual k2)

type Sum (a :: Sum k2)

Defined in Data.Singletons.Prelude.Foldable

type Sum (a :: Sum k2)

type Sum (a :: Product k2)

Defined in Data.Singletons.Prelude.Foldable

type Sum (a :: Product k2)

type Sum (arg :: NonEmpty a)

Defined in Data.Singletons.Prelude.Foldable

type Sum (arg :: NonEmpty a)

type Sum (arg :: Either a1 a2)

Defined in Data.Singletons.Prelude.Foldable

type Sum (arg :: Either a1 a2)

type Sum (arg :: (a1, a2))

Defined in Data.Singletons.Prelude.Foldable

type Sum (arg :: (a1, a2))

type Sum (arg :: Arg a1 a2)

Defined in Data.Singletons.Prelude.Semigroup

type Sum (arg :: Arg a1 a2)

type Sum (arg :: Const m a)

Defined in Data.Singletons.Prelude.Const

type Sum (arg :: Const m a)

sSum :: forall a (t :: t a). (SFoldable t, SNum a) => Sing t -> Sing (Apply SumSym0 t :: a)

type family Product (arg :: t a) :: a

Instances

type Product (a :: [k2])

Defined in Data.Singletons.Prelude.Foldable

type Product (a :: [k2])

type Product (arg :: Maybe a)

Defined in Data.Singletons.Prelude.Foldable

type Product (arg :: Maybe a)

type Product (arg :: Min a)

Defined in Data.Singletons.Prelude.Semigroup

type Product (arg :: Min a)

type Product (arg :: Max a)

Defined in Data.Singletons.Prelude.Semigroup

type Product (arg :: Max a)

type Product (arg :: First a)

Defined in Data.Singletons.Prelude.Semigroup

type Product (arg :: First a)

type Product (arg :: Last a)

Defined in Data.Singletons.Prelude.Semigroup

type Product (arg :: Last a)

type Product (arg :: Option a)

Defined in Data.Singletons.Prelude.Semigroup

type Product (arg :: Option a)

type Product (a :: Identity k2)

Defined in Data.Singletons.Prelude.Identity

type Product (a :: Identity k2)

type Product (arg :: First a)

Defined in Data.Singletons.Prelude.Foldable

type Product (arg :: First a)

type Product (arg :: Last a)

Defined in Data.Singletons.Prelude.Foldable

type Product (arg :: Last a)

type Product (a :: Dual k2)

Defined in Data.Singletons.Prelude.Foldable

type Product (a :: Dual k2)

type Product (a :: Sum k2)

Defined in Data.Singletons.Prelude.Foldable

type Product (a :: Sum k2)

type Product (a :: Product k2)

Defined in Data.Singletons.Prelude.Foldable

type Product (a :: Product k2)

type Product (arg :: NonEmpty a)

Defined in Data.Singletons.Prelude.Foldable

type Product (arg :: NonEmpty a)

type Product (arg :: Either a1 a2)

Defined in Data.Singletons.Prelude.Foldable

type Product (arg :: Either a1 a2)

type Product (arg :: (a1, a2))

Defined in Data.Singletons.Prelude.Foldable

type Product (arg :: (a1, a2))

type Product (arg :: Arg a1 a2)

Defined in Data.Singletons.Prelude.Semigroup

type Product (arg :: Arg a1 a2)

type Product (arg :: Const m a)

Defined in Data.Singletons.Prelude.Const

type Product (arg :: Const m a)

sProduct :: forall a (t :: t a). (SFoldable t, SNum a) => Sing t -> Sing (Apply ProductSym0 t :: a)

type family Maximum (arg :: t a) :: a

Instances

type Maximum (a :: [k2])

Defined in Data.Singletons.Prelude.Foldable

type Maximum (a :: [k2])

type Maximum (arg :: Maybe a)

Defined in Data.Singletons.Prelude.Foldable

type Maximum (arg :: Maybe a)

type Maximum (arg :: Min a)

Defined in Data.Singletons.Prelude.Semigroup

type Maximum (arg :: Min a)

type Maximum (arg :: Max a)

Defined in Data.Singletons.Prelude.Semigroup

type Maximum (arg :: Max a)

type Maximum (arg :: First a)

Defined in Data.Singletons.Prelude.Semigroup

type Maximum (arg :: First a)

type Maximum (arg :: Last a)

Defined in Data.Singletons.Prelude.Semigroup

type Maximum (arg :: Last a)

type Maximum (arg :: Option a)

Defined in Data.Singletons.Prelude.Semigroup

type Maximum (arg :: Option a)

type Maximum (a :: Identity k2)

Defined in Data.Singletons.Prelude.Identity

type Maximum (a :: Identity k2)

type Maximum (arg :: First a)

Defined in Data.Singletons.Prelude.Foldable

type Maximum (arg :: First a)

type Maximum (arg :: Last a)

Defined in Data.Singletons.Prelude.Foldable

type Maximum (arg :: Last a)

type Maximum (a :: Dual k2)

Defined in Data.Singletons.Prelude.Foldable

type Maximum (a :: Dual k2)

type Maximum (a :: Sum k2)

Defined in Data.Singletons.Prelude.Foldable

type Maximum (a :: Sum k2)

type Maximum (a :: Product k2)

Defined in Data.Singletons.Prelude.Foldable

type Maximum (a :: Product k2)

type Maximum (arg :: NonEmpty a)

Defined in Data.Singletons.Prelude.Foldable

type Maximum (arg :: NonEmpty a)

type Maximum (arg :: Either a1 a2)

Defined in Data.Singletons.Prelude.Foldable

type Maximum (arg :: Either a1 a2)

type Maximum (arg :: (a1, a2))

Defined in Data.Singletons.Prelude.Foldable

type Maximum (arg :: (a1, a2))

type Maximum (arg :: Arg a1 a2)

Defined in Data.Singletons.Prelude.Semigroup

type Maximum (arg :: Arg a1 a2)

type Maximum (arg :: Const m a)

Defined in Data.Singletons.Prelude.Const

type Maximum (arg :: Const m a)

sMaximum :: forall a (t :: t a). (SFoldable t, SOrd a) => Sing t -> Sing (Apply MaximumSym0 t :: a)

type family Minimum (arg :: t a) :: a

Instances

type Minimum (a :: [k2])

Defined in Data.Singletons.Prelude.Foldable

type Minimum (a :: [k2])

type Minimum (arg :: Maybe a)

Defined in Data.Singletons.Prelude.Foldable

type Minimum (arg :: Maybe a)

type Minimum (arg :: Min a)

Defined in Data.Singletons.Prelude.Semigroup

type Minimum (arg :: Min a)

type Minimum (arg :: Max a)

Defined in Data.Singletons.Prelude.Semigroup

type Minimum (arg :: Max a)

type Minimum (arg :: First a)

Defined in Data.Singletons.Prelude.Semigroup

type Minimum (arg :: First a)

type Minimum (arg :: Last a)

Defined in Data.Singletons.Prelude.Semigroup

type Minimum (arg :: Last a)

type Minimum (arg :: Option a)

Defined in Data.Singletons.Prelude.Semigroup

type Minimum (arg :: Option a)

type Minimum (a :: Identity k2)

Defined in Data.Singletons.Prelude.Identity

type Minimum (a :: Identity k2)

type Minimum (arg :: First a)

Defined in Data.Singletons.Prelude.Foldable

type Minimum (arg :: First a)

type Minimum (arg :: Last a)

Defined in Data.Singletons.Prelude.Foldable

type Minimum (arg :: Last a)

type Minimum (a :: Dual k2)

Defined in Data.Singletons.Prelude.Foldable

type Minimum (a :: Dual k2)

type Minimum (a :: Sum k2)

Defined in Data.Singletons.Prelude.Foldable

type Minimum (a :: Sum k2)

type Minimum (a :: Product k2)

Defined in Data.Singletons.Prelude.Foldable

type Minimum (a :: Product k2)

type Minimum (arg :: NonEmpty a)

Defined in Data.Singletons.Prelude.Foldable

type Minimum (arg :: NonEmpty a)

type Minimum (arg :: Either a1 a2)

Defined in Data.Singletons.Prelude.Foldable

type Minimum (arg :: Either a1 a2)

type Minimum (arg :: (a1, a2))

Defined in Data.Singletons.Prelude.Foldable

type Minimum (arg :: (a1, a2))

type Minimum (arg :: Arg a1 a2)

Defined in Data.Singletons.Prelude.Semigroup

type Minimum (arg :: Arg a1 a2)

type Minimum (arg :: Const m a)

Defined in Data.Singletons.Prelude.Const

type Minimum (arg :: Const m a)

sMinimum :: forall a (t :: t a). (SFoldable t, SOrd a) => Sing t -> Sing (Apply MinimumSym0 t :: a)

Building lists

Scans

type family Scanl (a :: (~>) b ((~>) a b)) (a :: b) (a :: [a]) :: [b] where ...

