singletons-2.3.1: A framework for generating singleton types

Copyright(C) 2016 Richard Eisenberg
LicenseBSD-style (see LICENSE)
MaintainerRichard Eisenberg (rae@cs.brynmawr.edu)
Stabilityexperimental
Portabilitynon-portable
Safe HaskellNone
LanguageHaskell2010

Data.Promotion.Prelude.Function

Contents

Description

Defines promoted functions from 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.

Synopsis

Prelude re-exports

type family Id (a :: a) :: a where ... #

Equations

Id x = x 

type family Const (a :: a) (a :: b) :: a where ... #

Equations

Const x _z_6989586621679289889 = x 

type family ((a :: TyFun b c -> Type) :. (a :: TyFun a b -> Type)) (a :: a) :: c where ... infixr 9 #

Equations

(f :. g) a_6989586621679289852 = Apply (Apply (Apply (Apply Lambda_6989586621679289857Sym0 f) g) a_6989586621679289852) a_6989586621679289852 

type family Flip (a :: TyFun a (TyFun b c -> Type) -> Type) (a :: b) (a :: a) :: c where ... #

Equations

Flip f x y = Apply (Apply f y) x 

type family (f :: TyFun a b -> *) $ (x :: a) :: b infixr 0 #

Instances

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

Other combinators

type family (a :: a) :& (a :: TyFun a b -> Type) :: b where ... #

Equations

x :& f = Apply f x 

type family On (a :: TyFun b (TyFun b c -> Type) -> Type) (a :: TyFun a b -> Type) (a :: a) (a :: a) :: c where ... #

Equations

On ty f a_6989586621679301879 a_6989586621679301881 = Apply (Apply (Apply (Apply (Apply (Apply Lambda_6989586621679301887Sym0 ty) f) a_6989586621679301879) a_6989586621679301881) a_6989586621679301879) a_6989586621679301881 

Defunctionalization symbols

data IdSym0 (l :: TyFun a6989586621679289770 a6989586621679289770) #

Instances

SuppressUnusedWarnings (TyFun a6989586621679289770 a6989586621679289770 -> *) (IdSym0 a6989586621679289770) # 

Methods

suppressUnusedWarnings :: Proxy (IdSym0 a6989586621679289770) t -> () #

type Apply a a (IdSym0 a) l # 
type Apply a a (IdSym0 a) l = Id a l

type IdSym1 (t :: a6989586621679289770) = Id t #

data ConstSym0 (l :: TyFun a6989586621679289768 (TyFun b6989586621679289769 a6989586621679289768 -> Type)) #

Instances

SuppressUnusedWarnings (TyFun a6989586621679289768 (TyFun b6989586621679289769 a6989586621679289768 -> Type) -> *) (ConstSym0 b6989586621679289769 a6989586621679289768) # 

Methods

suppressUnusedWarnings :: Proxy (ConstSym0 b6989586621679289769 a6989586621679289768) t -> () #

type Apply a6989586621679289768 (TyFun b6989586621679289769 a6989586621679289768 -> Type) (ConstSym0 b6989586621679289769 a6989586621679289768) l # 
type Apply a6989586621679289768 (TyFun b6989586621679289769 a6989586621679289768 -> Type) (ConstSym0 b6989586621679289769 a6989586621679289768) l = ConstSym1 b6989586621679289769 a6989586621679289768 l

data ConstSym1 (l :: a6989586621679289768) (l :: TyFun b6989586621679289769 a6989586621679289768) #

Instances

SuppressUnusedWarnings (a6989586621679289768 -> TyFun b6989586621679289769 a6989586621679289768 -> *) (ConstSym1 b6989586621679289769 a6989586621679289768) # 

Methods

suppressUnusedWarnings :: Proxy (ConstSym1 b6989586621679289769 a6989586621679289768) t -> () #

type Apply b a (ConstSym1 b a l1) l2 # 
type Apply b a (ConstSym1 b a l1) l2 = Const b a l1 l2

type ConstSym2 (t :: a6989586621679289768) (t :: b6989586621679289769) = Const t t #

data (:.$) (l :: TyFun (TyFun b6989586621679289765 c6989586621679289766 -> Type) (TyFun (TyFun a6989586621679289767 b6989586621679289765 -> Type) (TyFun a6989586621679289767 c6989586621679289766 -> Type) -> Type)) #

