TypeLet.UserAPI

Main classes

class Let (a :: k) (b :: k)

Type-level let

A constraint Let x t where x is an (existential) type variable and t is an arbitrary type represents a type-level let binding let x = t.

o Introduction form

Type-level let bindings should be introduced using letT or its slightly higher level cousin, letAs.

o Elimination form

To eliminate type-level let, use castEqual.

Instances

Let (a :: k) (a :: k)

Reflexivity

A constraint Let x t, where x is an existential (skolem) type variable and t is an arbitrary type, models a type-level let x = t. There is only a single instance for Let: reflexivity (a type is equal to itself).

User code normally does not work with Let directly, but instead uses one of the introduction forms (letT and letAs) which take care to introduce Let constraints of the right shape. When Let constraints are introduced manually, the plugin will report a type error if

• The left-hand side is not a skolem type variable
• The set of let-bindings in scope are cyclic.

Defined in TypeLet.UserAPI

class Equal (a :: k) (b :: k)

(Nominal) type equality, up to type-level let

This is a class without any definitions; 'Equal a b' is instead proved by the plugin. Suppose we have a bunch of type-level let constraints in scope

Let x1 t1
Let x2 t2
...

Then if σ is the corresponding idempotent substitution, two types a and b are considered Equal if σ(a) and σ(b) are nominally equal.

castEqual :: Equal a b => a -> b

Type-safe cast, using Equal as the notion of equality

See comments for Equal.

Introduction forms

data LetT (a :: k) where

LetT is used along with letT to introduce type-level let bindings.

See letT for more information.

Constructors

LetT :: Let b a => Proxy b -> LetT a

letT :: Proxy a -> LetT a

Primitive way to introduce type-level let binding.

Usage:

case letT (Proxy @t) of LetT (_ :: Proxy x) ->

This introduces a type-level let binding x = t.

letT' :: forall r a. Proxy a -> (forall b. Let b a => Proxy b -> r) -> r

CPS form of letT

While this is more convenient to use, the r parameter itself requires careful thought.

data LetAs f (a :: k) where

Used together with letAs to pair a type-level let binding with a cast

See letAs for details.

Constructors

LetAs :: Let b a => f b -> LetAs f a

letAs :: f a -> LetAs f a

Pair a type-level let binding with a cast

Often when we introduce a type-level let x = t, we then want to cast some term e :: t to a term e :: x; function letAs does these two things in one operation.

If we did the above as written, however, we would have a term e :: x where we know nothing about x at all (unless we cast again). This is typically not useful; instead, we go from a term e :: f t to a term e :: f x, let-binding the type index t but not the functor f.

letAs' :: forall r f a. f a -> (forall b. Let b a => f b -> r) -> r

CPS form of letAs

See also comments for letT'.

Re-exports

data Proxy (t :: k)

Proxy is a type that holds no data, but has a phantom parameter of arbitrary type (or even kind). Its use is to provide type information, even though there is no value available of that type (or it may be too costly to create one).

Historically, Proxy :: Proxy a is a safer alternative to the undefined :: a idiom.

>>> Proxy :: Proxy (Void, Int -> Int)
Proxy

Proxy can even hold types of higher kinds,

>>> Proxy :: Proxy Either
Proxy

>>> Proxy :: Proxy Functor
Proxy

>>> Proxy :: Proxy complicatedStructure
Proxy

Constructors

Proxy

Instances

Monad (Proxy :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

(>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b

(>>) :: Proxy a -> Proxy b -> Proxy b

return :: a -> Proxy a

Functor (Proxy :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

fmap :: (a -> b) -> Proxy a -> Proxy b

(<$) :: a -> Proxy b -> Proxy a

Applicative (Proxy :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

pure :: a -> Proxy a

(<*>) :: Proxy (a -> b) -> Proxy a -> Proxy b

liftA2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c

(*>) :: Proxy a -> Proxy b -> Proxy b

(<*) :: Proxy a -> Proxy b -> Proxy a

Foldable (Proxy :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => Proxy m -> m

