Copyright	(C) Koz Ross 2019
License	GPL version 3.0 or later
Maintainer	koz.ross@retro-freedom.nz
Stability	Experimental
Portability	GHC only
Safe Haskell	Trustworthy
Language	Haskell2010

Data.Finitary.Finiteness

Description

Knowing that a type a is an instance of Finitary gives us the knowledge that there is an isomorphism between a and Finite n for some KnownNat n. This gives us a lot of information, which we can exploit to automagically derive a range of type class instances.

Finiteness is a newtype wrapper providing this functionality, while 're-exporting' as many type class instances of the underlying type as possible. It is designed for use with DerivingVia - an example of use:

{-# LANGUAGE DerivingVia #-}
{-# LANGUAGE DeriveAnyClass #-}
{-# LANGUAGE DeriveGeneric #-}

import GHC.Generics
import Data.Finitary
import Data.Finitary.Finiteness
import Data.Word
import Control.DeepSeq
import Data.Hashable
import Data.Binary

data Foo = Bar | Baz (Word8, Word8) | Quux Word16
 deriving (Eq, Generic, Finitary)
 deriving (Ord, Bounded, NFData, Hashable, Binary) via (Finiteness Foo)

Currently, the following type class instances can be derived in this manner:

Ord
Bounded
NFData
Hashable
Binary

Additionally, Finiteness 'forwards' definitions of the following type classes:

Synopsis

newtype Finiteness a = Finiteness {
- unFiniteness :: a
}

Documentation

newtype Finiteness a Source #

Essentially Identity with a different name. Named this way due to the wordplay you get from use with DerivingVia.

Constructors

Finiteness
Fields unFiniteness :: a

Instances

Instances details

Functor Finiteness Source #
Instance details Defined in Data.Finitary.Finiteness Methods fmap :: (a -> b) -> Finiteness a -> Finiteness b # (<$) :: a -> Finiteness b -> Finiteness a #
(Finitary a, 1 <= Cardinality a) => Bounded (Finiteness a) Source #	Since any inhabited `Finitary` type is also `Bounded`, we can forward this definition also.
Instance details Defined in Data.Finitary.Finiteness Methods minBound :: Finiteness a # maxBound :: Finiteness a #
Eq a => Eq (Finiteness a) Source #
Instance details Defined in Data.Finitary.Finiteness Methods (==) :: Finiteness a -> Finiteness a -> Bool # (/=) :: Finiteness a -> Finiteness a -> Bool #
Data a => Data (Finiteness a) Source #
Instance details Defined in Data.Finitary.Finiteness Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Finiteness a -> c (Finiteness a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Finiteness a) # toConstr :: Finiteness a -> Constr # dataTypeOf :: Finiteness a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Finiteness a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Finiteness a)) # gmapT :: (forall b. Data b => b -> b) -> Finiteness a -> Finiteness a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Finiteness a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Finiteness a -> r # gmapQ :: (forall d. Data d => d -> u) -> Finiteness a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Finiteness a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Finiteness a -> m (Finiteness a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Finiteness a -> m (Finiteness a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Finiteness a -> m (Finiteness a) #
Finitary a => Ord (Finiteness a) Source #	`Ord` can be derived by deferring to the order on `Finite (Cardinality a)`.
Instance details Defined in Data.Finitary.Finiteness Methods compare :: Finiteness a -> Finiteness a -> Ordering # (<) :: Finiteness a -> Finiteness a -> Bool # (<=) :: Finiteness a -> Finiteness a -> Bool # (>) :: Finiteness a -> Finiteness a -> Bool # (>=) :: Finiteness a -> Finiteness a -> Bool # max :: Finiteness a -> Finiteness a -> Finiteness a # min :: Finiteness a -> Finiteness a -> Finiteness a #
Read a => Read (Finiteness a) Source #
Instance details Defined in Data.Finitary.Finiteness Methods readsPrec :: Int -> ReadS (Finiteness a) # readList :: ReadS [Finiteness a] # readPrec :: ReadPrec (Finiteness a) # readListPrec :: ReadPrec [Finiteness a] #
Show a => Show (Finiteness a) Source #
Instance details Defined in Data.Finitary.Finiteness Methods showsPrec :: Int -> Finiteness a -> ShowS # show :: Finiteness a -> String # showList :: [Finiteness a] -> ShowS #
Semigroup a => Semigroup (Finiteness a) Source #
Instance details Defined in Data.Finitary.Finiteness Methods (<>) :: Finiteness a -> Finiteness a -> Finiteness a # sconcat :: NonEmpty (Finiteness a) -> Finiteness a # stimes :: Integral b => b -> Finiteness a -> Finiteness a #
Monoid a => Monoid (Finiteness a) Source #
Instance details Defined in Data.Finitary.Finiteness Methods mempty :: Finiteness a # mappend :: Finiteness a -> Finiteness a -> Finiteness a # mconcat :: [Finiteness a] -> Finiteness a #
Finitary a => Binary (Finiteness a) Source #	Any `Finitary` type can be converted to a binary representation by converting its index.
Instance details Defined in Data.Finitary.Finiteness Methods put :: Finiteness a -> Put # get :: Get (Finiteness a) # putList :: [Finiteness a] -> Put #
Finitary a => NFData (Finiteness a) Source #	We can force evaluation of a `Finitary` type by converting it to its index.
Instance details Defined in Data.Finitary.Finiteness Methods rnf :: Finiteness a -> () #
Finitary a => Finitary (Finiteness a) Source #	`Finiteness` merely replicates the `Finitary` behaviour of the underlying type.
Instance details Defined in Data.Finitary.Finiteness Associated Types type Cardinality (Finiteness a) :: Nat Methods fromFinite :: Finite (Cardinality (Finiteness a)) -> Finiteness a toFinite :: Finiteness a -> Finite (Cardinality (Finiteness a)) start :: Finiteness a end :: Finiteness a previous :: Alternative f => Finiteness a -> f (Finiteness a) next :: Alternative f => Finiteness a -> f (Finiteness a)
Finitary a => Hashable (Finiteness a) Source #	Any `Finitary` type can be hashed by hashing its index.
Instance details Defined in Data.Finitary.Finiteness Methods hashWithSalt :: Int -> Finiteness a -> Int hash :: Finiteness a -> Int
type Cardinality (Finiteness a) Source #
Instance details Defined in Data.Finitary.Finiteness type Cardinality (Finiteness a) = Cardinality a