Instances

SuppressUnusedWarnings (TyFun (TyFun b6989586621679289765 c6989586621679289766 -> Type) (TyFun (TyFun a6989586621679289767 b6989586621679289765 -> Type) (TyFun a6989586621679289767 c6989586621679289766 -> Type) -> Type) -> *) ((:.$) b6989586621679289765 a6989586621679289767 c6989586621679289766) # 

Methods

suppressUnusedWarnings :: Proxy ((b6989586621679289765 :.$ a6989586621679289767) c6989586621679289766) t -> () #

type Apply (TyFun b6989586621679289765 c6989586621679289766 -> Type) (TyFun (TyFun a6989586621679289767 b6989586621679289765 -> Type) (TyFun a6989586621679289767 c6989586621679289766 -> Type) -> Type) ((:.$) b6989586621679289765 a6989586621679289767 c6989586621679289766) l # 
type Apply (TyFun b6989586621679289765 c6989586621679289766 -> Type) (TyFun (TyFun a6989586621679289767 b6989586621679289765 -> Type) (TyFun a6989586621679289767 c6989586621679289766 -> Type) -> Type) ((:.$) b6989586621679289765 a6989586621679289767 c6989586621679289766) l = (:.$$) b6989586621679289765 a6989586621679289767 c6989586621679289766 l

data (l :: TyFun b6989586621679289765 c6989586621679289766 -> Type) :.$$ (l :: TyFun (TyFun a6989586621679289767 b6989586621679289765 -> Type) (TyFun a6989586621679289767 c6989586621679289766 -> Type)) #

Instances

SuppressUnusedWarnings ((TyFun b6989586621679289765 c6989586621679289766 -> Type) -> TyFun (TyFun a6989586621679289767 b6989586621679289765 -> Type) (TyFun a6989586621679289767 c6989586621679289766 -> Type) -> *) ((:.$$) b6989586621679289765 a6989586621679289767 c6989586621679289766) # 

Methods

suppressUnusedWarnings :: Proxy ((b6989586621679289765 :.$$ a6989586621679289767) c6989586621679289766) t -> () #

type Apply (TyFun a6989586621679289767 b6989586621679289765 -> Type) (TyFun a6989586621679289767 c6989586621679289766 -> Type) ((:.$$) b6989586621679289765 a6989586621679289767 c6989586621679289766 l1) l2 # 
type Apply (TyFun a6989586621679289767 b6989586621679289765 -> Type) (TyFun a6989586621679289767 c6989586621679289766 -> Type) ((:.$$) b6989586621679289765 a6989586621679289767 c6989586621679289766 l1) l2 = (:.$$$) b6989586621679289765 a6989586621679289767 c6989586621679289766 l1 l2

data ((l :: TyFun b6989586621679289765 c6989586621679289766 -> Type) :.$$$ (l :: TyFun a6989586621679289767 b6989586621679289765 -> Type)) (l :: TyFun a6989586621679289767 c6989586621679289766) #

Instances

SuppressUnusedWarnings ((TyFun b6989586621679289765 c6989586621679289766 -> Type) -> (TyFun a6989586621679289767 b6989586621679289765 -> Type) -> TyFun a6989586621679289767 c6989586621679289766 -> *) ((:.$$$) b6989586621679289765 a6989586621679289767 c6989586621679289766) # 

Methods

suppressUnusedWarnings :: Proxy ((b6989586621679289765 :.$$$ a6989586621679289767) c6989586621679289766) t -> () #

type Apply a c ((:.$$$) b a c l1 l2) l3 # 
type Apply a c ((:.$$$) b a c l1 l2) l3 = (:.) b a c l1 l2 l3

type (:.$$$$) (t :: TyFun b6989586621679289765 c6989586621679289766 -> Type) (t :: TyFun a6989586621679289767 b6989586621679289765 -> Type) (t :: a6989586621679289767) = (:.) t t t #

data FlipSym0 (l :: TyFun (TyFun a6989586621679289762 (TyFun b6989586621679289763 c6989586621679289764 -> Type) -> Type) (TyFun b6989586621679289763 (TyFun a6989586621679289762 c6989586621679289764 -> Type) -> Type)) #

