Safe Haskell	None
Language	Haskell2010

Test.TypeSpec.Internal.Apply

Contents

Tuple construction
List construction
Convert data types to Partially applicable type functions
Execute an action and map a pure function over the result.
Flip Type Functions
Type Function composition
Type-Level const
Defunctionalization

Description

Useful abstractions for type level programming using. This reimplements parts of the singletons library, which is just too heavy of a dependency to carry around, when only three small types are used of it.

Synopsis

type family (ma :: monad a) >>= (f :: a ~> (monad b :: Type)) :: monad b
type (>>) ma mb = ma >>= Const' mb
type family (f :: m (a ~> b)) <*> (ma :: m a) :: m b where ...
data Pair'' :: a ~> (b ~> (a, b))
data Pair' :: a -> b ~> (a, b)
data Cons'' :: a ~> ([a] ~> [a])
data Cons' :: a -> [a] ~> [a]
data TyCon1 :: (a -> b) -> a ~> b
data TyCon2 :: (a -> b -> c) -> a ~> (b ~> c)
data (<$>$$) :: (a ~> b) ~> (m a ~> m b)
data (<$>$) :: (a ~> b) -> m a ~> m b
type family (f :: a ~> b) <$> (ma :: m a) :: m b
data Flip' :: (a ~> (b ~> c)) ~> (b ~> (a ~> c))
data Flip :: (a ~> (b ~> c)) -> b ~> (a ~> c)
data Flip_ :: (a ~> (b ~> c)) -> b -> a ~> c
type family Flip__ (f :: a ~> (b ~> c)) (y :: b) (x :: a) :: c where ...
data Compose'' :: (b ~> c) ~> ((a ~> b) ~> (a ~> c))
data Compose' :: (b ~> c) -> (a ~> b) ~> (a ~> c)
data Compose :: (b ~> c) -> (a ~> b) -> a ~> c
type family Compose_ (f :: b ~> c) (g :: a ~> b) (x :: a) :: c where ...
type family Const (a :: t) (b :: t') :: t where ...
data Const' :: a -> b ~> a
data Const'' :: a ~> (b ~> a)
data TyFun :: Type -> Type -> Type
type (~>) a b = TyFun a b -> Type
type family Apply (f :: a ~> b) (x :: a) :: b

Documentation

type family (ma :: monad a) >>= (f :: a ~> (monad b :: Type)) :: monad b Source #

Bind to actions.

Instances

type (Left b2 :: Either a2 a1) >>= (f :: a1 ~> Either a2 b1) Source #
Instance details Defined in Test.TypeSpec.Internal.Either type (Left b2 :: Either a2 a1) >>= (f :: a1 ~> Either a2 b1) = (Left b2 :: Either a2 b1)
type (Right a3 :: Either a2 a1) >>= (f :: a1 ~> Either a2 b) Source #
Instance details Defined in Test.TypeSpec.Internal.Either type (Right a3 :: Either a2 a1) >>= (f :: a1 ~> Either a2 b) = Apply f a3

type (>>) ma mb = ma >>= Const' mb Source #

Execute one action and then the next, ignore the result of the first.

type family (f :: m (a ~> b)) <*> (ma :: m a) :: m b where ... Source #

Execute an action that returns a function than map function over the result of the next action.

Equations

mf <*> mx = mf >>= Apply (Flip (<$>$$)) mx

Tuple construction

data Pair'' :: a ~> (b ~> (a, b)) Source #

Instances

type Apply (Pair'' :: TyFun a (b ~> (a, b)) -> Type) (x :: a) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Pair'' :: TyFun a (b ~> (a, b)) -> Type) (x :: a) = (Pair' x :: TyFun b (a, b) -> Type)

data Pair' :: a -> b ~> (a, b) Source #

Instances

type Apply (Pair' x :: TyFun k1 (k2, k1) -> Type) (y :: k1) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Pair' x :: TyFun k1 (k2, k1) -> Type) (y :: k1) = (,) x y

