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105 lines
3.1 KiB
Markdown
105 lines
3.1 KiB
Markdown
# First-class type families [](https://hackage.haskell.org/package/first-class-families) [](https://travis-ci.org/Lysxia/first-class-families)
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First-class type families are type-level functions that can be
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composed using higher-order functions.
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The core of the idea is an extensible kind of "type-level expressions"
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and an open type family for evaluating such expressions.
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```haskell
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type Exp (k :: Type) :: Type
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type family Eval (e :: Exp k) :: k
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```
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This library provides that core foundation,
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and also exports basic first-class type families.
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## Example
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For example, consider this simple type family:
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```haskell
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type family FromMaybe (a :: k) (m :: Maybe k) :: k
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type instance FromMaybe a 'Nothing = a
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type instance FromMaybe a ('Just b) = b
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```
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With first-class-families (fcfs), it translates to a `data` declaration
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and instances for a single `Eval` family:
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```haskell
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import Fcf
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data FromMaybe :: k -> Maybe k -> Exp k
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type instance Eval (FromMaybe a 'Nothing) = a
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type instance Eval (FromMaybe a ('Just b)) = b
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```
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That way, the `FromMaybe` constructor can be partially applied,
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and passed to higher-order fcfs such as `Map`:
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```haskell
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Eval (Map (FromMaybe 0) '[ 'Just 1, 'Nothing ]) = '[ 1, 0 ] :: [Nat]
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```
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Essential language extensions:
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```haskell
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{-# LANGUAGE
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DataKinds,
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PolyKinds,
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TypeFamilies,
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TypeInType,
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TypeOperators,
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UndecidableInstances #-}
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```
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## Overview
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- `Fcf.Core`: definition of `Exp` and `Eval`.
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- `Fcf.Combinators`: general combinators to compose first-class families.
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- `Fcf.Data.*`: first-class families on common data types.
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- `Fcf.Class.*`: overloaded first-class families.
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- `Fcf.Utils`: miscellaneous.
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The top-level module `Fcf` is a prelude to get acquainted with the library.
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For regular use, import what you need from the specialized modules
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above, preferably with explicit import lists.
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```haskell
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import Fcf -- Simple but fragile
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import Fcf.Class.Functor (FMap) -- Explicit and robust
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```
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## Features
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### Overloaded type families
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Value-level functions can be overloaded using type classes.
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Type families---type-level functions---are open by design,
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so overloading is as easy as just declaring them with more general types.
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```haskell
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data Map :: (a -> Exp b) -> f a -> Exp (f b)
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-- Instances for f = []
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type instance Eval (Map f '[]) = '[]
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type instance Eval (Map f (x ': xs)) = Eval (f x) ': Eval (Map f xs)
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-- Instances for f = Maybe
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type instance Eval (Map f 'Nothing) = 'Nothing
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type instance Eval (Map f ('Just x)) = 'Just (Eval (f x))
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```
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## See also
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- [Haskell with only one type family](http://blog.poisson.chat/posts/2018-08-06-one-type-family.html)
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- [Overloaded type families](https://blog.poisson.chat/posts/2018-09-29-overloaded-families.html)
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- [The *singletons* library](https://hackage.haskell.org/package/singletons)
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---
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Contributions are welcome. Feel free to open an issue or make a PR on
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[Github](https://github.com/Lysxia/first-class-families)!
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