{-# LANGUAGE TypeFamilies #-}
module Data.Universe.Instances.Base (
-- | Instances of 'Universe' and 'Finite' for built-in types.
Universe(..), Finite(..)
) where
import Control.Monad
import Data.Int
import Data.Map ((!), fromList)
import Data.Monoid
import Data.Ratio
import Data.Universe.Class
import Data.Universe.Helpers
import Data.Word
instance Universe () where universe = universeDef
instance Universe Bool where universe = universeDef
instance Universe Char where universe = universeDef
instance Universe Ordering where universe = universeDef
instance Universe Integer where universe = [0, -1..] +++ [1..]
instance Universe Int where universe = universeDef
instance Universe Int8 where universe = universeDef
instance Universe Int16 where universe = universeDef
instance Universe Int32 where universe = universeDef
instance Universe Int64 where universe = universeDef
instance Universe Word where universe = universeDef
instance Universe Word8 where universe = universeDef
instance Universe Word16 where universe = universeDef
instance Universe Word32 where universe = universeDef
instance Universe Word64 where universe = universeDef
instance (Universe a, Universe b) => Universe (Either a b) where universe = map Left universe +++ map Right universe
instance Universe a => Universe (Maybe a ) where universe = Nothing : map Just universe
instance (Universe a, Universe b) => Universe (a, b) where universe = universe +*+ universe
instance (Universe a, Universe b, Universe c) => Universe (a, b, c) where universe = [(a,b,c) | ((a,b),c) <- universe +*+ universe +*+ universe]
instance (Universe a, Universe b, Universe c, Universe d) => Universe (a, b, c, d) where universe = [(a,b,c,d) | (((a,b),c),d) <- universe +*+ universe +*+ universe +*+ universe]
instance (Universe a, Universe b, Universe c, Universe d, Universe e) => Universe (a, b, c, d, e) where universe = [(a,b,c,d,e) | ((((a,b),c),d),e) <- universe +*+ universe +*+ universe +*+ universe +*+ universe]
instance Universe a => Universe [a] where
universe = diagonal $ [[]] : [[h:t | t <- universe] | h <- universe]
instance Universe All where universe = map All universe
instance Universe Any where universe = map Any universe
instance Universe a => Universe (Sum a) where universe = map Sum universe
instance Universe a => Universe (Product a) where universe = map Product universe
instance Universe a => Universe (Dual a) where universe = map Dual universe
instance Universe a => Universe (First a) where universe = map First universe
instance Universe a => Universe (Last a) where universe = map Last universe
-- see http://mathlesstraveled.com/2008/01/07/recounting-the-rationals-part-ii-fractions-grow-on-trees/
--
-- also, Brent Yorgey writes:
--
-- positiveRationals2 :: [Ratio Integer]
-- positiveRationals2 = iterate' next 1
-- where
-- next x = let (n,y) = properFraction x in recip (fromInteger n + 1 - y)
-- iterate' f x = let x' = f x in x' `seq` (x : iterate' f x')
--
-- Compiling this code with -O2 and doing some informal tests seems to
-- show that positiveRationals and positiveRationals2 have almost exactly
-- the same efficiency for generating the entire list (e.g. the times for
-- finding the sum of the first 100000 rationals are pretty much
-- indistinguishable). positiveRationals is still the clear winner for
-- generating just the nth rational for some particular n -- some simple
-- experiments seem to indicate that doing this with positiveRationals2
-- scales linearly while with positiveRationals it scales sub-linearly,
-- as expected.
--
-- Surprisingly, replacing % with :% in positiveRationals seems to make
-- no appreciable difference.
positiveRationals :: [Ratio Integer]
positiveRationals = 1 : map lChild positiveRationals +++ map rChild positiveRationals where
lChild frac = numerator frac % (numerator frac + denominator frac)
rChild frac = (numerator frac + denominator frac) % denominator frac
instance a ~ Integer => Universe (Ratio a) where universe = 0 : map negate positiveRationals +++ positiveRationals
-- could change the Ord constraint to an Eq one, but come on, how many finite
-- types can't be ordered?
instance (Finite a, Ord a, Universe b) => Universe (a -> b) where
universe = map tableToFunction tables where
tables = choices [universe | _ <- monoUniverse]
tableToFunction = (!) . fromList . zip monoUniverse
monoUniverse = universeF
instance Finite ()
instance Finite Bool
instance Finite Char
instance Finite Ordering
instance Finite Int
instance Finite Int8
instance Finite Int16
instance Finite Int32
instance Finite Int64
instance Finite Word
instance Finite Word8
instance Finite Word16
instance Finite Word32
instance Finite Word64
instance Finite a => Finite (Maybe a )
instance (Finite a, Finite b) => Finite (Either a b) where universeF = map Left universe ++ map Right universe
instance (Finite a, Finite b) => Finite (a, b) where universeF = liftM2 (,) universeF universeF
instance (Finite a, Finite b, Finite c) => Finite (a, b, c) where universeF = liftM3 (,,) universeF universeF universeF
instance (Finite a, Finite b, Finite c, Finite d) => Finite (a, b, c, d) where universeF = liftM4 (,,,) universeF universeF universeF universeF
instance (Finite a, Finite b, Finite c, Finite d, Finite e) => Finite (a, b, c, d, e) where universeF = liftM5 (,,,,) universeF universeF universeF universeF universeF
instance Finite All where universeF = map All universeF
instance Finite Any where universeF = map Any universeF
instance Finite a => Finite (Sum a) where universeF = map Sum universeF
instance Finite a => Finite (Product a) where universeF = map Product universeF
instance Finite a => Finite (Dual a) where universeF = map Dual universeF
instance Finite a => Finite (First a) where universeF = map First universeF
instance Finite a => Finite (Last a) where universeF = map Last universeF
instance (Ord a, Finite a, Finite b) => Finite (a -> b) where
universeF = map tableToFunction tables where
tables = sequence [universeF | _ <- monoUniverse]
tableToFunction = (!) . fromList . zip monoUniverse
monoUniverse = universeF
-- to add when somebody asks for it: instance (Eq a, Finite a) => Finite (Endo a) (+Universe)