Instances

SuppressUnusedWarnings (TyFun (TyFun a6989586621679289762 (TyFun b6989586621679289763 c6989586621679289764 -> Type) -> Type) (TyFun b6989586621679289763 (TyFun a6989586621679289762 c6989586621679289764 -> Type) -> Type) -> *) (FlipSym0 b6989586621679289763 a6989586621679289762 c6989586621679289764) # 

Methods

suppressUnusedWarnings :: Proxy (FlipSym0 b6989586621679289763 a6989586621679289762 c6989586621679289764) t -> () #

type Apply (TyFun a6989586621679289762 (TyFun b6989586621679289763 c6989586621679289764 -> Type) -> Type) (TyFun b6989586621679289763 (TyFun a6989586621679289762 c6989586621679289764 -> Type) -> Type) (FlipSym0 b6989586621679289763 a6989586621679289762 c6989586621679289764) l # 
type Apply (TyFun a6989586621679289762 (TyFun b6989586621679289763 c6989586621679289764 -> Type) -> Type) (TyFun b6989586621679289763 (TyFun a6989586621679289762 c6989586621679289764 -> Type) -> Type) (FlipSym0 b6989586621679289763 a6989586621679289762 c6989586621679289764) l = FlipSym1 b6989586621679289763 a6989586621679289762 c6989586621679289764 l

data FlipSym1 (l :: TyFun a6989586621679289762 (TyFun b6989586621679289763 c6989586621679289764 -> Type) -> Type) (l :: TyFun b6989586621679289763 (TyFun a6989586621679289762 c6989586621679289764 -> Type)) #

Instances

SuppressUnusedWarnings ((TyFun a6989586621679289762 (TyFun b6989586621679289763 c6989586621679289764 -> Type) -> Type) -> TyFun b6989586621679289763 (TyFun a6989586621679289762 c6989586621679289764 -> Type) -> *) (FlipSym1 b6989586621679289763 a6989586621679289762 c6989586621679289764) # 

Methods

suppressUnusedWarnings :: Proxy (FlipSym1 b6989586621679289763 a6989586621679289762 c6989586621679289764) t -> () #

type Apply b6989586621679289763 (TyFun a6989586621679289762 c6989586621679289764 -> Type) (FlipSym1 b6989586621679289763 a6989586621679289762 c6989586621679289764 l1) l2 # 
type Apply b6989586621679289763 (TyFun a6989586621679289762 c6989586621679289764 -> Type) (FlipSym1 b6989586621679289763 a6989586621679289762 c6989586621679289764 l1) l2 = FlipSym2 b6989586621679289763 a6989586621679289762 c6989586621679289764 l1 l2

data FlipSym2 (l :: TyFun a6989586621679289762 (TyFun b6989586621679289763 c6989586621679289764 -> Type) -> Type) (l :: b6989586621679289763) (l :: TyFun a6989586621679289762 c6989586621679289764) #

Instances

SuppressUnusedWarnings ((TyFun a6989586621679289762 (TyFun b6989586621679289763 c6989586621679289764 -> Type) -> Type) -> b6989586621679289763 -> TyFun a6989586621679289762 c6989586621679289764 -> *) (FlipSym2 b6989586621679289763 a6989586621679289762 c6989586621679289764) # 

Methods

suppressUnusedWarnings :: Proxy (FlipSym2 b6989586621679289763 a6989586621679289762 c6989586621679289764) t -> () #

type Apply a c (FlipSym2 b a c l1 l2) l3 # 
type Apply a c (FlipSym2 b a c l1 l2) l3 = Flip b a c l1 l2 l3

type FlipSym3 (t :: TyFun a6989586621679289762 (TyFun b6989586621679289763 c6989586621679289764 -> Type) -> Type) (t :: b6989586621679289763) (t :: a6989586621679289762) = Flip t t t #

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

Instances

type Apply (TyFun a b -> *) (TyFun a b -> *) (($$) a b) arg # 
type Apply (TyFun a b -> *) (TyFun a b -> *) (($$) a b) arg = ($$$) a b arg

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

Instances

type Apply a k (($$$) a k f) arg # 
type Apply a k (($$$) a k f) arg = ($$$$) a k f arg

type ($$$$) a b = ($) a b #

data (:&$) (l :: TyFun a6989586621679301833 (TyFun (TyFun a6989586621679301833 b6989586621679301834 -> Type) b6989586621679301834 -> Type)) #