Equations

Scanl f q ls = Apply (Apply (:@#@$) q) (Case_6989586621679939634 f q ls ls)

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

type family Scanl1 (a :: (~>) a ((~>) a a)) (a :: [a]) :: [a] where ...

Equations

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

Scanl1 _ '[] = '[]

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

type family Scanr (a :: (~>) a ((~>) b b)) (a :: b) (a :: [a]) :: [b] where ...

Equations

Scanr _ q0 '[] = Apply (Apply (:@#@$) q0) '[]

Scanr f q0 ((:) x xs) = Case_6989586621679939620 f q0 x xs (Let6989586621679939615Scrutinee_6989586621679930008Sym4 f q0 x xs)

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

type family Scanr1 (a :: (~>) a ((~>) a a)) (a :: [a]) :: [a] where ...

Equations

Scanr1 _ '[] = '[]

Scanr1 _ '[x] = Apply (Apply (:@#@$) x) '[]

Scanr1 f ((:) x ((:) wild_6989586621679930020 wild_6989586621679930022)) = Case_6989586621679939599 f x wild_6989586621679930020 wild_6989586621679930022 (Let6989586621679939594Scrutinee_6989586621679930014Sym4 f x wild_6989586621679930020 wild_6989586621679930022)

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

Accumulating maps

type family MapAccumL (a :: (~>) a ((~>) b (a, c))) (a :: a) (a :: t b) :: (a, t c) where ...

Equations

MapAccumL f s t = Case_6989586621680741097 f s t (Let6989586621680741093Scrutinee_6989586621680740628Sym3 f s t)

sMapAccumL :: forall t a b c (t :: (~>) a ((~>) b (a, c))) (t :: a) (t :: t b). STraversable t => Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply MapAccumLSym0 t) t) t :: (a, t c))

type family MapAccumR (a :: (~>) a ((~>) b (a, c))) (a :: a) (a :: t b) :: (a, t c) where ...

Equations

MapAccumR f s t = Case_6989586621680741080 f s t (Let6989586621680741076Scrutinee_6989586621680740632Sym3 f s t)

sMapAccumR :: forall t a b c (t :: (~>) a ((~>) b (a, c))) (t :: a) (t :: t b). STraversable t => Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply MapAccumRSym0 t) t) t :: (a, t c))

Cyclical lists

type family Replicate (a :: Nat) (a :: a) :: [a] where ...

Equations

Replicate n x = Case_6989586621679938731 n x (Let6989586621679938728Scrutinee_6989586621679930116Sym2 n x)

sReplicate :: forall a (t :: Nat) (t :: a). Sing t -> Sing t -> Sing (Apply (Apply ReplicateSym0 t) t :: [a])

Unfolding

type family Unfoldr (a :: (~>) b (Maybe (a, b))) (a :: b) :: [a] where ...

Equations

Unfoldr f b = Case_6989586621679939447 f b (Let6989586621679939444Scrutinee_6989586621679930024Sym2 f b)

sUnfoldr :: forall b a (t :: (~>) b (Maybe (a, b))) (t :: b). Sing t -> Sing t -> Sing (Apply (Apply UnfoldrSym0 t) t :: [a])

Sublists

Extracting sublists

type family Take (a :: Nat) (a :: [a]) :: [a] where ...

Equations

Take _ '[] = '[]

Take n ((:) x xs) = Case_6989586621679938829 n x xs (Let6989586621679938825Scrutinee_6989586621679930100Sym3 n x xs)

sTake :: forall a (t :: Nat) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply TakeSym0 t) t :: [a])

type family Drop (a :: Nat) (a :: [a]) :: [a] where ...

Equations

Drop _ '[] = '[]

Drop n ((:) x xs) = Case_6989586621679938815 n x xs (Let6989586621679938811Scrutinee_6989586621679930102Sym3 n x xs)

sDrop :: forall a (t :: Nat) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply DropSym0 t) t :: [a])

type family SplitAt (a :: Nat) (a :: [a]) :: ([a], [a]) where ...

Equations

SplitAt n xs = Apply (Apply Tuple2Sym0 (Apply (Apply TakeSym0 n) xs)) (Apply (Apply DropSym0 n) xs)

sSplitAt :: forall a (t :: Nat) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply SplitAtSym0 t) t :: ([a], [a]))

type family TakeWhile (a :: (~>) a Bool) (a :: [a]) :: [a] where ...

Equations

TakeWhile _ '[] = '[]

TakeWhile p ((:) x xs) = Case_6989586621679938987 p x xs (Let6989586621679938983Scrutinee_6989586621679930090Sym3 p x xs)

sTakeWhile :: forall a (t :: (~>) a Bool) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply TakeWhileSym0 t) t :: [a])

type family DropWhile (a :: (~>) a Bool) (a :: [a]) :: [a] where ...

Equations

DropWhile _ '[] = '[]

DropWhile p ((:) x xs') = Case_6989586621679938973 p x xs' (Let6989586621679938969Scrutinee_6989586621679930092Sym3 p x xs')

sDropWhile :: forall a (t :: (~>) a Bool) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply DropWhileSym0 t) t :: [a])

type family DropWhileEnd (a :: (~>) a Bool) (a :: [a]) :: [a] where ...

Equations

DropWhileEnd p a_6989586621679940018 = Apply (Apply (Apply FoldrSym0 (Apply (Apply Lambda_6989586621679940022Sym0 p) a_6989586621679940018)) '[]) a_6989586621679940018

sDropWhileEnd :: forall a (t :: (~>) a Bool) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply DropWhileEndSym0 t) t :: [a])

type family Span (a :: (~>) a Bool) (a :: [a]) :: ([a], [a]) where ...

Equations

Span _ '[] = Apply (Apply Tuple2Sym0 Let6989586621679938885XsSym0) Let6989586621679938885XsSym0

Span p ((:) x xs') = Case_6989586621679938897 p x xs' (Let6989586621679938893Scrutinee_6989586621679930096Sym3 p x xs')

sSpan :: forall a (t :: (~>) a Bool) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply SpanSym0 t) t :: ([a], [a]))

type family Break (a :: (~>) a Bool) (a :: [a]) :: ([a], [a]) where ...

Equations

Break _ '[] = Apply (Apply Tuple2Sym0 Let6989586621679938842XsSym0) Let6989586621679938842XsSym0

Break p ((:) x xs') = Case_6989586621679938854 p x xs' (Let6989586621679938850Scrutinee_6989586621679930098Sym3 p x xs')

sBreak :: forall a (t :: (~>) a Bool) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply BreakSym0 t) t :: ([a], [a]))

type family StripPrefix (a :: [a]) (a :: [a]) :: Maybe [a] where ...

