| Copyright | (C) 2016 Richard Eisenberg |
|---|---|
| License | BSD-style (see LICENSE) |
| Maintainer | Richard Eisenberg (rae@cs.brynmawr.edu) |
| Stability | experimental |
| Portability | non-portable |
| Safe Haskell | None |
| Language | Haskell2010 |
Data.Singletons.Prelude.Function
Contents
Description
Defines singleton versions of the definitions in Data.Function.
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.Function. Also, please excuse
the apparent repeated variable names. This is due to an interaction
between Template Haskell and Haddock.
- type family Id (a :: a) :: a where ...
- sId :: forall (t :: a). Sing t -> Sing (Apply IdSym0 t :: a)
- type family Const (a :: a) (a :: b) :: a where ...
- sConst :: forall (t :: a) (t :: b). Sing t -> Sing t -> Sing (Apply (Apply ConstSym0 t) t :: a)
- type family ((a :: TyFun b c -> Type) :. (a :: TyFun a b -> Type)) (a :: a) :: c where ...
- (%:.) :: forall (t :: TyFun b c -> Type) (t :: TyFun a b -> Type) (t :: a). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply (:.$) t) t) t :: c)
- type family Flip (a :: TyFun a (TyFun b c -> Type) -> Type) (a :: b) (a :: a) :: c where ...
- sFlip :: forall (t :: TyFun a (TyFun b c -> Type) -> Type) (t :: b) (t :: a). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply FlipSym0 t) t) t :: c)
- type family (f :: TyFun a b -> *) $ (x :: a) :: b
- (%$) :: forall (f :: TyFun a b -> *) (x :: a). Sing f -> Sing x -> Sing ((($$) @@ f) @@ x)
- type family (a :: a) :& (a :: TyFun a b -> Type) :: b where ...
- (%:&) :: forall (t :: a) (t :: TyFun a b -> Type). Sing t -> Sing t -> Sing (Apply (Apply (:&$) t) t :: b)
- type family On (a :: TyFun b (TyFun b c -> Type) -> Type) (a :: TyFun a b -> Type) (a :: a) (a :: a) :: c where ...
- sOn :: forall (t :: TyFun b (TyFun b c -> Type) -> Type) (t :: TyFun a b -> Type) (t :: a) (t :: a). Sing t -> Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply (Apply OnSym0 t) t) t) t :: c)
- data IdSym0 (l :: TyFun a6989586621679281044 a6989586621679281044)
- type IdSym1 (t :: a6989586621679281044) = Id t
- data ConstSym0 (l :: TyFun a6989586621679281042 (TyFun b6989586621679281043 a6989586621679281042 -> Type))
- data ConstSym1 (l :: a6989586621679281042) (l :: TyFun b6989586621679281043 a6989586621679281042)
- type ConstSym2 (t :: a6989586621679281042) (t :: b6989586621679281043) = Const t t
- data (:.$) (l :: TyFun (TyFun b6989586621679281039 c6989586621679281040 -> Type) (TyFun (TyFun a6989586621679281041 b6989586621679281039 -> Type) (TyFun a6989586621679281041 c6989586621679281040 -> Type) -> Type))
- data (l :: TyFun b6989586621679281039 c6989586621679281040 -> Type) :.$$ (l :: TyFun (TyFun a6989586621679281041 b6989586621679281039 -> Type) (TyFun a6989586621679281041 c6989586621679281040 -> Type))
- data ((l :: TyFun b6989586621679281039 c6989586621679281040 -> Type) :.$$$ (l :: TyFun a6989586621679281041 b6989586621679281039 -> Type)) (l :: TyFun a6989586621679281041 c6989586621679281040)
- type (:.$$$$) (t :: TyFun b6989586621679281039 c6989586621679281040 -> Type) (t :: TyFun a6989586621679281041 b6989586621679281039 -> Type) (t :: a6989586621679281041) = (:.) t t t
- data FlipSym0 (l :: TyFun (TyFun a6989586621679281036 (TyFun b6989586621679281037 c6989586621679281038 -> Type) -> Type) (TyFun b6989586621679281037 (TyFun a6989586621679281036 c6989586621679281038 -> Type) -> Type))