List construction

data Cons'' :: a ~> ([a] ~> [a]) Source #

Instances

type Apply (Cons'' :: TyFun a ([a] ~> [a]) -> Type) (x :: a) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Cons'' :: TyFun a ([a] ~> [a]) -> Type) (x :: a) = Cons' x

data Cons' :: a -> [a] ~> [a] Source #

Instances

type Apply (Cons' x :: TyFun [a] [a] -> Type) (xs :: [a]) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Cons' x :: TyFun [a] [a] -> Type) (xs :: [a]) = x ': xs

Convert data types to Partially applicable type functions

data TyCon1 :: (a -> b) -> a ~> b Source #

Instances

type Apply (TyCon1 f :: TyFun a b -> Type) (x :: a) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (TyCon1 f :: TyFun a b -> Type) (x :: a) = f x

data TyCon2 :: (a -> b -> c) -> a ~> (b ~> c) Source #

Instances

type Apply (TyCon2 f :: TyFun a1 (a2 ~> b) -> Type) (x :: a1) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (TyCon2 f :: TyFun a1 (a2 ~> b) -> Type) (x :: a1) = TyCon1 (f x)

Execute an action and map a pure function over the result.

data (<$>$$) :: (a ~> b) ~> (m a ~> m b) Source #

Instances

type Apply ((<$>$$) :: TyFun (a ~> b) (m a ~> m b) -> Type) (f :: a ~> b) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply ((<$>$$) :: TyFun (a ~> b) (m a ~> m b) -> Type) (f :: a ~> b) = ((<$>$) f :: TyFun (m a) (m b) -> Type)

data (<$>$) :: (a ~> b) -> m a ~> m b Source #

Instances

type Apply ((<$>$) f :: TyFun (m a) (m b) -> Type) (x :: m a) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply ((<$>$) f :: TyFun (m a) (m b) -> Type) (x :: m a) = f <$> x

type family (f :: a ~> b) <$> (ma :: m a) :: m b Source #

Instances

type (f :: a1 ~> b) <$> (Left a3 :: Either a2 a1) Source #
Instance details Defined in Test.TypeSpec.Internal.Either type (f :: a1 ~> b) <$> (Left a3 :: Either a2 a1) = (Left a3 :: Either a2 b)
type (f :: a1 ~> b) <$> (Right a3 :: Either a2 a1) Source #
Instance details Defined in Test.TypeSpec.Internal.Either type (f :: a1 ~> b) <$> (Right a3 :: Either a2 a1) = (Right (Apply f a3) :: Either a2 b)

Flip Type Functions

data Flip' :: (a ~> (b ~> c)) ~> (b ~> (a ~> c)) Source #

Instances

type Apply (Flip' :: TyFun (a ~> (b ~> c)) (b ~> (a ~> c)) -> Type) (f :: a ~> (b ~> c)) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Flip' :: TyFun (a ~> (b ~> c)) (b ~> (a ~> c)) -> Type) (f :: a ~> (b ~> c)) = Flip f

data Flip :: (a ~> (b ~> c)) -> b ~> (a ~> c) Source #

Instances

type Apply (Flip f :: TyFun b (a ~> c) -> Type) (y :: b) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Flip f :: TyFun b (a ~> c) -> Type) (y :: b) = Flip_ f y

data Flip_ :: (a ~> (b ~> c)) -> b -> a ~> c Source #

Instances

type Apply (Flip_ f y :: TyFun a c -> Type) (x :: a) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Flip_ f y :: TyFun a c -> Type) (x :: a) = Flip__ f y x

type family Flip__ (f :: a ~> (b ~> c)) (y :: b) (x :: a) :: c where ... Source #