Equations

StripPrefix '[] ys = Apply JustSym0 ys

StripPrefix arg_6989586621680055731 arg_6989586621680055733 = Case_6989586621680068380 arg_6989586621680055731 arg_6989586621680055733 (Apply (Apply Tuple2Sym0 arg_6989586621680055731) arg_6989586621680055733)

type family Group (a :: [a]) :: [[a]] where ...

Equations

Group xs = Apply (Apply GroupBySym0 (==@#@$)) xs

sGroup :: forall a (t :: [a]). SEq a => Sing t -> Sing (Apply GroupSym0 t :: [[a]])

type family Inits (a :: [a]) :: [[a]] where ...

Equations

Inits xs = Apply (Apply (:@#@$) '[]) (Case_6989586621679939433 xs xs)

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

type family Tails (a :: [a]) :: [[a]] where ...

Equations

Tails xs = Apply (Apply (:@#@$) xs) (Case_6989586621679939426 xs xs)

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

Predicates

type family IsPrefixOf (a :: [a]) (a :: [a]) :: Bool where ...

Equations

IsPrefixOf '[] '[] = TrueSym0

IsPrefixOf '[] ((:) _ _) = TrueSym0

IsPrefixOf ((:) _ _) '[] = FalseSym0

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

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

type family IsSuffixOf (a :: [a]) (a :: [a]) :: Bool where ...

Equations

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

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

type family IsInfixOf (a :: [a]) (a :: [a]) :: Bool where ...

Equations

IsInfixOf needle haystack = Apply (Apply AnySym0 (Apply IsPrefixOfSym0 needle)) (Apply TailsSym0 haystack)

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

Searching lists

Searching by equality

type family Elem (arg :: a) (arg :: t a) :: Bool

Instances

type Elem (a1 :: k1) (a2 :: [k1])

Defined in Data.Singletons.Prelude.Foldable

type Elem (a1 :: k1) (a2 :: [k1])

type Elem (arg1 :: a) (arg2 :: Maybe a)

Defined in Data.Singletons.Prelude.Foldable

type Elem (arg1 :: a) (arg2 :: Maybe a)

type Elem (arg1 :: a) (arg2 :: Min a)

Defined in Data.Singletons.Prelude.Semigroup

type Elem (arg1 :: a) (arg2 :: Min a)

type Elem (arg1 :: a) (arg2 :: Max a)

Defined in Data.Singletons.Prelude.Semigroup

type Elem (arg1 :: a) (arg2 :: Max a)

type Elem (arg1 :: a) (arg2 :: First a)

Defined in Data.Singletons.Prelude.Semigroup

type Elem (arg1 :: a) (arg2 :: First a)

type Elem (arg1 :: a) (arg2 :: Last a)

Defined in Data.Singletons.Prelude.Semigroup

type Elem (arg1 :: a) (arg2 :: Last a)

type Elem (arg1 :: a) (arg2 :: Option a)

Defined in Data.Singletons.Prelude.Semigroup

type Elem (arg1 :: a) (arg2 :: Option a)

type Elem (a1 :: k1) (a2 :: Identity k1)

Defined in Data.Singletons.Prelude.Identity

type Elem (a1 :: k1) (a2 :: Identity k1)

type Elem (arg1 :: a) (arg2 :: First a)

Defined in Data.Singletons.Prelude.Foldable

type Elem (arg1 :: a) (arg2 :: First a)

type Elem (arg1 :: a) (arg2 :: Last a)

Defined in Data.Singletons.Prelude.Foldable

type Elem (arg1 :: a) (arg2 :: Last a)

type Elem (a1 :: k1) (a2 :: Dual k1)

Defined in Data.Singletons.Prelude.Foldable

type Elem (a1 :: k1) (a2 :: Dual k1)

type Elem (a1 :: k1) (a2 :: Sum k1)

Defined in Data.Singletons.Prelude.Foldable

type Elem (a1 :: k1) (a2 :: Sum k1)

type Elem (a1 :: k1) (a2 :: Product k1)

Defined in Data.Singletons.Prelude.Foldable

type Elem (a1 :: k1) (a2 :: Product k1)

type Elem (arg1 :: a) (arg2 :: NonEmpty a)

Defined in Data.Singletons.Prelude.Foldable

type Elem (arg1 :: a) (arg2 :: NonEmpty a)

type Elem (arg1 :: a1) (arg2 :: Either a2 a1)

Defined in Data.Singletons.Prelude.Foldable

type Elem (arg1 :: a1) (arg2 :: Either a2 a1)

type Elem (arg1 :: a1) (arg2 :: (a2, a1))

Defined in Data.Singletons.Prelude.Foldable

type Elem (arg1 :: a1) (arg2 :: (a2, a1))

type Elem (arg1 :: a1) (arg2 :: Arg a2 a1)

Defined in Data.Singletons.Prelude.Semigroup

type Elem (arg1 :: a1) (arg2 :: Arg a2 a1)

type Elem (arg1 :: a) (arg2 :: Const m a)

Defined in Data.Singletons.Prelude.Const

type Elem (arg1 :: a) (arg2 :: Const m a)

sElem :: forall a (t :: a) (t :: t a). (SFoldable t, SEq a) => Sing t -> Sing t -> Sing (Apply (Apply ElemSym0 t) t :: Bool)

type family NotElem (a :: a) (a :: t a) :: Bool where ...

Equations

NotElem x a_6989586621680438923 = Apply (Apply (Apply (.@#@$) NotSym0) (Apply ElemSym0 x)) a_6989586621680438923

sNotElem :: forall t a (t :: a) (t :: t a). (SFoldable t, SEq a) => Sing t -> Sing t -> Sing (Apply (Apply NotElemSym0 t) t :: Bool)

type family Lookup (a :: a) (a :: [(a, b)]) :: Maybe b where ...

Equations

Lookup _key '[] = NothingSym0

Lookup key ((:) '(x, y) xys) = Case_6989586621679938801 key x y xys (Let6989586621679938796Scrutinee_6989586621679930112Sym4 key x y xys)

sLookup :: forall a b (t :: a) (t :: [(a, b)]). SEq a => Sing t -> Sing t -> Sing (Apply (Apply LookupSym0 t) t :: Maybe b)

Searching with a predicate

type family Find (a :: (~>) a Bool) (a :: t a) :: Maybe a where ...

Equations

Find p y = Case_6989586621680438915 p y (Let6989586621680438898Scrutinee_6989586621680438785Sym2 p y)

sFind :: forall t a (t :: (~>) a Bool) (t :: t a). SFoldable t => Sing t -> Sing t -> Sing (Apply (Apply FindSym0 t) t :: Maybe a)

type family Filter (a :: (~>) a Bool) (a :: [a]) :: [a] where ...

Equations

Filter _p '[] = '[]

Filter p ((:) x xs) = Case_6989586621679939002 p x xs (Let6989586621679938998Scrutinee_6989586621679930078Sym3 p x xs)

sFilter :: forall a (t :: (~>) a Bool) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply FilterSym0 t) t :: [a])

type family Partition (a :: (~>) a Bool) (a :: [a]) :: ([a], [a]) where ...

Equations

Partition p xs = Apply (Apply (Apply FoldrSym0 (Apply SelectSym0 p)) (Apply (Apply Tuple2Sym0 '[]) '[])) xs

sPartition :: forall a (t :: (~>) a Bool) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply PartitionSym0 t) t :: ([a], [a]))

Indexing lists

type family (a :: [a]) !! (a :: Nat) :: a where ... infixl 9

Equations

'[] !! _ = Apply ErrorSym0 "Data.Singletons.List.!!: index too large"

((:) x xs) !! n = Case_6989586621679938719 x xs n (Let6989586621679938715Scrutinee_6989586621679930118Sym3 x xs n)

(%!!) :: forall a (t :: [a]) (t :: Nat). Sing t -> Sing t -> Sing (Apply (Apply (!!@#@$) t) t :: a) infixl 9

type family ElemIndex (a :: a) (a :: [a]) :: Maybe Nat where ...