foldMap :: Monoid m => (a -> m) -> Proxy a -> m

foldMap' :: Monoid m => (a -> m) -> Proxy a -> m

foldr :: (a -> b -> b) -> b -> Proxy a -> b

foldr' :: (a -> b -> b) -> b -> Proxy a -> b

foldl :: (b -> a -> b) -> b -> Proxy a -> b

foldl' :: (b -> a -> b) -> b -> Proxy a -> b

foldr1 :: (a -> a -> a) -> Proxy a -> a

foldl1 :: (a -> a -> a) -> Proxy a -> a

toList :: Proxy a -> [a]

null :: Proxy a -> Bool

length :: Proxy a -> Int

elem :: Eq a => a -> Proxy a -> Bool

maximum :: Ord a => Proxy a -> a

minimum :: Ord a => Proxy a -> a

sum :: Num a => Proxy a -> a

product :: Num a => Proxy a -> a

Traversable (Proxy :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Proxy a -> f (Proxy b)

sequenceA :: Applicative f => Proxy (f a) -> f (Proxy a)

mapM :: Monad m => (a -> m b) -> Proxy a -> m (Proxy b)

sequence :: Monad m => Proxy (m a) -> m (Proxy a)

Alternative (Proxy :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Proxy

Methods

empty :: Proxy a

(<|>) :: Proxy a -> Proxy a -> Proxy a

some :: Proxy a -> Proxy [a]

many :: Proxy a -> Proxy [a]

MonadPlus (Proxy :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Proxy

Methods

mzero :: Proxy a

mplus :: Proxy a -> Proxy a -> Proxy a

Bounded (Proxy t)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

minBound :: Proxy t

maxBound :: Proxy t

Enum (Proxy s)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

succ :: Proxy s -> Proxy s

pred :: Proxy s -> Proxy s

toEnum :: Int -> Proxy s

fromEnum :: Proxy s -> Int

enumFrom :: Proxy s -> [Proxy s]

enumFromThen :: Proxy s -> Proxy s -> [Proxy s]

enumFromTo :: Proxy s -> Proxy s -> [Proxy s]

enumFromThenTo :: Proxy s -> Proxy s -> Proxy s -> [Proxy s]

Eq (Proxy s)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

(==) :: Proxy s -> Proxy s -> Bool

(/=) :: Proxy s -> Proxy s -> Bool

Ord (Proxy s)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

compare :: Proxy s -> Proxy s -> Ordering

(<) :: Proxy s -> Proxy s -> Bool

(<=) :: Proxy s -> Proxy s -> Bool

(>) :: Proxy s -> Proxy s -> Bool

(>=) :: Proxy s -> Proxy s -> Bool

max :: Proxy s -> Proxy s -> Proxy s

min :: Proxy s -> Proxy s -> Proxy s

Read (Proxy t)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

readsPrec :: Int -> ReadS (Proxy t)

readList :: ReadS [Proxy t]

readPrec :: ReadPrec (Proxy t)

readListPrec :: ReadPrec [Proxy t]

Show (Proxy s)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

showsPrec :: Int -> Proxy s -> ShowS

show :: Proxy s -> String

showList :: [Proxy s] -> ShowS

Ix (Proxy s)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

range :: (Proxy s, Proxy s) -> [Proxy s]

index :: (Proxy s, Proxy s) -> Proxy s -> Int

unsafeIndex :: (Proxy s, Proxy s) -> Proxy s -> Int

inRange :: (Proxy s, Proxy s) -> Proxy s -> Bool

rangeSize :: (Proxy s, Proxy s) -> Int

unsafeRangeSize :: (Proxy s, Proxy s) -> Int

Semigroup (Proxy s)

Since: base-4.9.0.0

Defined in Data.Proxy

Methods

(<>) :: Proxy s -> Proxy s -> Proxy s

sconcat :: NonEmpty (Proxy s) -> Proxy s

stimes :: Integral b => b -> Proxy s -> Proxy s

Monoid (Proxy s)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

mempty :: Proxy s

mappend :: Proxy s -> Proxy s -> Proxy s

mconcat :: [Proxy s] -> Proxy s