Exploring lists as instances of MonadPlus in Haskell by implementing filter

gistfile1.hs

> import Control.Monad(MonadPlus(mzero),liftM,unless)

The regular filter can be implemented recursively:

> f1 _ [] = []
> f1 test (a:as) | test a = a : f1 test as | otherwise = f1 test as

Or the recursion can be abstracted:

> f2 test list = foldr (\ a rest -> if test a then a : rest else rest) [] list

Since a list is an instance of MonadPlus, implement generalized filter, which also works with Maybe:

> f3 test list = do { a <- list; if test a then return a else mzero }

Now, for some gratuitous obfuscation:

Replace the if with unless:

> f4 test list = do { a <- list; liftM (const a) (unless (test a) mzero) }

Remove the do notation:

> f4' test list = list >>= \ a -> liftM (const a) (unless (test a) mzero)

Converting to point-free, using the S combinator:

> f4'' test list = list >>= s (liftM . const) (flip unless mzero . test)
>   where s t u v = t v (u v)

> f4''' test = (>>= s (liftM . const) ((flip unless mzero .) test)
>   where s t u v = t v (u v)

Finally:

> f5 :: MonadPlus m => (a -> Bool) -> m a -> m a
> f5=flip(>>=).s(liftM.const).(flip unless mzero.)where s t u v=t v(u v)