Equations

ElemIndex x a_6989586621679939377 = Apply (Apply FindIndexSym0 (Apply (==@#@$) x)) a_6989586621679939377

sElemIndex :: forall a (t :: a) (t :: [a]). SEq a => Sing t -> Sing t -> Sing (Apply (Apply ElemIndexSym0 t) t :: Maybe Nat)

type family ElemIndices (a :: a) (a :: [a]) :: [Nat] where ...

Equations

ElemIndices x a_6989586621679939361 = Apply (Apply FindIndicesSym0 (Apply (==@#@$) x)) a_6989586621679939361

sElemIndices :: forall a (t :: a) (t :: [a]). SEq a => Sing t -> Sing t -> Sing (Apply (Apply ElemIndicesSym0 t) t :: [Nat])

type family FindIndex (a :: (~>) a Bool) (a :: [a]) :: Maybe Nat where ...

Equations

FindIndex p a_6989586621679939369 = Apply (Apply (Apply (.@#@$) ListToMaybeSym0) (Apply FindIndicesSym0 p)) a_6989586621679939369

sFindIndex :: forall a (t :: (~>) a Bool) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply FindIndexSym0 t) t :: Maybe Nat)

type family FindIndices (a :: (~>) a Bool) (a :: [a]) :: [Nat] where ...

Equations

FindIndices p xs = Apply (Apply MapSym0 SndSym0) (Apply (Apply FilterSym0 (Apply (Apply Lambda_6989586621679939346Sym0 p) xs)) (Apply (Apply ZipSym0 xs) (Apply (Apply (Let6989586621679939337BuildListSym2 p xs) (FromInteger 0)) xs)))

sFindIndices :: forall a (t :: (~>) a Bool) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply FindIndicesSym0 t) t :: [Nat])

Zipping and unzipping lists

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

Equations

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

Zip '[] '[] = '[]

Zip ((:) _ _) '[] = '[]

Zip '[] ((:) _ _) = '[]

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

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

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 '[] '[] ((:) _ _) = '[]

Zip3 '[] ((:) _ _) '[] = '[]

Zip3 '[] ((:) _ _) ((:) _ _) = '[]

Zip3 ((:) _ _) '[] '[] = '[]

Zip3 ((:) _ _) '[] ((:) _ _) = '[]

Zip3 ((:) _ _) ((:) _ _) '[] = '[]

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

type family Zip4 (a :: [a]) (a :: [b]) (a :: [c]) (a :: [d]) :: [(a, b, c, d)] where ...

Equations

Zip4 a_6989586621680068353 a_6989586621680068355 a_6989586621680068357 a_6989586621680068359 = Apply (Apply (Apply (Apply (Apply ZipWith4Sym0 Tuple4Sym0) a_6989586621680068353) a_6989586621680068355) a_6989586621680068357) a_6989586621680068359

type family Zip5 (a :: [a]) (a :: [b]) (a :: [c]) (a :: [d]) (a :: [e]) :: [(a, b, c, d, e)] where ...

Equations

Zip5 a_6989586621680068328 a_6989586621680068330 a_6989586621680068332 a_6989586621680068334 a_6989586621680068336 = Apply (Apply (Apply (Apply (Apply (Apply ZipWith5Sym0 Tuple5Sym0) a_6989586621680068328) a_6989586621680068330) a_6989586621680068332) a_6989586621680068334) a_6989586621680068336

type family Zip6 (a :: [a]) (a :: [b]) (a :: [c]) (a :: [d]) (a :: [e]) (a :: [f]) :: [(a, b, c, d, e, f)] where ...

Equations

Zip6 a_6989586621680068298 a_6989586621680068300 a_6989586621680068302 a_6989586621680068304 a_6989586621680068306 a_6989586621680068308 = Apply (Apply (Apply (Apply (Apply (Apply (Apply ZipWith6Sym0 Tuple6Sym0) a_6989586621680068298) a_6989586621680068300) a_6989586621680068302) a_6989586621680068304) a_6989586621680068306) a_6989586621680068308

type family Zip7 (a :: [a]) (a :: [b]) (a :: [c]) (a :: [d]) (a :: [e]) (a :: [f]) (a :: [g]) :: [(a, b, c, d, e, f, g)] where ...

Equations

Zip7 a_6989586621680068263 a_6989586621680068265 a_6989586621680068267 a_6989586621680068269 a_6989586621680068271 a_6989586621680068273 a_6989586621680068275 = Apply (Apply (Apply (Apply (Apply (Apply (Apply (Apply ZipWith7Sym0 Tuple7Sym0) a_6989586621680068263) a_6989586621680068265) a_6989586621680068267) a_6989586621680068269) a_6989586621680068271) a_6989586621680068273) a_6989586621680068275

type family ZipWith (a :: (~>) a ((~>) b c)) (a :: [a]) (a :: [b]) :: [c] where ...

Equations

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

ZipWith _ '[] '[] = '[]

ZipWith _ ((:) _ _) '[] = '[]

ZipWith _ '[] ((:) _ _) = '[]

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

type family ZipWith3 (a :: (~>) a ((~>) b ((~>) c d))) (a :: [a]) (a :: [b]) (a :: [c]) :: [d] where ...

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 _ '[] '[] '[] = '[]

ZipWith3 _ '[] '[] ((:) _ _) = '[]

ZipWith3 _ '[] ((:) _ _) '[] = '[]

ZipWith3 _ '[] ((:) _ _) ((:) _ _) = '[]

ZipWith3 _ ((:) _ _) '[] '[] = '[]

ZipWith3 _ ((:) _ _) '[] ((:) _ _) = '[]

ZipWith3 _ ((:) _ _) ((:) _ _) '[] = '[]

sZipWith3 :: forall a b c d (t :: (~>) a ((~>) b ((~>) c d))) (t :: [a]) (t :: [b]) (t :: [c]). Sing t -> Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply (Apply ZipWith3Sym0 t) t) t) t :: [d])

type family ZipWith4 (a :: (~>) a ((~>) b ((~>) c ((~>) d e)))) (a :: [a]) (a :: [b]) (a :: [c]) (a :: [d]) :: [e] where ...

Equations

ZipWith4 z ((:) a as) ((:) b bs) ((:) c cs) ((:) d ds) = Apply (Apply (:@#@$) (Apply (Apply (Apply (Apply z a) b) c) d)) (Apply (Apply (Apply (Apply (Apply ZipWith4Sym0 z) as) bs) cs) ds)

ZipWith4 _ _ _ _ _ = '[]

type family ZipWith5 (a :: (~>) a ((~>) b ((~>) c ((~>) d ((~>) e f))))) (a :: [a]) (a :: [b]) (a :: [c]) (a :: [d]) (a :: [e]) :: [f] where ...

Equations

ZipWith5 z ((:) a as) ((:) b bs) ((:) c cs) ((:) d ds) ((:) e es) = Apply (Apply (:@#@$) (Apply (Apply (Apply (Apply (Apply z a) b) c) d) e)) (Apply (Apply (Apply (Apply (Apply (Apply ZipWith5Sym0 z) as) bs) cs) ds) es)

ZipWith5 _ _ _ _ _ _ = '[]

type family ZipWith6 (a :: (~>) a ((~>) b ((~>) c ((~>) d ((~>) e ((~>) f g)))))) (a :: [a]) (a :: [b]) (a :: [c]) (a :: [d]) (a :: [e]) (a :: [f]) :: [g] where ...

Equations

ZipWith6 z ((:) a as) ((:) b bs) ((:) c cs) ((:) d ds) ((:) e es) ((:) f fs) = Apply (Apply (:@#@$) (Apply (Apply (Apply (Apply (Apply (Apply z a) b) c) d) e) f)) (Apply (Apply (Apply (Apply (Apply (Apply (Apply ZipWith6Sym0 z) as) bs) cs) ds) es) fs)

ZipWith6 _ _ _ _ _ _ _ = '[]

type family ZipWith7 (a :: (~>) a ((~>) b ((~>) c ((~>) d ((~>) e ((~>) f ((~>) g h))))))) (a :: [a]) (a :: [b]) (a :: [c]) (a :: [d]) (a :: [e]) (a :: [f]) (a :: [g]) :: [h] where ...

