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I wrote some toy code to play with the concept of Arrows. I wanted to see if I could write an Arrow which encoded the concept of a stateful function - giving a different value after different calls. {-# LANGUAGE Arrows#-} module StatefulFunc where import Control.Category import Control.Arrow newtype StatefulFunc a b = SF { unSF :: a -> (StatefulFunc a b, b) } idSF :: StatefulFunc a a idSF = SF $ \a -> (idSF, a) dotSF :: StatefulFunc b c -> StatefulFunc a b -> StatefulFunc a c dotSF f g = SF $ \a -> let (g', b) = unSF g a (f', c) = unSF f b in (dotSF f' g', c) instance Category StatefulFunc where id = idSF (.) = dotSF arrSF :: (a -> b) -> StatefulFunc a b arrSF f = ret where ret = SF fun fun a = (ret, f a) bothSF :: StatefulFunc a b -> StatefulFunc a' b' -> StatefulFunc (a, a') (b, b') bothSF f g = SF $ \(a,a') -> let (f', b) = unSF f a (g', b') = unSF g a' in (bothSF f' g', (b, b')) splitSF :: StatefulFunc a b -> StatefulFunc a b' -> StatefulFunc a (b, b') splitSF f g = SF $ \a -> let (f', b) = unSF f a (g', b') = unSF g a in (splitSF f' g', (b, b')) instance Arrow StatefulFunc where arr = arrSF first = flip bothSF idSF second = bothSF idSF (***) = bothSF (&&&) = splitSF eitherSF :: StatefulFunc a b -> StatefulFunc a' b' -> StatefulFunc (Either a a') (Either b b') eitherSF f g = SF $ \e -> case e of Left a -> let (f', b) = unSF f a in (eitherSF f' g, Left b) Right a' -> let (g', b') = unSF g a' in (eitherSF f g', Right b') mergeSF :: StatefulFunc a b -> StatefulFunc a' b -> StatefulFunc (Either a a') b mergeSF f g = SF $ \e -> case e of Left a -> let (f', b) = unSF f a in (mergeSF f' g, b) Right a' -> let (g', b) = unSF g a' in (mergeSF f g', b) instance ArrowChoice StatefulFunc where left = flip eitherSF idSF right = eitherSF idSF (+++) = eitherSF (

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