- data FlipSym1 (l :: TyFun a6989586621679281036 (TyFun b6989586621679281037 c6989586621679281038 -> Type) -> Type) (l :: TyFun b6989586621679281037 (TyFun a6989586621679281036 c6989586621679281038 -> Type))
- data FlipSym2 (l :: TyFun a6989586621679281036 (TyFun b6989586621679281037 c6989586621679281038 -> Type) -> Type) (l :: b6989586621679281037) (l :: TyFun a6989586621679281036 c6989586621679281038)
- type FlipSym3 (t :: TyFun a6989586621679281036 (TyFun b6989586621679281037 c6989586621679281038 -> Type) -> Type) (t :: b6989586621679281037) (t :: a6989586621679281036) = Flip t t t
- data ($$) :: TyFun (TyFun a b -> *) (TyFun a b -> *) -> *
- data ($$$) :: (TyFun a b -> *) -> TyFun a b -> *
- type ($$$$) a b = ($) a b
- data (:&$) (l :: TyFun a6989586621679292901 (TyFun (TyFun a6989586621679292901 b6989586621679292902 -> Type) b6989586621679292902 -> Type))
- data (l :: a6989586621679292901) :&$$ (l :: TyFun (TyFun a6989586621679292901 b6989586621679292902 -> Type) b6989586621679292902)
- type (:&$$$) (t :: a6989586621679292901) (t :: TyFun a6989586621679292901 b6989586621679292902 -> Type) = (:&) t t
- data OnSym0 (l :: TyFun (TyFun b6989586621679292903 (TyFun b6989586621679292903 c6989586621679292904 -> Type) -> Type) (TyFun (TyFun a6989586621679292905 b6989586621679292903 -> Type) (TyFun a6989586621679292905 (TyFun a6989586621679292905 c6989586621679292904 -> Type) -> Type) -> Type))
- data OnSym1 (l :: TyFun b6989586621679292903 (TyFun b6989586621679292903 c6989586621679292904 -> Type) -> Type) (l :: TyFun (TyFun a6989586621679292905 b6989586621679292903 -> Type) (TyFun a6989586621679292905 (TyFun a6989586621679292905 c6989586621679292904 -> Type) -> Type))
- data OnSym2 (l :: TyFun b6989586621679292903 (TyFun b6989586621679292903 c6989586621679292904 -> Type) -> Type) (l :: TyFun a6989586621679292905 b6989586621679292903 -> Type) (l :: TyFun a6989586621679292905 (TyFun a6989586621679292905 c6989586621679292904 -> Type))
- data OnSym3 (l :: TyFun b6989586621679292903 (TyFun b6989586621679292903 c6989586621679292904 -> Type) -> Type) (l :: TyFun a6989586621679292905 b6989586621679292903 -> Type) (l :: a6989586621679292905) (l :: TyFun a6989586621679292905 c6989586621679292904)
- type OnSym4 (t :: TyFun b6989586621679292903 (TyFun b6989586621679292903 c6989586621679292904 -> Type) -> Type) (t :: TyFun a6989586621679292905 b6989586621679292903 -> Type) (t :: a6989586621679292905) (t :: a6989586621679292905) = On t t t t
Prelude re-exports
type family Const (a :: a) (a :: b) :: a where ... Source #
Equations
| Const x _z_6989586621679281163 = x |
sConst :: forall (t :: a) (t :: b). Sing t -> Sing t -> Sing (Apply (Apply ConstSym0 t) t :: a) Source #
type family ((a :: TyFun b c -> Type) :. (a :: TyFun a b -> Type)) (a :: a) :: c where ... infixr 9 Source #
(%:.) :: forall (t :: TyFun b c -> Type) (t :: TyFun a b -> Type) (t :: a). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply (:.$) t) t) t :: c) infixr 9 Source #
type family Flip (a :: TyFun a (TyFun b c -> Type) -> Type) (a :: b) (a :: a) :: c where ... Source #
sFlip :: forall (t :: TyFun a (TyFun b c -> Type) -> Type) (t :: b) (t :: a). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply FlipSym0 t) t) t :: c) Source #
(%$) :: forall (f :: TyFun a b -> *) (x :: a). Sing f -> Sing x -> Sing ((($$) @@ f) @@ x) infixr 0 Source #
