Data.Extensible.Internal

A bunch of combinators that contains magic

Documentation

data Membership xs x

The position of x in the type level set xs.

Instances

Typeable ([k] -> k -> *) (Membership k)

Eq (Membership k xs x)

Ord (Membership k xs x)

Show (Membership k xs x)

runMembership :: Membership (y : xs) x -> Either (x :~: y) (Membership xs x)

Embodies a type equivalence to ensure that the Membership points the first element.

compareMembership :: Membership xs x -> Membership xs y -> Either Ordering (x :~: y)

ord :: Int -> Q Exp

Generates a Membership that corresponds to the given ordinal (0-origin).

data Nav xs x where

Constructors

Here :: Nav (x : xs) x

NavL :: Membership (Half xs) x -> Nav (e : xs) x

NavR :: Membership (Half (Tail xs)) x -> Nav (e : xs) x

navigate :: Membership xs x -> Nav xs x

here :: Membership (x : xs) x

navNext :: Membership xs y -> Membership (x : xs) y

navL :: Membership (Half xs) y -> Membership (x : xs) y

navR :: Membership (Half (Tail xs)) y -> Membership (x : xs) y

class Member xs x where

Member x xs or x ∈ xs indicates that x is an element of xs.

Methods

membership :: Membership xs x

Instances

((~) * (Check k1 Nat x (Lookup k1 x xs)) (Expecting k one), ToInt k one) => Member k xs x

type (∈) x xs = Member xs x

Unicode flipped alias for Member

data Nat

Constructors

Zero

DNat Nat

SDNat Nat

Instances

ToInt Nat Zero

ToInt Nat n => ToInt Nat (SDNat n)

ToInt Nat n => ToInt Nat (DNat n)

class ToInt n where

Methods

theInt :: proxy n -> Int

Instances

ToInt Nat Zero

ToInt Nat n => ToInt Nat (SDNat n)

ToInt Nat n => ToInt Nat (DNat n)

type family Lookup x xs :: [Nat]

Equations

Lookup x (x : xs) = Zero : Lookup x xs

Lookup x (y : ys) = MapSucc (Lookup x ys)

Lookup x [] = []

type family Succ x :: Nat

Equations

Succ Zero = SDNat Zero

Succ (DNat n) = SDNat n

Succ (SDNat n) = DNat (Succ n)

type family MapSucc xs :: [Nat]

Equations

MapSucc [] = []

MapSucc (x : xs) = Succ x : MapSucc xs

type family Half xs :: [k]

Equations

Half [] = []

Half (x : (y : zs)) = x : Half zs

Half (x : []) = `[x]`

type family Tail xs :: [k]

Equations

Tail (x : xs) = xs

Tail [] = []

lemmaHalfTail :: proxy xs -> p (x : Half (Tail xs)) -> p (Half (x : xs))

GHC can't prove this

lemmaMerging :: p (Merge (Half xs) (Half (Tail xs))) -> p xs

type family xs ++ ys :: [k] infixr 5

Equations

[] ++ ys = ys

(x : xs) ++ ys = x : (xs ++ ys)

type family Map f xs :: [k]

Equations

Map f [] = []

Map f (x : xs) = f x : Map f xs

type family Merge xs ys :: [k]

Equations

Merge (x : xs) (y : ys) = x : (y : Merge xs ys)

Merge xs [] = xs

Merge [] ys = ys

type family Concat xs :: [k]

Equations

Concat [] = []

Concat (x : xs) = x ++ Concat xs

type family Check x xs

Equations

Check x `[n]` = Expecting n

Check x [] = Missing x

Check x xs = Ambiguous x

data Expecting a

A type sugar to make type error more readable.

data Missing a

A type sugar to make type error more readable.

data Ambiguous a

A type sugar to make type error more readable.

module Data.Type.Equality

module Data.Proxy