Equations

ZipWith7 z ((:) a as) ((:) b bs) ((:) c cs) ((:) d ds) ((:) e es) ((:) f fs) ((:) g gs) = Apply (Apply (:@#@$) (Apply (Apply (Apply (Apply (Apply (Apply (Apply z a) b) c) d) e) f) g)) (Apply (Apply (Apply (Apply (Apply (Apply (Apply (Apply ZipWith7Sym0 z) as) bs) cs) ds) es) fs) gs)

ZipWith7 _ _ _ _ _ _ _ _ = '[]

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

Equations

Unzip xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_6989586621679939269Sym0 xs)) (Apply (Apply Tuple2Sym0 '[]) '[])) xs

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

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

Equations

Unzip3 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_6989586621679939248Sym0 xs)) (Apply (Apply (Apply Tuple3Sym0 '[]) '[]) '[])) xs

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

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

Equations

Unzip4 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_6989586621679939225Sym0 xs)) (Apply (Apply (Apply (Apply Tuple4Sym0 '[]) '[]) '[]) '[])) xs

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

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

Equations

Unzip5 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_6989586621679939200Sym0 xs)) (Apply (Apply (Apply (Apply (Apply Tuple5Sym0 '[]) '[]) '[]) '[]) '[])) xs

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

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

Equations

Unzip6 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_6989586621679939173Sym0 xs)) (Apply (Apply (Apply (Apply (Apply (Apply Tuple6Sym0 '[]) '[]) '[]) '[]) '[]) '[])) xs

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

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

Equations

Unzip7 xs = Apply (Apply (Apply FoldrSym0 (Apply Lambda_6989586621679939144Sym0 xs)) (Apply (Apply (Apply (Apply (Apply (Apply (Apply Tuple7Sym0 '[]) '[]) '[]) '[]) '[]) '[]) '[])) xs

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

Special lists

Functions on Symbols

type family Unlines (a :: [Symbol]) :: Symbol where ...

Equations

Unlines '[] = ""

Unlines ((:) l ls) = Apply (Apply (<>@#@$) l) (Apply (Apply (<>@#@$) "\n") (Apply UnlinesSym0 ls))

sUnlines :: forall (t :: [Symbol]). Sing t -> Sing (Apply UnlinesSym0 t :: Symbol)

type family Unwords (a :: [Symbol]) :: Symbol where ...

Equations

Unwords '[] = ""

Unwords ((:) w ws) = Apply (Apply (<>@#@$) w) (Apply (Let6989586621679939130GoSym2 w ws) ws)

sUnwords :: forall (t :: [Symbol]). Sing t -> Sing (Apply UnwordsSym0 t :: Symbol)

"Set" operations

type family Nub (a :: [a]) :: [a] where ...

Equations

Nub l = Apply (Apply (Let6989586621679939398Nub'Sym1 l) l) '[]

sNub :: forall a (t :: [a]). SEq a => Sing t -> Sing (Apply NubSym0 t :: [a])

type family Delete (a :: a) (a :: [a]) :: [a] where ...

Equations

Delete a_6989586621679939106 a_6989586621679939108 = Apply (Apply (Apply DeleteBySym0 (==@#@$)) a_6989586621679939106) a_6989586621679939108

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

type family (a :: [a]) \\ (a :: [a]) :: [a] where ... infix 5

Equations

a_6989586621679939116 \\ a_6989586621679939118 = Apply (Apply (Apply FoldlSym0 (Apply FlipSym0 DeleteSym0)) a_6989586621679939116) a_6989586621679939118

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

type family Union (a :: [a]) (a :: [a]) :: [a] where ...

Equations

Union a_6989586621679939096 a_6989586621679939098 = Apply (Apply (Apply UnionBySym0 (==@#@$)) a_6989586621679939096) a_6989586621679939098

sUnion :: forall a (t :: [a]) (t :: [a]). SEq a => Sing t -> Sing t -> Sing (Apply (Apply UnionSym0 t) t :: [a])

type family Intersect (a :: [a]) (a :: [a]) :: [a] where ...

Equations

Intersect a_6989586621679939691 a_6989586621679939693 = Apply (Apply (Apply IntersectBySym0 (==@#@$)) a_6989586621679939691) a_6989586621679939693

sIntersect :: forall a (t :: [a]) (t :: [a]). SEq a => Sing t -> Sing t -> Sing (Apply (Apply IntersectSym0 t) t :: [a])

Ordered lists

type family Insert (a :: a) (a :: [a]) :: [a] where ...

Equations

Insert e ls = Apply (Apply (Apply InsertBySym0 CompareSym0) e) ls

sInsert :: forall a (t :: a) (t :: [a]). SOrd a => Sing t -> Sing t -> Sing (Apply (Apply InsertSym0 t) t :: [a])

type family Sort (a :: [a]) :: [a] where ...

Equations

Sort a_6989586621679939051 = Apply (Apply SortBySym0 CompareSym0) a_6989586621679939051

sSort :: forall a (t :: [a]). SOrd a => Sing t -> Sing (Apply SortSym0 t :: [a])

Generalized functions

The "By" operations

User-supplied equality (replacing an Eq context)

The predicate is assumed to define an equivalence.

type family NubBy (a :: (~>) a ((~>) a Bool)) (a :: [a]) :: [a] where ...

Equations

NubBy eq l = Apply (Apply (Let6989586621679938689NubBy'Sym2 eq l) l) '[]

sNubBy :: forall a (t :: (~>) a ((~>) a Bool)) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply NubBySym0 t) t :: [a])

type family DeleteBy (a :: (~>) a ((~>) a Bool)) (a :: a) (a :: [a]) :: [a] where ...

Equations

DeleteBy _ _ '[] = '[]

DeleteBy eq x ((:) y ys) = Case_6989586621679939071 eq x y ys (Let6989586621679939066Scrutinee_6989586621679930062Sym4 eq x y ys)

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

type family DeleteFirstsBy (a :: (~>) a ((~>) a Bool)) (a :: [a]) (a :: [a]) :: [a] where ...

Equations

DeleteFirstsBy eq a_6989586621679939080 a_6989586621679939082 = Apply (Apply (Apply FoldlSym0 (Apply FlipSym0 (Apply DeleteBySym0 eq))) a_6989586621679939080) a_6989586621679939082

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

type family UnionBy (a :: (~>) a ((~>) a Bool)) (a :: [a]) (a :: [a]) :: [a] where ...

Equations

UnionBy eq xs ys = Apply (Apply (++@#@$) xs) (Apply (Apply (Apply FoldlSym0 (Apply FlipSym0 (Apply DeleteBySym0 eq))) (Apply (Apply NubBySym0 eq) ys)) xs)

sUnionBy :: forall a (t :: (~>) a ((~>) a Bool)) (t :: [a]) (t :: [a]). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply UnionBySym0 t) t) t :: [a])

type family IntersectBy (a :: (~>) a ((~>) a Bool)) (a :: [a]) (a :: [a]) :: [a] where ...

Equations

IntersectBy _ '[] '[] = '[]

IntersectBy _ '[] ((:) _ _) = '[]

IntersectBy _ ((:) _ _) '[] = '[]

IntersectBy eq ((:) wild_6989586621679930082 wild_6989586621679930084) ((:) wild_6989586621679930086 wild_6989586621679930088) = Apply (Apply (>>=@#@$) (Let6989586621679939670XsSym5 eq wild_6989586621679930082 wild_6989586621679930084 wild_6989586621679930086 wild_6989586621679930088)) (Apply (Apply (Apply (Apply (Apply Lambda_6989586621679939681Sym0 eq) wild_6989586621679930082) wild_6989586621679930084) wild_6989586621679930086) wild_6989586621679930088)

sIntersectBy :: forall a (t :: (~>) a ((~>) a Bool)) (t :: [a]) (t :: [a]). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply IntersectBySym0 t) t) t :: [a])

type family GroupBy (a :: (~>) a ((~>) a Bool)) (a :: [a]) :: [[a]] where ...