Other combinators
(%:&) :: forall (t :: a) (t :: TyFun a b -> Type). Sing t -> Sing t -> Sing (Apply (Apply (:&$) t) t :: b) Source #
type family On (a :: TyFun b (TyFun b c -> Type) -> Type) (a :: TyFun a b -> Type) (a :: a) (a :: a) :: c where ... Source #
sOn :: forall (t :: TyFun b (TyFun b c -> Type) -> Type) (t :: TyFun a b -> Type) (t :: a) (t :: a). Sing t -> Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply (Apply OnSym0 t) t) t) t :: c) Source #
Defunctionalization symbols
data ConstSym0 (l :: TyFun a6989586621679281042 (TyFun b6989586621679281043 a6989586621679281042 -> Type)) Source #
Instances
| SuppressUnusedWarnings (TyFun a6989586621679281042 (TyFun b6989586621679281043 a6989586621679281042 -> Type) -> *) (ConstSym0 b6989586621679281043 a6989586621679281042) Source # | |
| type Apply a6989586621679281042 (TyFun b6989586621679281043 a6989586621679281042 -> Type) (ConstSym0 b6989586621679281043 a6989586621679281042) l Source # | |
data ConstSym1 (l :: a6989586621679281042) (l :: TyFun b6989586621679281043 a6989586621679281042) Source #
data (:.$) (l :: TyFun (TyFun b6989586621679281039 c6989586621679281040 -> Type) (TyFun (TyFun a6989586621679281041 b6989586621679281039 -> Type) (TyFun a6989586621679281041 c6989586621679281040 -> Type) -> Type)) Source #
Instances
| SuppressUnusedWarnings (TyFun (TyFun b6989586621679281039 c6989586621679281040 -> Type) (TyFun (TyFun a6989586621679281041 b6989586621679281039 -> Type) (TyFun a6989586621679281041 c6989586621679281040 -> Type) -> Type) -> *) ((:.$) b6989586621679281039 a6989586621679281041 c6989586621679281040) Source # | |
| type Apply (TyFun b6989586621679281039 c6989586621679281040 -> Type) (TyFun (TyFun a6989586621679281041 b6989586621679281039 -> Type) (TyFun a6989586621679281041 c6989586621679281040 -> Type) -> Type) ((:.$) b6989586621679281039 a6989586621679281041 c6989586621679281040) l Source # | |
data (l :: TyFun b6989586621679281039 c6989586621679281040 -> Type) :.$$ (l :: TyFun (TyFun a6989586621679281041 b6989586621679281039 -> Type) (TyFun a6989586621679281041 c6989586621679281040 -> Type)) Source #
Instances
| SuppressUnusedWarnings ((TyFun b6989586621679281039 c6989586621679281040 -> Type) -> TyFun (TyFun a6989586621679281041 b6989586621679281039 -> Type) (TyFun a6989586621679281041 c6989586621679281040 -> Type) -> *) ((:.$$) b6989586621679281039 a6989586621679281041 c6989586621679281040) Source # | |
| type Apply (TyFun a6989586621679281041 b6989586621679281039 -> Type) (TyFun a6989586621679281041 c6989586621679281040 -> Type) ((:.$$) b6989586621679281039 a6989586621679281041 c6989586621679281040 l1) l2 Source # | |
data ((l :: TyFun b6989586621679281039 c6989586621679281040 -> Type) :.$$$ (l :: TyFun a6989586621679281041 b6989586621679281039 -> Type)) (l :: TyFun a6989586621679281041 c6989586621679281040) Source #
Instances
| SuppressUnusedWarnings ((TyFun b6989586621679281039 c6989586621679281040 -> Type) -> (TyFun a6989586621679281041 b6989586621679281039 -> Type) -> TyFun a6989586621679281041 c6989586621679281040 -> *) ((:.$$$) b6989586621679281039 a6989586621679281041 c6989586621679281040) Source # | |
| type Apply a c ((:.$$$) b a c l1 l2) l3 Source # | |
type (:.$$$$) (t :: TyFun b6989586621679281039 c6989586621679281040 -> Type) (t :: TyFun a6989586621679281041 b6989586621679281039 -> Type) (t :: a6989586621679281041) = (:.) t t t Source #