Equations

Flip__ f y x = Apply (Apply f x) y

Type Function composition

data Compose'' :: (b ~> c) ~> ((a ~> b) ~> (a ~> c)) Source #

Instances

type Apply (Compose'' :: TyFun (b ~> c) ((a ~> b) ~> (a ~> c)) -> Type) (f :: b ~> c) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Compose'' :: TyFun (b ~> c) ((a ~> b) ~> (a ~> c)) -> Type) (f :: b ~> c) = (Compose' f :: TyFun (a ~> b) (a ~> c) -> Type)

data Compose' :: (b ~> c) -> (a ~> b) ~> (a ~> c) Source #

Instances

type Apply (Compose' f :: TyFun (a ~> b) (a ~> c) -> Type) (g :: a ~> b) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Compose' f :: TyFun (a ~> b) (a ~> c) -> Type) (g :: a ~> b) = Compose f g

data Compose :: (b ~> c) -> (a ~> b) -> a ~> c Source #

Instances

type Apply (Compose f g :: TyFun a c -> Type) (x :: a) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Compose f g :: TyFun a c -> Type) (x :: a) = Compose_ f g x

type family Compose_ (f :: b ~> c) (g :: a ~> b) (x :: a) :: c where ... Source #

Equations

Compose_ f g x = Apply f (Apply g x)

Type-Level `const`

type family Const (a :: t) (b :: t') :: t where ... Source #

Equations

Const a b = a

data Const' :: a -> b ~> a Source #

Instances

type Apply (Const' a :: TyFun t' t -> Type) (b :: t') Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Const' a :: TyFun t' t -> Type) (b :: t') = Const a b

data Const'' :: a ~> (b ~> a) Source #

Instances

type Apply (Const'' :: TyFun a1 (b ~> a1) -> Type) (a2 :: a1) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Const'' :: TyFun a1 (b ~> a1) -> Type) (a2 :: a1) = (Const' a2 :: TyFun b a1 -> Type)

Defunctionalization

data TyFun :: Type -> Type -> Type Source #

Instances

type Apply (Cons'' :: TyFun a ([a] ~> [a]) -> Type) (x :: a) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Cons'' :: TyFun a ([a] ~> [a]) -> Type) (x :: a) = Cons' x
type Apply (Const'' :: TyFun a1 (b ~> a1) -> Type) (a2 :: a1) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Const'' :: TyFun a1 (b ~> a1) -> Type) (a2 :: a1) = (Const' a2 :: TyFun b a1 -> Type)
type Apply (Pair'' :: TyFun a (b ~> (a, b)) -> Type) (x :: a) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Pair'' :: TyFun a (b ~> (a, b)) -> Type) (x :: a) = (Pair' x :: TyFun b (a, b) -> Type)
type Apply (Flip f :: TyFun b (a ~> c) -> Type) (y :: b) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Flip f :: TyFun b (a ~> c) -> Type) (y :: b) = Flip_ f y
type Apply (TyCon2 f :: TyFun a1 (a2 ~> b) -> Type) (x :: a1) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (TyCon2 f :: TyFun a1 (a2 ~> b) -> Type) (x :: a1) = TyCon1 (f x)
type Apply (Flip' :: TyFun (a ~> (b ~> c)) (b ~> (a ~> c)) -> Type) (f :: a ~> (b ~> c)) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Flip' :: TyFun (a ~> (b ~> c)) (b ~> (a ~> c)) -> Type) (f :: a ~> (b ~> c)) = Flip f
type Apply ((<$>$$) :: TyFun (a ~> b) (m a ~> m b) -> Type) (f :: a ~> b) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply ((<$>$$) :: TyFun (a ~> b) (m a ~> m b) -> Type) (f :: a ~> b) = ((<$>$) f :: TyFun (m a) (m b) -> Type)
type Apply (Compose'' :: TyFun (b ~> c) ((a ~> b) ~> (a ~> c)) -> Type) (f :: b ~> c) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Compose'' :: TyFun (b ~> c) ((a ~> b) ~> (a ~> c)) -> Type) (f :: b ~> c) = (Compose' f :: TyFun (a ~> b) (a ~> c) -> Type)
type Apply (Compose' f :: TyFun (a ~> b) (a ~> c) -> Type) (g :: a ~> b) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Compose' f :: TyFun (a ~> b) (a ~> c) -> Type) (g :: a ~> b) = Compose f g