Equations

GroupBy _ '[] = '[]

GroupBy eq ((:) x xs) = Apply (Apply (:@#@$) (Apply (Apply (:@#@$) x) (Let6989586621679938931YsSym3 eq x xs))) (Apply (Apply GroupBySym0 eq) (Let6989586621679938931ZsSym3 eq x xs))

sGroupBy :: forall a (t :: (~>) a ((~>) a Bool)) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply GroupBySym0 t) t :: [[a]])

User-supplied comparison (replacing an Ord context)

The function is assumed to define a total ordering.

type family SortBy (a :: (~>) a ((~>) a Ordering)) (a :: [a]) :: [a] where ...

Equations

SortBy cmp a_6989586621679939047 = Apply (Apply (Apply FoldrSym0 (Apply InsertBySym0 cmp)) '[]) a_6989586621679939047

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

type family InsertBy (a :: (~>) a ((~>) a Ordering)) (a :: a) (a :: [a]) :: [a] where ...

Equations

InsertBy _ x '[] = Apply (Apply (:@#@$) x) '[]

InsertBy cmp x ((:) y ys') = Case_6989586621679939034 cmp x y ys' (Let6989586621679939029Scrutinee_6989586621679930064Sym4 cmp x y ys')

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

type family MaximumBy (a :: (~>) a ((~>) a Ordering)) (a :: t a) :: a where ...

Equations

MaximumBy cmp a_6989586621680438956 = Apply (Apply Foldl1Sym0 (Let6989586621680438960Max'Sym2 cmp a_6989586621680438956)) a_6989586621680438956

sMaximumBy :: forall t a (t :: (~>) a ((~>) a Ordering)) (t :: t a). SFoldable t => Sing t -> Sing t -> Sing (Apply (Apply MaximumBySym0 t) t :: a)

type family MinimumBy (a :: (~>) a ((~>) a Ordering)) (a :: t a) :: a where ...

Equations

MinimumBy cmp a_6989586621680438931 = Apply (Apply Foldl1Sym0 (Let6989586621680438935Min'Sym2 cmp a_6989586621680438931)) a_6989586621680438931

sMinimumBy :: forall t a (t :: (~>) a ((~>) a Ordering)) (t :: t a). SFoldable t => Sing t -> Sing t -> Sing (Apply (Apply MinimumBySym0 t) t :: a)

The "generic" operations

The prefix `generic' indicates an overloaded function that is a generalized version of a Prelude function.

type family GenericLength (a :: [a]) :: i where ...

Equations

GenericLength '[] = FromInteger 0

GenericLength ((:) _ xs) = Apply (Apply (+@#@$) (FromInteger 1)) (Apply GenericLengthSym0 xs)

sGenericLength :: forall i a (t :: [a]). SNum i => Sing t -> Sing (Apply GenericLengthSym0 t :: i)

type family GenericTake (a :: i) (a :: [a]) :: [a] where ...

Equations

GenericTake a_6989586621680068153 a_6989586621680068155 = Apply (Apply TakeSym0 a_6989586621680068153) a_6989586621680068155

type family GenericDrop (a :: i) (a :: [a]) :: [a] where ...

Equations

GenericDrop a_6989586621680068143 a_6989586621680068145 = Apply (Apply DropSym0 a_6989586621680068143) a_6989586621680068145

type family GenericSplitAt (a :: i) (a :: [a]) :: ([a], [a]) where ...

Equations

GenericSplitAt a_6989586621680068133 a_6989586621680068135 = Apply (Apply SplitAtSym0 a_6989586621680068133) a_6989586621680068135

type family GenericIndex (a :: [a]) (a :: i) :: a where ...

Equations

GenericIndex a_6989586621680068123 a_6989586621680068125 = Apply (Apply (!!@#@$) a_6989586621680068123) a_6989586621680068125

type family GenericReplicate (a :: i) (a :: a) :: [a] where ...

Equations

GenericReplicate a_6989586621680068113 a_6989586621680068115 = Apply (Apply ReplicateSym0 a_6989586621680068113) a_6989586621680068115

Defunctionalization symbols

type NilSym0 = '[]

data (:@#@$) :: forall (a3530822107858468865 :: Type). (~>) a3530822107858468865 ((~>) [a3530822107858468865] [(a3530822107858468865 :: Type)]) infixr 5

Instances

SingI ((:@#@$) :: TyFun a ([a] ~> [a]) -> Type)

Defined in Data.Singletons.Prelude.Instances

Methods

sing :: Sing (:@#@$)

SuppressUnusedWarnings ((:@#@$) :: TyFun a3530822107858468865 ([a3530822107858468865] ~> [a3530822107858468865]) -> Type)

Defined in Data.Singletons.Prelude.Instances

Methods

suppressUnusedWarnings :: ()

type Apply ((:@#@$) :: TyFun a3530822107858468865 ([a3530822107858468865] ~> [a3530822107858468865]) -> Type) (t6989586621679291660 :: a3530822107858468865)

Defined in Data.Singletons.Prelude.Instances

type Apply ((:@#@$) :: TyFun a3530822107858468865 ([a3530822107858468865] ~> [a3530822107858468865]) -> Type) (t6989586621679291660 :: a3530822107858468865) = (:@#@$$) t6989586621679291660

data (:@#@$$) (t6989586621679291660 :: (a3530822107858468865 :: Type)) :: (~>) [a3530822107858468865] [(a3530822107858468865 :: Type)] infixr 5

Instances

SingI d => SingI ((:@#@$$) d :: TyFun [a] [a] -> Type)

Defined in Data.Singletons.Prelude.Instances

Methods

sing :: Sing ((:@#@$$) d)

SuppressUnusedWarnings ((:@#@$$) t6989586621679291660 :: TyFun [a3530822107858468865] [a3530822107858468865] -> Type)

Defined in Data.Singletons.Prelude.Instances

Methods

suppressUnusedWarnings :: ()

type Apply ((:@#@$$) t6989586621679291660 :: TyFun [a] [a] -> Type) (t6989586621679291661 :: [a])

Defined in Data.Singletons.Prelude.Instances

type Apply ((:@#@$$) t6989586621679291660 :: TyFun [a] [a] -> Type) (t6989586621679291661 :: [a]) = t6989586621679291660 ': t6989586621679291661

type (:@#@$$$) (t6989586621679291660 :: a3530822107858468865) (t6989586621679291661 :: [a3530822107858468865]) = (:) t6989586621679291660 t6989586621679291661

type (++@#@$$$) (a6989586621679511994 :: [a6989586621679511797]) (a6989586621679511995 :: [a6989586621679511797]) = (++) a6989586621679511994 a6989586621679511995

data (++@#@$$) (a6989586621679511994 :: [a6989586621679511797]) :: (~>) [a6989586621679511797] [a6989586621679511797] infixr 5

Instances

SingI d => SingI ((++@#@$$) d :: TyFun [a] [a] -> Type)

Defined in Data.Singletons.Prelude.Base

Methods

sing :: Sing ((++@#@$$) d)

SuppressUnusedWarnings ((++@#@$$) a6989586621679511994 :: TyFun [a6989586621679511797] [a6989586621679511797] -> Type)

Defined in Data.Singletons.Prelude.Base

Methods

suppressUnusedWarnings :: ()

type Apply ((++@#@$$) a6989586621679511994 :: TyFun [a] [a] -> Type) (a6989586621679511995 :: [a])