data FlipSym0 (l :: TyFun (TyFun a6989586621679281036 (TyFun b6989586621679281037 c6989586621679281038 -> Type) -> Type) (TyFun b6989586621679281037 (TyFun a6989586621679281036 c6989586621679281038 -> Type) -> Type)) Source #
Instances
| SuppressUnusedWarnings (TyFun (TyFun a6989586621679281036 (TyFun b6989586621679281037 c6989586621679281038 -> Type) -> Type) (TyFun b6989586621679281037 (TyFun a6989586621679281036 c6989586621679281038 -> Type) -> Type) -> *) (FlipSym0 b6989586621679281037 a6989586621679281036 c6989586621679281038) Source # | |
| type Apply (TyFun a6989586621679281036 (TyFun b6989586621679281037 c6989586621679281038 -> Type) -> Type) (TyFun b6989586621679281037 (TyFun a6989586621679281036 c6989586621679281038 -> Type) -> Type) (FlipSym0 b6989586621679281037 a6989586621679281036 c6989586621679281038) l Source # | |
data FlipSym1 (l :: TyFun a6989586621679281036 (TyFun b6989586621679281037 c6989586621679281038 -> Type) -> Type) (l :: TyFun b6989586621679281037 (TyFun a6989586621679281036 c6989586621679281038 -> Type)) Source #
Instances
| SuppressUnusedWarnings ((TyFun a6989586621679281036 (TyFun b6989586621679281037 c6989586621679281038 -> Type) -> Type) -> TyFun b6989586621679281037 (TyFun a6989586621679281036 c6989586621679281038 -> Type) -> *) (FlipSym1 b6989586621679281037 a6989586621679281036 c6989586621679281038) Source # | |
| type Apply b6989586621679281037 (TyFun a6989586621679281036 c6989586621679281038 -> Type) (FlipSym1 b6989586621679281037 a6989586621679281036 c6989586621679281038 l1) l2 Source # | |
data FlipSym2 (l :: TyFun a6989586621679281036 (TyFun b6989586621679281037 c6989586621679281038 -> Type) -> Type) (l :: b6989586621679281037) (l :: TyFun a6989586621679281036 c6989586621679281038) Source #
Instances
| SuppressUnusedWarnings ((TyFun a6989586621679281036 (TyFun b6989586621679281037 c6989586621679281038 -> Type) -> Type) -> b6989586621679281037 -> TyFun a6989586621679281036 c6989586621679281038 -> *) (FlipSym2 b6989586621679281037 a6989586621679281036 c6989586621679281038) Source # | |
| type Apply a c (FlipSym2 b a c l1 l2) l3 Source # | |
type FlipSym3 (t :: TyFun a6989586621679281036 (TyFun b6989586621679281037 c6989586621679281038 -> Type) -> Type) (t :: b6989586621679281037) (t :: a6989586621679281036) = Flip t t t Source #
data (:&$) (l :: TyFun a6989586621679292901 (TyFun (TyFun a6989586621679292901 b6989586621679292902 -> Type) b6989586621679292902 -> Type)) Source #
Instances
| SuppressUnusedWarnings (TyFun a6989586621679292901 (TyFun (TyFun a6989586621679292901 b6989586621679292902 -> Type) b6989586621679292902 -> Type) -> *) ((:&$) a6989586621679292901 b6989586621679292902) Source # | |
| type Apply a6989586621679292901 (TyFun (TyFun a6989586621679292901 b6989586621679292902 -> Type) b6989586621679292902 -> Type) ((:&$) a6989586621679292901 b6989586621679292902) l Source # | |
data (l :: a6989586621679292901) :&$$ (l :: TyFun (TyFun a6989586621679292901 b6989586621679292902 -> Type) b6989586621679292902) Source #
type (:&$$$) (t :: a6989586621679292901) (t :: TyFun a6989586621679292901 b6989586621679292902 -> Type) = (:&) t t Source #
