Safe Haskell | None |
---|---|

Language | Haskell2010 |

## Synopsis

- type family All (p :: k -> Constraint) (as :: [k]) :: Constraint where ...
- type family If (b :: Bool) (l :: k) (r :: k) :: k where ...
- type family Foldr (c :: k -> l -> l) (n :: l) (as :: [k]) :: l where ...
- type family Foldr' (c :: Function k (Function l l -> Type) -> Type) (n :: l) (as :: [k]) :: l where ...
- type family Map (f :: Function k l -> Type) (as :: [k]) :: [l] where ...
- data ConsMap0 :: (Function k l -> Type) -> Function k (Function [l] [l] -> Type) -> Type
- data ConsMap1 :: (Function k l -> Type) -> k -> Function [l] [l] -> Type
- type family Constant (b :: l) (as :: [k]) :: [l] where ...
- type Arrows (as :: [Type]) (r :: Type) = Foldr (->) r as
- type Products (as :: [Type]) = Foldr (,) () as
- type family IsBase (t :: Type) :: Bool where ...
- type family Domains (t :: Type) :: [Type] where ...
- type family Domains' (t :: Type) :: [Type] where ...
- type family CoDomain (t :: Type) :: Type where ...
- type family CoDomain' (t :: Type) :: Type where ...
- class Currying as b where
- data Function :: Type -> Type -> Type
- data Constant0 :: Function a (Function b a -> Type) -> Type
- data Constant1 :: Type -> Function b a -> Type
- type family Apply (t :: Function k l -> Type) (u :: k) :: l

# Documentation

type family All (p :: k -> Constraint) (as :: [k]) :: Constraint where ... Source #

`All p as`

ensures that the constraint `p`

is satisfied by
all the `types`

in `as`

.
(Types is between scare-quotes here because the code is
actually kind polymorphic)

type family Foldr' (c :: Function k (Function l l -> Type) -> Type) (n :: l) (as :: [k]) :: l where ... Source #

Version of `Foldr`

taking a defunctionalised argument so
that we can use partially applied functions.

type Arrows (as :: [Type]) (r :: Type) = Foldr (->) r as Source #

`Arrows [a1,..,an] r`

corresponds to `a1 -> .. -> an -> r`

| `Products [a1,..,an]`

corresponds to `(a1, (..,( an, ())..))`

type family IsBase (t :: Type) :: Bool where ... Source #

`IsBase t`

is `'True`

whenever `t`

is *not* a function space.

type family Domains (t :: Type) :: [Type] where ... Source #

Using `IsBase`

we can define notions of `Domains`

and `CoDomains`

which *reduce* under positive information `IsBase t ~ 'True`

even
though the shape of `t`

is not formally exposed

class Currying as b where Source #

`Currying as b`

witnesses the isomorphism between `Arrows as b`

and `Products as -> b`

. It is defined as a type class rather
than by recursion on a singleton for `as`

so all of that these
conversions are inlined at compile time for concrete arguments.

uncurrys :: Proxy as -> Proxy b -> Arrows as b -> Products as -> b Source #

currys :: Proxy as -> Proxy b -> (Products as -> b) -> Arrows as b Source #

type family Apply (t :: Function k l -> Type) (u :: k) :: l Source #

## Instances

type Apply (Constant1 a :: Function k Type -> Type) (b :: k) Source # | |

type Apply (ConsMap1 f a2 :: Function [a1] [a1] -> Type) (tl :: [a1]) Source # | |

type Apply (Constant0 :: Function Type (Function b Type -> Type) -> Type) (a :: Type) Source # | |

type Apply (ConsMap0 f :: Function k (Function [l] [l] -> Type) -> Type) (a :: k) Source # | |