Stefan O'Rear schrieb:
On Mon, Aug 13, 2007 at 04:35:12PM +0200, apfelmus wrote:
My assumption is that we have an equivalence
forall a,b . m (a -> m b) ~ (a -> m b)
because any side effect executed by the extra m on the outside can well be delayed until we are supplied a value a. Well, at least when all arguments are fully applied, for some notion of "fully applied"
(\a x -> a >>= ($ x)) ((\f -> return f) X) ==> (β) (\a x -> a >>= ($ x)) (return X) ==> (β) (\x -> (return X) >>= ($ x)) ==> (monad law) (\x -> ($ x) X) ==> (β on the sugar-hidden 'flip') (\x -> X x) ==> (η) X
Up to subtle strictness bugs arising from my use of η :), you're safe.
Yes, but that's only one direction :) The other one is the problem: return . (\f x -> f >>= ($ x)) =?= id Here's a counterexample f :: IO (a -> IO a) f = writeAHaskellProgram >> return return f' :: IO (a -> IO a) f' = return $ (\f x -> f >>= ($ x)) $ f ==> (β) return $ \x -> (writeAHaskellProgram >> return return) >>= ($ x) ==> (BIND) return $ \x -> writeAHaskellProgram >> (return return >>= ($ x)) ==> (LUNIT) return $ \x -> writeAHaskellProgram >> (($ x) return) ==> (β) return $ \x -> writeAHaskellProgram >> return x Those two are different, because clever = f >> return () = writeAHaskellProgram clever' = f' >> return () = return () are clearly different ;) Regards, apfelmus