Instances

SuppressUnusedWarnings (TyFun a6989586621679301833 (TyFun (TyFun a6989586621679301833 b6989586621679301834 -> Type) b6989586621679301834 -> Type) -> *) ((:&$) a6989586621679301833 b6989586621679301834) # 

Methods

suppressUnusedWarnings :: Proxy (a6989586621679301833 :&$ b6989586621679301834) t -> () #

type Apply a6989586621679301833 (TyFun (TyFun a6989586621679301833 b6989586621679301834 -> Type) b6989586621679301834 -> Type) ((:&$) a6989586621679301833 b6989586621679301834) l # 
type Apply a6989586621679301833 (TyFun (TyFun a6989586621679301833 b6989586621679301834 -> Type) b6989586621679301834 -> Type) ((:&$) a6989586621679301833 b6989586621679301834) l = (:&$$) a6989586621679301833 b6989586621679301834 l

data (l :: a6989586621679301833) :&$$ (l :: TyFun (TyFun a6989586621679301833 b6989586621679301834 -> Type) b6989586621679301834) #

Instances

SuppressUnusedWarnings (a6989586621679301833 -> TyFun (TyFun a6989586621679301833 b6989586621679301834 -> Type) b6989586621679301834 -> *) ((:&$$) a6989586621679301833 b6989586621679301834) # 

Methods

suppressUnusedWarnings :: Proxy (a6989586621679301833 :&$$ b6989586621679301834) t -> () #

type Apply (TyFun a b -> Type) b ((:&$$) a b l1) l2 # 
type Apply (TyFun a b -> Type) b ((:&$$) a b l1) l2 = (:&) a b l1 l2

type (:&$$$) (t :: a6989586621679301833) (t :: TyFun a6989586621679301833 b6989586621679301834 -> Type) = (:&) t t #

data OnSym0 (l :: TyFun (TyFun b6989586621679301835 (TyFun b6989586621679301835 c6989586621679301836 -> Type) -> Type) (TyFun (TyFun a6989586621679301837 b6989586621679301835 -> Type) (TyFun a6989586621679301837 (TyFun a6989586621679301837 c6989586621679301836 -> Type) -> Type) -> Type)) #

Instances

SuppressUnusedWarnings (TyFun (TyFun b6989586621679301835 (TyFun b6989586621679301835 c6989586621679301836 -> Type) -> Type) (TyFun (TyFun a6989586621679301837 b6989586621679301835 -> Type) (TyFun a6989586621679301837 (TyFun a6989586621679301837 c6989586621679301836 -> Type) -> Type) -> Type) -> *) (OnSym0 b6989586621679301835 a6989586621679301837 c6989586621679301836) # 

Methods

suppressUnusedWarnings :: Proxy (OnSym0 b6989586621679301835 a6989586621679301837 c6989586621679301836) t -> () #

type Apply (TyFun b6989586621679301835 (TyFun b6989586621679301835 c6989586621679301836 -> Type) -> Type) (TyFun (TyFun a6989586621679301837 b6989586621679301835 -> Type) (TyFun a6989586621679301837 (TyFun a6989586621679301837 c6989586621679301836 -> Type) -> Type) -> Type) (OnSym0 b6989586621679301835 a6989586621679301837 c6989586621679301836) l # 
type Apply (TyFun b6989586621679301835 (TyFun b6989586621679301835 c6989586621679301836 -> Type) -> Type) (TyFun (TyFun a6989586621679301837 b6989586621679301835 -> Type) (TyFun a6989586621679301837 (TyFun a6989586621679301837 c6989586621679301836 -> Type) -> Type) -> Type) (OnSym0 b6989586621679301835 a6989586621679301837 c6989586621679301836) l = OnSym1 b6989586621679301835 a6989586621679301837 c6989586621679301836 l

data OnSym1 (l :: TyFun b6989586621679301835 (TyFun b6989586621679301835 c6989586621679301836 -> Type) -> Type) (l :: TyFun (TyFun a6989586621679301837 b6989586621679301835 -> Type) (TyFun a6989586621679301837 (TyFun a6989586621679301837 c6989586621679301836 -> Type) -> Type)) #