Defined in Data.Singletons.Prelude.Base

type Apply ((++@#@$$) a6989586621679511994 :: TyFun [a] [a] -> Type) (a6989586621679511995 :: [a]) = a6989586621679511994 ++ a6989586621679511995

data (++@#@$) :: forall a6989586621679511797. (~>) [a6989586621679511797] ((~>) [a6989586621679511797] [a6989586621679511797]) infixr 5

Instances

SingI ((++@#@$) :: TyFun [a] ([a] ~> [a]) -> Type)

Defined in Data.Singletons.Prelude.Base

Methods

sing :: Sing (++@#@$)

SuppressUnusedWarnings ((++@#@$) :: TyFun [a6989586621679511797] ([a6989586621679511797] ~> [a6989586621679511797]) -> Type)

Defined in Data.Singletons.Prelude.Base

Methods

suppressUnusedWarnings :: ()

type Apply ((++@#@$) :: TyFun [a6989586621679511797] ([a6989586621679511797] ~> [a6989586621679511797]) -> Type) (a6989586621679511994 :: [a6989586621679511797])

Defined in Data.Singletons.Prelude.Base

type Apply ((++@#@$) :: TyFun [a6989586621679511797] ([a6989586621679511797] ~> [a6989586621679511797]) -> Type) (a6989586621679511994 :: [a6989586621679511797]) = (++@#@$$) a6989586621679511994

data HeadSym0 :: forall a6989586621679929539. (~>) [a6989586621679929539] a6989586621679929539

Instances

SingI (HeadSym0 :: TyFun [a] a -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

sing :: Sing HeadSym0

SuppressUnusedWarnings (HeadSym0 :: TyFun [a6989586621679929539] a6989586621679929539 -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

suppressUnusedWarnings :: ()

type Apply (HeadSym0 :: TyFun [a] a -> Type) (a6989586621679940062 :: [a])

Defined in Data.Singletons.Prelude.List.Internal

type Apply (HeadSym0 :: TyFun [a] a -> Type) (a6989586621679940062 :: [a]) = Head a6989586621679940062

type HeadSym1 (a6989586621679940062 :: [a6989586621679929539]) = Head a6989586621679940062

data LastSym0 :: forall a6989586621679929538. (~>) [a6989586621679929538] a6989586621679929538

Instances

SingI (LastSym0 :: TyFun [a] a -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

sing :: Sing LastSym0

SuppressUnusedWarnings (LastSym0 :: TyFun [a6989586621679929538] a6989586621679929538 -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

suppressUnusedWarnings :: ()

type Apply (LastSym0 :: TyFun [a] a -> Type) (a6989586621679940057 :: [a])

Defined in Data.Singletons.Prelude.List.Internal

type Apply (LastSym0 :: TyFun [a] a -> Type) (a6989586621679940057 :: [a]) = Last a6989586621679940057

type LastSym1 (a6989586621679940057 :: [a6989586621679929538]) = Last a6989586621679940057

data TailSym0 :: forall a6989586621679929537. (~>) [a6989586621679929537] [a6989586621679929537]

Instances

SingI (TailSym0 :: TyFun [a] [a] -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

sing :: Sing TailSym0

SuppressUnusedWarnings (TailSym0 :: TyFun [a6989586621679929537] [a6989586621679929537] -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

suppressUnusedWarnings :: ()

type Apply (TailSym0 :: TyFun [a] [a] -> Type) (a6989586621679940054 :: [a])

Defined in Data.Singletons.Prelude.List.Internal

type Apply (TailSym0 :: TyFun [a] [a] -> Type) (a6989586621679940054 :: [a]) = Tail a6989586621679940054

type TailSym1 (a6989586621679940054 :: [a6989586621679929537]) = Tail a6989586621679940054

data InitSym0 :: forall a6989586621679929536. (~>) [a6989586621679929536] [a6989586621679929536]

Instances

SingI (InitSym0 :: TyFun [a] [a] -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

sing :: Sing InitSym0

SuppressUnusedWarnings (InitSym0 :: TyFun [a6989586621679929536] [a6989586621679929536] -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

suppressUnusedWarnings :: ()

type Apply (InitSym0 :: TyFun [a] [a] -> Type) (a6989586621679940040 :: [a])

Defined in Data.Singletons.Prelude.List.Internal

type Apply (InitSym0 :: TyFun [a] [a] -> Type) (a6989586621679940040 :: [a]) = Init a6989586621679940040

type InitSym1 (a6989586621679940040 :: [a6989586621679929536]) = Init a6989586621679940040

data NullSym0 :: forall a6989586621680438541 t6989586621680438526. (~>) (t6989586621680438526 a6989586621680438541) Bool

Instances

SFoldable t => SingI (NullSym0 :: TyFun (t a) Bool -> Type)

Defined in Data.Singletons.Prelude.Foldable

Methods

sing :: Sing NullSym0

SuppressUnusedWarnings (NullSym0 :: TyFun (t6989586621680438526 a6989586621680438541) Bool -> Type)

Defined in Data.Singletons.Prelude.Foldable

Methods

suppressUnusedWarnings :: ()

type Apply (NullSym0 :: TyFun (t a) Bool -> Type) (arg6989586621680439189 :: t a)

Defined in Data.Singletons.Prelude.Foldable

type Apply (NullSym0 :: TyFun (t a) Bool -> Type) (arg6989586621680439189 :: t a) = Null arg6989586621680439189

type NullSym1 (arg6989586621680439189 :: t6989586621680438526 a6989586621680438541) = Null arg6989586621680439189

data LengthSym0 :: forall a6989586621680438542 t6989586621680438526. (~>) (t6989586621680438526 a6989586621680438542) Nat

Instances

SFoldable t => SingI (LengthSym0 :: TyFun (t a) Nat -> Type)

Defined in Data.Singletons.Prelude.Foldable

Methods

sing :: Sing LengthSym0

SuppressUnusedWarnings (LengthSym0 :: TyFun (t6989586621680438526 a6989586621680438542) Nat -> Type)

Defined in Data.Singletons.Prelude.Foldable

Methods

suppressUnusedWarnings :: ()

type Apply (LengthSym0 :: TyFun (t a) Nat -> Type) (arg6989586621680439191 :: t a)

Defined in Data.Singletons.Prelude.Foldable

type Apply (LengthSym0 :: TyFun (t a) Nat -> Type) (arg6989586621680439191 :: t a) = Length arg6989586621680439191

type LengthSym1 (arg6989586621680439191 :: t6989586621680438526 a6989586621680438542) = Length arg6989586621680439191

data MapSym0 :: forall a6989586621679511798 b6989586621679511799. (~>) ((~>) a6989586621679511798 b6989586621679511799) ((~>) [a6989586621679511798] [b6989586621679511799])

Instances

SingI (MapSym0 :: TyFun (a ~> b) ([a] ~> [b]) -> Type)

Defined in Data.Singletons.Prelude.Base

Methods

sing :: Sing MapSym0

SuppressUnusedWarnings (MapSym0 :: TyFun (a6989586621679511798 ~> b6989586621679511799) ([a6989586621679511798] ~> [b6989586621679511799]) -> Type)

Defined in Data.Singletons.Prelude.Base

Methods

suppressUnusedWarnings :: ()

type Apply (MapSym0 :: TyFun (a6989586621679511798 ~> b6989586621679511799) ([a6989586621679511798] ~> [b6989586621679511799]) -> Type) (a6989586621679512002 :: a6989586621679511798 ~> b6989586621679511799)

Defined in Data.Singletons.Prelude.Base

type Apply (MapSym0 :: TyFun (a6989586621679511798 ~> b6989586621679511799) ([a6989586621679511798] ~> [b6989586621679511799]) -> Type) (a6989586621679512002 :: a6989586621679511798 ~> b6989586621679511799) = MapSym1 a6989586621679512002

data MapSym1 (a6989586621679512002 :: (~>) a6989586621679511798 b6989586621679511799) :: (~>) [a6989586621679511798] [b6989586621679511799]

