Copyright	(C) 2014 Jan Stolarek
License	BSD-style (see LICENSE)
Maintainer	Jan Stolarek (jan.stolarek@p.lodz.pl)
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.Singletons.Prelude.Base

Contents

Basic functions
Defunctionalization symbols

Description

Implements singletonized versions of functions from GHC.Base module.

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.Tuple. Also, please excuse the apparent repeated variable names. This is due to an interaction between Template Haskell and Haddock.

Synopsis

Basic functions

type family Foldr a a a :: b Source

Equations

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

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

type family Map a a :: [] b Source

Equations

Map z [] = []
Map f ((:) x xs) = Apply (Apply (:$) (Apply f x)) (Apply (Apply MapSym0 f) xs)

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

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

Equations

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

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

type Otherwise = (TrueSym0 :: Bool) Source

sOtherwise :: Sing OtherwiseSym0 Source

type family Id a :: a Source

Equations

Id x = x

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

type family Const a a :: a Source

Equations

Const x z = x

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

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

Equations

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

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

type family f $ x :: b Source

Instances

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

type family f $! x :: b Source

Instances

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

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

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

type family Flip a a a :: c Source

Equations

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

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

type family AsTypeOf a a :: a Source

Equations

AsTypeOf a_1627849051 a_1627849053 = Apply (Apply ConstSym0 a_1627849051) a_1627849053

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

type family Seq a a :: b Source

Equations

Seq z x = x

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

Defunctionalization symbols

data FoldrSym0 l Source

Instances

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

data FoldrSym1 l l Source

Instances

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

data FoldrSym2 l l l Source

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> ) -> ) -> k -> TyFun [k] k -> *) (FoldrSym2 k k)
type Apply k [k1] (FoldrSym2 k k1 l1 l2) l0 = FoldrSym3 k k1 l1 l2 l0

type FoldrSym3 t t t = Foldr t t t Source

data MapSym0 l Source

Instances

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

data MapSym1 l l Source

Instances

SuppressUnusedWarnings ((TyFun k k -> ) -> TyFun [k] [k] -> ) (MapSym1 k k)
type Apply [k1] [k] (MapSym1 k k1 l1) l0 = MapSym2 k k1 l1 l0

type MapSym2 t t = Map t t Source

data (:++$) l Source

Instances

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

data l :++$$ l Source

Instances

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

type OtherwiseSym0 = Otherwise Source

data IdSym0 l Source

Instances

SuppressUnusedWarnings (TyFun k k -> *) (IdSym0 k)
type Apply k k (IdSym0 k) l0 = IdSym1 k l0

type IdSym1 t = Id t Source

data ConstSym0 l Source

Instances

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

data ConstSym1 l l Source

Instances

SuppressUnusedWarnings (k -> TyFun k k -> *) (ConstSym1 k k)
type Apply k1 k (ConstSym1 k1 k l1) l0 = ConstSym2 k1 k l1 l0

type ConstSym2 t t = Const t t Source

data (:.$) l Source

Instances

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

data l :.$$ l Source

Instances

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

data (l :.$$$ l) l Source

Instances

SuppressUnusedWarnings ((TyFun k k -> ) -> (TyFun k k -> ) -> TyFun k k -> *) ((:.$$$) k k k)
type Apply k1 k ((:.$$$) k1 k2 k l1 l2) l0

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

Instances

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

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

Instances

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

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

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

Instances

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

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

Instances

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

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

data FlipSym0 l Source

Instances

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

data FlipSym1 l l Source

Instances

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

data FlipSym2 l l l Source

Instances

SuppressUnusedWarnings ((TyFun k (TyFun k k -> ) -> ) -> k -> TyFun k k -> *) (FlipSym2 k k k)
type Apply k1 k (FlipSym2 k1 k k2 l1 l2) l0

data AsTypeOfSym0 l Source

Instances

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

data AsTypeOfSym1 l l Source

Instances

SuppressUnusedWarnings (k -> TyFun k k -> *) (AsTypeOfSym1 k)
type Apply k k (AsTypeOfSym1 k l1) l0 = AsTypeOfSym2 k l1 l0

type AsTypeOfSym2 t t = AsTypeOf t t Source

data SeqSym0 l Source

Instances

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

data SeqSym1 l l Source

Instances

SuppressUnusedWarnings (k -> TyFun k k -> *) (SeqSym1 k k)
type Apply k k (SeqSym1 k k1 l1) l0 = SeqSym2 k k1 l1 l0

type SeqSym2 t t = Seq t t Source