data OnSym0 (l :: TyFun (TyFun b6989586621679292903 (TyFun b6989586621679292903 c6989586621679292904 -> Type) -> Type) (TyFun (TyFun a6989586621679292905 b6989586621679292903 -> Type) (TyFun a6989586621679292905 (TyFun a6989586621679292905 c6989586621679292904 -> Type) -> Type) -> Type)) Source #
Instances
| SuppressUnusedWarnings (TyFun (TyFun b6989586621679292903 (TyFun b6989586621679292903 c6989586621679292904 -> Type) -> Type) (TyFun (TyFun a6989586621679292905 b6989586621679292903 -> Type) (TyFun a6989586621679292905 (TyFun a6989586621679292905 c6989586621679292904 -> Type) -> Type) -> Type) -> *) (OnSym0 b6989586621679292903 a6989586621679292905 c6989586621679292904) Source # | |
| type Apply (TyFun b6989586621679292903 (TyFun b6989586621679292903 c6989586621679292904 -> Type) -> Type) (TyFun (TyFun a6989586621679292905 b6989586621679292903 -> Type) (TyFun a6989586621679292905 (TyFun a6989586621679292905 c6989586621679292904 -> Type) -> Type) -> Type) (OnSym0 b6989586621679292903 a6989586621679292905 c6989586621679292904) l Source # | |
data OnSym1 (l :: TyFun b6989586621679292903 (TyFun b6989586621679292903 c6989586621679292904 -> Type) -> Type) (l :: TyFun (TyFun a6989586621679292905 b6989586621679292903 -> Type) (TyFun a6989586621679292905 (TyFun a6989586621679292905 c6989586621679292904 -> Type) -> Type)) Source #
Instances
| SuppressUnusedWarnings ((TyFun b6989586621679292903 (TyFun b6989586621679292903 c6989586621679292904 -> Type) -> Type) -> TyFun (TyFun a6989586621679292905 b6989586621679292903 -> Type) (TyFun a6989586621679292905 (TyFun a6989586621679292905 c6989586621679292904 -> Type) -> Type) -> *) (OnSym1 b6989586621679292903 a6989586621679292905 c6989586621679292904) Source # | |
| type Apply (TyFun a6989586621679292905 b6989586621679292903 -> Type) (TyFun a6989586621679292905 (TyFun a6989586621679292905 c6989586621679292904 -> Type) -> Type) (OnSym1 b6989586621679292903 a6989586621679292905 c6989586621679292904 l1) l2 Source # | |
data OnSym2 (l :: TyFun b6989586621679292903 (TyFun b6989586621679292903 c6989586621679292904 -> Type) -> Type) (l :: TyFun a6989586621679292905 b6989586621679292903 -> Type) (l :: TyFun a6989586621679292905 (TyFun a6989586621679292905 c6989586621679292904 -> Type)) Source #
Instances
| SuppressUnusedWarnings ((TyFun b6989586621679292903 (TyFun b6989586621679292903 c6989586621679292904 -> Type) -> Type) -> (TyFun a6989586621679292905 b6989586621679292903 -> Type) -> TyFun a6989586621679292905 (TyFun a6989586621679292905 c6989586621679292904 -> Type) -> *) (OnSym2 b6989586621679292903 a6989586621679292905 c6989586621679292904) Source # | |
| type Apply a6989586621679292905 (TyFun a6989586621679292905 c6989586621679292904 -> Type) (OnSym2 b6989586621679292903 a6989586621679292905 c6989586621679292904 l1 l2) l3 Source # | |
data OnSym3 (l :: TyFun b6989586621679292903 (TyFun b6989586621679292903 c6989586621679292904 -> Type) -> Type) (l :: TyFun a6989586621679292905 b6989586621679292903 -> Type) (l :: a6989586621679292905) (l :: TyFun a6989586621679292905 c6989586621679292904) Source #
Instances
| SuppressUnusedWarnings ((TyFun b6989586621679292903 (TyFun b6989586621679292903 c6989586621679292904 -> Type) -> Type) -> (TyFun a6989586621679292905 b6989586621679292903 -> Type) -> a6989586621679292905 -> TyFun a6989586621679292905 c6989586621679292904 -> *) (OnSym3 b6989586621679292903 a6989586621679292905 c6989586621679292904) Source # | |
| type Apply a c (OnSym3 b a c l1 l2 l3) l4 Source # | |