Function Composition Do Notation

Question

Is there a "do notation" syntactic sugar for simple function composition?

(i.e. (.) :: (b -> c) -> (a -> b) -> a -> c)

I'd like to be able to store results of some compositions for later (while still continuing the chain.

I'd rather not use the RebindableSyntax extension if possible.

I'm looking for something like this:

composed :: [String] -> [String]
composed = do
    fmap (++ "!!!")
    maxLength <- maximum . fmap length
    filter ((== maxLength) . length)

composed ["alice", "bob", "david"]
-- outputs: ["alice!!!", "david!!!"]

I'm not sure something like this is possible, since the result of the earlier function essentially has to pass "through" the bind of maxLength, but I'm open to hearing of any other similarly expressive options. Basically I need to collect information as I go through the composition in order to use it later.

Perhaps I could do something like this with a state monad?

Thanks for your help!

Edit

This sort of thing kinda works:

split :: (a -> b) -> (b -> a -> c) -> a -> c
split ab bac a = bac (ab a) a

composed :: [String] -> [String]
composed = do
    fmap (++ "!!!")
    split 
        (maximum . fmap length)
        (\maxLength -> (filter ((== maxLength) . length)))

Answer 1

One possible way to achieve something like that are arrows. Basically, in “storing interstitial results” you're just splitting up the information flow through the composition chain. That's what the &&& (fanout) combinator does.

import Control.Arrow

composed = fmap (++ "!!!")
       >>> ((. length) . (==) . maximum . fmap length &&& id)
       >>> uncurry filter

This definitely isn't good human-comprehensible code though.

A state monad would seem to allow something related too, but the problem is that the state type is fixed through the do block's monadic chain. That's not really flexible enough to pick up different-typed values throughout the composition chain. While it is certainly possible to circumvent this (amongst them, indeed, RebindableSyntax), this too isn't a good idea IMO.

Answer 2

The type of (<*>) specialised to the function instance of Applicative is:

(<*>) :: (r -> a -> b) -> (r -> a) -> (r -> b)

The resulting r -> b function passes its argument to both the r -> a -> b and the r -> a functions, and then uses the a value produced by the r -> a function as the second argument of the r -> a -> b one.

What does this have to do with your function? filter is a function of two arguments, a predicate and a list. Now, a key aspect of what you are trying to do is that the predicate is generated from the list. That means the core of your function can be expressed in terms of (<*>):

-- Using the predicate-generating function from leftaroundabout's answer.
maxLengthOnly :: Foldable t => [t a] -> [t a]
maxLengthOnly = flip filter <*> ((. length) . (==) . maximum . fmap length)

composed :: [String] -> [String]
composed = maxLengthOnly . fmap (++ "!!!")

This maxLengthOnly definition would be a quite nice one-liner if the pointfree predicate-generating function weren't so clunky.

Since the Applicative instance of functions is equivalent in power to the Monad one, maxLengthOnly can also be phrased as:

maxLengthOnly = (. length) . (==) . maximum . fmap length >>= filter

(The split you added to your question, by the way, is (>>=) for functions.)

A different way of writing it with Applicative is:

maxLengthOnly = filter <$> ((. length) . (==) . maximum . fmap length) <*> id

It is no coincidence that this looks a lot like leftaroundabout's solution: for functions, (,) <$> f <*> g = liftA2 (,) f g = f &&& g.

Finally, it is also worth noting that, while it is tempting to replace id in the latest version of maxLengthOnly with fmap (++ "!!!"), that won't work because fmap (++ "!!!") changes the length of the strings, and therefore affects the result of the predicate. With a function that doesn't invalidate the predicate, though, it would work pretty well:

nicerComposed = filter
    <$> ((. length) . (==) . maximum . fmap length) <*> fmap reverse

GHCi> nicerComposed ["alice","bob","david"]
["ecila","divad"]

Answer 3

As leftaroundabout mentioned, you can use Arrows to write your function. But, there is a feature in ghc Haskell compiler, which is proc-notation for Arrows. It is very similar to well-known do-notation, but, unfortunately, not many people aware of it.

With proc-notation you can write your desired function in next more redable and elegant way:

{-# LANGUAGE Arrows #-}

import Control.Arrow (returnA)
import Data.List     (maximum)

composed :: [String] -> [String]
composed = proc l -> do
    bangedL <- fmap (++"!!!")        -< l
    maxLen  <- maximum . fmap length -< bangedL
    returnA -< filter ((== maxLen) . length) bangedL

And this works in ghci as expected:

ghci> composed ["alice", "bob", "david"]
["alice!!!","david!!!"]

If you are interested, you can read some tutorials with nice pictures to understand what is arrow and how this powerful feature works so you can dive deeper into it:

https://www.haskell.org/arrows/index.html

https://en.wikibooks.org/wiki/Haskell/Understanding_arrows