first-class-families: First class type families

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First class type families, eval-style defunctionalization

See Fcf.

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Versions	0.1.0.0, 0.2.0.0, 0.3.0.0, 0.3.0.1, 0.4.0.0, 0.5.0.0, 0.6.0.0, 0.7.0.0, 0.8.0.0, 0.8.0.0, 0.8.0.1, 0.8.1.0
Change log	CHANGELOG.md
Dependencies	base (>=4.9 && <4.14) [details]
License	MIT
Copyright	2018 Li-yao Xia
Author	Li-yao Xia
Maintainer	lysxia@gmail.com
Category	Other
Home page	https://github.com/Lysxia/first-class-families#readme
Source repo	head: git clone https://github.com/Lysxia/first-class-families
Uploaded	by lyxia at 2020-03-01T22:32:20Z

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First-class type families

For example, consider this simple type family:

type family   FromMaybe (a :: k) (m :: Maybe k) :: k
type instance FromMaybe a 'Nothing  = a
type instance FromMaybe a ('Just b) = b

With first-class-families (fcfs), it translates to a data declaration and instances for a single Eval family:

import Fcf

data FromMaybe :: k -> Maybe k -> Exp k
type instance Eval (FromMaybe a 'Nothing)  = a
type instance Eval (FromMaybe a ('Just b)) = b

That way, the FromMaybe constructor can be partially applied, and passed to higher-order fcfs such as Map:

Eval (Map (FromMaybe 0) '[ 'Just 1, 'Nothing ])  =  '[ 1, 0 ] :: [Nat]

Essential language extensions:

{-# LANGUAGE
    DataKinds,
    PolyKinds,
    TypeFamilies,
    TypeInType,
    TypeOperators,
    UndecidableInstances #-}