let it leave me like a long breath

module Data.Enumerable
	( Enumerable (count)
	, roll
	, select
	, enumerate

	, rangeEnum
	, rangeNum
	, from
	) where

import Control.Applicative
import Data.Maybe (fromMaybe)
import Utility.Rand

data Enumerable a
	= EnumerableNil
	| Enumerable
		{ count :: Integer
		, selector :: Integer -> a
		}

instance Functor Enumerable where
	fmap f (Enumerable c g) = Enumerable c $ f . g
	fmap _ EnumerableNil = EnumerableNil

instance Monoid (Enumerable a) where
	mempty = EnumerableNil
	mappend = (<|>)

-- one after the other
instance Applicative Enumerable where
	pure v = Enumerable 1 $ const v
	(Enumerable c f) <*> (Enumerable c' g) =
		Enumerable (c * c') $ \i -> let
				j = i `mod` c
				k = i `div` c
			in f j $ g k
	-- a zero infects everything else
	_ <*> _ = EnumerableNil

-- one or the other
instance Alternative Enumerable where
	empty = EnumerableNil
	(Enumerable c v) <|> (Enumerable c' v') = Enumerable (c + c') $ \i -> case i - c of
		x | x >= 0 -> v' x
			| otherwise -> v i
	EnumerableNil <|> f = f
	f <|> EnumerableNil = f

{-
instance Monad Enumerable where
	return = pure
	(Enumerable c v) >>= f = ...? the thing is we don't really know how the output varies w/ the input. so we MIGHT be like, oh, just evaluate every `i` and then wrap the resulting value up so we have a bunch of Enumerables that we can sequence. but then we have to evaluate every `i`, which is not practical. additionally, we don't know if those variations actually matter: f >>= return == f, but here we'd end up with a very different value. consequently, i don't think it's possible for this to be an Monad instance, even if it is maybe a monad conceptually. or at least, it's certainly not going to be implemented in this fashion.
	_ >>= _ = EnumerableNil

monad laws:
	return a >>= f    ≡ f a
	m >>= return      ≡ m
	(f >=> g) >=> g   ≡ f >=> (g >=> h)
		(m >>= f) >>= g ≡ m >>= (\x -> f x >>= g)

instance MonadPlus Enumerable where
	mzero = EnumerableNil
	mplus = (<|>)
-}

roll :: RandomGen g => Enumerable a -> Rand g a
roll enum = do
	i <- liftRand $ randomR (0, count enum-1)
	case select enum i of
		Nothing -> error $ "incoherent enumerable value"
		Just x -> return x

select :: Enumerable a -> Integer -> Maybe a
select enum i
	| i < 0 || i >= count enum = Nothing
	| otherwise = Just $ selector enum i

enumerate :: Enumerable a -> [a]
enumerate enum = fromMaybe (error "incoherent enumerable value") . select enum
	<$> [0..count enum-1]

-- different ways of specifying a range of values. it's assumed that these atomic elements will have counts less than Int's maxBound and thus can be constructed like this safely.
rangeEnum :: Enum a => (a, a) -> Enumerable a
rangeEnum (lo, hi) = Enumerable (fromIntegral all) $ \i -> toEnum $ fromEnum lo + fromIntegral i
	where
		all = fromEnum hi - fromEnum lo + 1

rangeNum :: Integral a => (a, a) -> Enumerable a
rangeNum (lo, hi) = Enumerable (fromIntegral all) $ \i -> lo + fromIntegral i
	where
		all = hi - lo + 1

-- this does require evaluating the entire input list, so don't make it too huge
from :: [a] -> Enumerable a
from [] = EnumerableNil
from vs = Enumerable (fromIntegral $ length vs) $ \i -> vs !! fromIntegral i