Instances

SuppressUnusedWarnings ((TyFun b6989586621679301835 (TyFun b6989586621679301835 c6989586621679301836 -> Type) -> Type) -> TyFun (TyFun a6989586621679301837 b6989586621679301835 -> Type) (TyFun a6989586621679301837 (TyFun a6989586621679301837 c6989586621679301836 -> Type) -> Type) -> *) (OnSym1 b6989586621679301835 a6989586621679301837 c6989586621679301836) # 

Methods

suppressUnusedWarnings :: Proxy (OnSym1 b6989586621679301835 a6989586621679301837 c6989586621679301836) t -> () #

type Apply (TyFun a6989586621679301837 b6989586621679301835 -> Type) (TyFun a6989586621679301837 (TyFun a6989586621679301837 c6989586621679301836 -> Type) -> Type) (OnSym1 b6989586621679301835 a6989586621679301837 c6989586621679301836 l1) l2 # 
type Apply (TyFun a6989586621679301837 b6989586621679301835 -> Type) (TyFun a6989586621679301837 (TyFun a6989586621679301837 c6989586621679301836 -> Type) -> Type) (OnSym1 b6989586621679301835 a6989586621679301837 c6989586621679301836 l1) l2 = OnSym2 b6989586621679301835 a6989586621679301837 c6989586621679301836 l1 l2

data OnSym2 (l :: TyFun b6989586621679301835 (TyFun b6989586621679301835 c6989586621679301836 -> Type) -> Type) (l :: TyFun a6989586621679301837 b6989586621679301835 -> Type) (l :: TyFun a6989586621679301837 (TyFun a6989586621679301837 c6989586621679301836 -> Type)) #

Instances

SuppressUnusedWarnings ((TyFun b6989586621679301835 (TyFun b6989586621679301835 c6989586621679301836 -> Type) -> Type) -> (TyFun a6989586621679301837 b6989586621679301835 -> Type) -> TyFun a6989586621679301837 (TyFun a6989586621679301837 c6989586621679301836 -> Type) -> *) (OnSym2 b6989586621679301835 a6989586621679301837 c6989586621679301836) # 

Methods

suppressUnusedWarnings :: Proxy (OnSym2 b6989586621679301835 a6989586621679301837 c6989586621679301836) t -> () #

type Apply a6989586621679301837 (TyFun a6989586621679301837 c6989586621679301836 -> Type) (OnSym2 b6989586621679301835 a6989586621679301837 c6989586621679301836 l1 l2) l3 # 
type Apply a6989586621679301837 (TyFun a6989586621679301837 c6989586621679301836 -> Type) (OnSym2 b6989586621679301835 a6989586621679301837 c6989586621679301836 l1 l2) l3 = OnSym3 b6989586621679301835 a6989586621679301837 c6989586621679301836 l1 l2 l3

data OnSym3 (l :: TyFun b6989586621679301835 (TyFun b6989586621679301835 c6989586621679301836 -> Type) -> Type) (l :: TyFun a6989586621679301837 b6989586621679301835 -> Type) (l :: a6989586621679301837) (l :: TyFun a6989586621679301837 c6989586621679301836) #

Instances

SuppressUnusedWarnings ((TyFun b6989586621679301835 (TyFun b6989586621679301835 c6989586621679301836 -> Type) -> Type) -> (TyFun a6989586621679301837 b6989586621679301835 -> Type) -> a6989586621679301837 -> TyFun a6989586621679301837 c6989586621679301836 -> *) (OnSym3 b6989586621679301835 a6989586621679301837 c6989586621679301836) # 

Methods

suppressUnusedWarnings :: Proxy (OnSym3 b6989586621679301835 a6989586621679301837 c6989586621679301836) t -> () #

type Apply a c (OnSym3 b a c l1 l2 l3) l4 # 
type Apply a c (OnSym3 b a c l1 l2 l3) l4 = On b a c l1 l2 l3 l4

type OnSym4 (t :: TyFun b6989586621679301835 (TyFun b6989586621679301835 c6989586621679301836 -> Type) -> Type) (t :: TyFun a6989586621679301837 b6989586621679301835 -> Type) (t :: a6989586621679301837) (t :: a6989586621679301837) = On t t t t #