Instances

SingI d => SingI (MapSym1 d :: TyFun [a] [b] -> Type)

Defined in Data.Singletons.Prelude.Base

Methods

sing :: Sing (MapSym1 d)

SuppressUnusedWarnings (MapSym1 a6989586621679512002 :: TyFun [a6989586621679511798] [b6989586621679511799] -> Type)

Defined in Data.Singletons.Prelude.Base

Methods

suppressUnusedWarnings :: ()

type Apply (MapSym1 a6989586621679512002 :: TyFun [a] [b] -> Type) (a6989586621679512003 :: [a])

Defined in Data.Singletons.Prelude.Base

type Apply (MapSym1 a6989586621679512002 :: TyFun [a] [b] -> Type) (a6989586621679512003 :: [a]) = Map a6989586621679512002 a6989586621679512003

type MapSym2 (a6989586621679512002 :: (~>) a6989586621679511798 b6989586621679511799) (a6989586621679512003 :: [a6989586621679511798]) = Map a6989586621679512002 a6989586621679512003

data ReverseSym0 :: forall a6989586621679929534. (~>) [a6989586621679929534] [a6989586621679929534]

Instances

SingI (ReverseSym0 :: TyFun [a] [a] -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

sing :: Sing ReverseSym0

SuppressUnusedWarnings (ReverseSym0 :: TyFun [a6989586621679929534] [a6989586621679929534] -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

suppressUnusedWarnings :: ()

type Apply (ReverseSym0 :: TyFun [a] [a] -> Type) (a6989586621679939993 :: [a])

Defined in Data.Singletons.Prelude.List.Internal

type Apply (ReverseSym0 :: TyFun [a] [a] -> Type) (a6989586621679939993 :: [a]) = Reverse a6989586621679939993

type ReverseSym1 (a6989586621679939993 :: [a6989586621679929534]) = Reverse a6989586621679939993

data IntersperseSym0 :: forall a6989586621679929533. (~>) a6989586621679929533 ((~>) [a6989586621679929533] [a6989586621679929533])

Instances

SingI (IntersperseSym0 :: TyFun a ([a] ~> [a]) -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

sing :: Sing IntersperseSym0

SuppressUnusedWarnings (IntersperseSym0 :: TyFun a6989586621679929533 ([a6989586621679929533] ~> [a6989586621679929533]) -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

suppressUnusedWarnings :: ()

type Apply (IntersperseSym0 :: TyFun a6989586621679929533 ([a6989586621679929533] ~> [a6989586621679929533]) -> Type) (a6989586621679939980 :: a6989586621679929533)

Defined in Data.Singletons.Prelude.List.Internal

type Apply (IntersperseSym0 :: TyFun a6989586621679929533 ([a6989586621679929533] ~> [a6989586621679929533]) -> Type) (a6989586621679939980 :: a6989586621679929533) = IntersperseSym1 a6989586621679939980

data IntersperseSym1 (a6989586621679939980 :: a6989586621679929533) :: (~>) [a6989586621679929533] [a6989586621679929533]

Instances

SingI d => SingI (IntersperseSym1 d :: TyFun [a] [a] -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

sing :: Sing (IntersperseSym1 d)

SuppressUnusedWarnings (IntersperseSym1 a6989586621679939980 :: TyFun [a6989586621679929533] [a6989586621679929533] -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

suppressUnusedWarnings :: ()

type Apply (IntersperseSym1 a6989586621679939980 :: TyFun [a] [a] -> Type) (a6989586621679939981 :: [a])

Defined in Data.Singletons.Prelude.List.Internal

type Apply (IntersperseSym1 a6989586621679939980 :: TyFun [a] [a] -> Type) (a6989586621679939981 :: [a]) = Intersperse a6989586621679939980 a6989586621679939981

type IntersperseSym2 (a6989586621679939980 :: a6989586621679929533) (a6989586621679939981 :: [a6989586621679929533]) = Intersperse a6989586621679939980 a6989586621679939981

data IntercalateSym0 :: forall a6989586621679929532. (~>) [a6989586621679929532] ((~>) [[a6989586621679929532]] [a6989586621679929532])

Instances

SingI (IntercalateSym0 :: TyFun [a] ([[a]] ~> [a]) -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

sing :: Sing IntercalateSym0

SuppressUnusedWarnings (IntercalateSym0 :: TyFun [a6989586621679929532] ([[a6989586621679929532]] ~> [a6989586621679929532]) -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

suppressUnusedWarnings :: ()

type Apply (IntercalateSym0 :: TyFun [a6989586621679929532] ([[a6989586621679929532]] ~> [a6989586621679929532]) -> Type) (a6989586621679939987 :: [a6989586621679929532])

Defined in Data.Singletons.Prelude.List.Internal

type Apply (IntercalateSym0 :: TyFun [a6989586621679929532] ([[a6989586621679929532]] ~> [a6989586621679929532]) -> Type) (a6989586621679939987 :: [a6989586621679929532]) = IntercalateSym1 a6989586621679939987

data IntercalateSym1 (a6989586621679939987 :: [a6989586621679929532]) :: (~>) [[a6989586621679929532]] [a6989586621679929532]

Instances

SingI d => SingI (IntercalateSym1 d :: TyFun [[a]] [a] -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

sing :: Sing (IntercalateSym1 d)

SuppressUnusedWarnings (IntercalateSym1 a6989586621679939987 :: TyFun [[a6989586621679929532]] [a6989586621679929532] -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

suppressUnusedWarnings :: ()

type Apply (IntercalateSym1 a6989586621679939987 :: TyFun [[a]] [a] -> Type) (a6989586621679939988 :: [[a]])

Defined in Data.Singletons.Prelude.List.Internal

type Apply (IntercalateSym1 a6989586621679939987 :: TyFun [[a]] [a] -> Type) (a6989586621679939988 :: [[a]]) = Intercalate a6989586621679939987 a6989586621679939988

type IntercalateSym2 (a6989586621679939987 :: [a6989586621679929532]) (a6989586621679939988 :: [[a6989586621679929532]]) = Intercalate a6989586621679939987 a6989586621679939988

data TransposeSym0 :: forall a6989586621679929419. (~>) [[a6989586621679929419]] [[a6989586621679929419]]

Instances

SingI (TransposeSym0 :: TyFun [[a]] [[a]] -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

sing :: Sing TransposeSym0

SuppressUnusedWarnings (TransposeSym0 :: TyFun [[a6989586621679929419]] [[a6989586621679929419]] -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

suppressUnusedWarnings :: ()

type Apply (TransposeSym0 :: TyFun [[a]] [[a]] -> Type) (a6989586621679940065 :: [[a]])

Defined in Data.Singletons.Prelude.List.Internal

type Apply (TransposeSym0 :: TyFun [[a]] [[a]] -> Type) (a6989586621679940065 :: [[a]]) = Transpose a6989586621679940065

type TransposeSym1 (a6989586621679940065 :: [[a6989586621679929419]]) = Transpose a6989586621679940065

data SubsequencesSym0 :: forall a6989586621679929531. (~>) [a6989586621679929531] [[a6989586621679929531]]

Instances

SingI (SubsequencesSym0 :: TyFun [a] [[a]] -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

sing :: Sing SubsequencesSym0

SuppressUnusedWarnings (SubsequencesSym0 :: TyFun [a6989586621679929531] [[a6989586621679929531]] -> Type)

Defined in Data.Singletons.Prelude.List.Internal

Methods

suppressUnusedWarnings :: ()

type Apply (SubsequencesSym0 :: TyFun [a] [[a]] -> Type) (a6989586621679939977 :: [a])

Defined in Data.Singletons.Prelude.List.Internal

type Apply (SubsequencesSym0 :: TyFun [a] [[a]] -> Type) (a6989586621679939977 :: [a]) = Subsequences a6989586621679939977

type SubsequencesSym1 (a6989586621679939977 :: [a6989586621679929531]) = Subsequences a6989586621679939977

data