type (~>) a b = TyFun a b -> Type infixr 0 Source #

type family Apply (f :: a ~> b) (x :: a) :: b Source #

Instances

type Apply (Const' a :: TyFun t' t -> Type) (b :: t') Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Const' a :: TyFun t' t -> Type) (b :: t') = Const a b
type Apply (TyCon1 f :: TyFun a b -> Type) (x :: a) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (TyCon1 f :: TyFun a b -> Type) (x :: a) = f x
type Apply (Compose f g :: TyFun a c -> Type) (x :: a) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Compose f g :: TyFun a c -> Type) (x :: a) = Compose_ f g x
type Apply (Flip_ f y :: TyFun a c -> Type) (x :: a) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Flip_ f y :: TyFun a c -> Type) (x :: a) = Flip__ f y x
type Apply (Cons' x :: TyFun [a] [a] -> Type) (xs :: [a]) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Cons' x :: TyFun [a] [a] -> Type) (xs :: [a]) = x ': xs
type Apply ((<$>$) f :: TyFun (m a) (m b) -> Type) (x :: m a) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply ((<$>$) f :: TyFun (m a) (m b) -> Type) (x :: m a) = f <$> x
type Apply (Cons'' :: TyFun a ([a] ~> [a]) -> Type) (x :: a) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Cons'' :: TyFun a ([a] ~> [a]) -> Type) (x :: a) = Cons' x
type Apply (Const'' :: TyFun a1 (b ~> a1) -> Type) (a2 :: a1) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Const'' :: TyFun a1 (b ~> a1) -> Type) (a2 :: a1) = (Const' a2 :: TyFun b a1 -> Type)
type Apply (Pair'' :: TyFun a (b ~> (a, b)) -> Type) (x :: a) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Pair'' :: TyFun a (b ~> (a, b)) -> Type) (x :: a) = (Pair' x :: TyFun b (a, b) -> Type)
type Apply (Pair' x :: TyFun k1 (k2, k1) -> Type) (y :: k1) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Pair' x :: TyFun k1 (k2, k1) -> Type) (y :: k1) = (,) x y
type Apply (Flip f :: TyFun b (a ~> c) -> Type) (y :: b) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Flip f :: TyFun b (a ~> c) -> Type) (y :: b) = Flip_ f y
type Apply (TyCon2 f :: TyFun a1 (a2 ~> b) -> Type) (x :: a1) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (TyCon2 f :: TyFun a1 (a2 ~> b) -> Type) (x :: a1) = TyCon1 (f x)
type Apply (Flip' :: TyFun (a ~> (b ~> c)) (b ~> (a ~> c)) -> Type) (f :: a ~> (b ~> c)) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Flip' :: TyFun (a ~> (b ~> c)) (b ~> (a ~> c)) -> Type) (f :: a ~> (b ~> c)) = Flip f
type Apply ((<$>$$) :: TyFun (a ~> b) (m a ~> m b) -> Type) (f :: a ~> b) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply ((<$>$$) :: TyFun (a ~> b) (m a ~> m b) -> Type) (f :: a ~> b) = ((<$>$) f :: TyFun (m a) (m b) -> Type)
type Apply (Compose'' :: TyFun (b ~> c) ((a ~> b) ~> (a ~> c)) -> Type) (f :: b ~> c) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Compose'' :: TyFun (b ~> c) ((a ~> b) ~> (a ~> c)) -> Type) (f :: b ~> c) = (Compose' f :: TyFun (a ~> b) (a ~> c) -> Type)
type Apply (Compose' f :: TyFun (a ~> b) (a ~> c) -> Type) (g :: a ~> b) Source #
Instance details Defined in Test.TypeSpec.Internal.Apply type Apply (Compose' f :: TyFun (a ~> b) (a ~> c) -> Type) (g :: a ~> b) = Compose f g

Documentation

Tuple construction

List construction

Convert data types to Partially applicable type functions

Execute an action and map a pure function over the result.

Flip Type Functions

Type Function composition

Type-Level const

Defunctionalization

Type-Level `const`