Partial application using flip

A simple but mildly interesting Haskell trick
Published on October 15, 2019 under the tag haskell

I have been writing Haskell for a reasonable time now – I believe I am coming up on ten years – so sadly the frequency with which I discover delightful things about the language has decreased.

However, I was talking with HVR about the Handle pattern, and the topic of argument order came up. This lead me to a neat use case for flip that I hadn’t seen before.

This blogpost should be approachable for beginners, but when you’re completely new to Haskell and some terms are confusing, I would recommend looking at the Type Classes or Learn You a Haskell materials first.

A few extensions are required to show some intermediary results, but – spoiler alert – they turn out to be unnecessary in the end:

{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleInstances     #-}
{-# LANGUAGE FlexibleContexts      #-}

Currying and partial application

In Haskell, it is idiomatic to specify arguments that are unlikely to change in between function calls first.

For example, let’s look at the type of M.insertWith:

import qualified Data.Map as M
  :: Ord k
  => (a -> a -> a)  -- ^ Merge values
  -> k              -- ^ Key to insert
  -> a              -- ^ Value to insert
  -> M.Map k a      -- ^ Map to insert into
  -> M.Map k a      -- ^ New map

This function allows us to insert an item into a map, or if it’s already there, merge it with an existing element. When we’re doing something related to counting items, we can “specialize” this function by partially applying it to obtain a function which adds a count:

  :: Ord k
  => k            -- ^ Key to increment
  -> Int          -- ^ Amount to increment
  -> M.Map k Int  -- ^ Current count
  -> M.Map k Int  -- ^ New count
increaseCount = M.insertWith (+)

And then we can do things like increaseCount "apples" 4 basket. The extremely succinct definition of increaseCount is only possible because functions in Haskell are always considered curried: every function takes just one element.

Sockets, Handles and more

However – there is a second idiomatic aspect of argument ordering. For imperative code, it is common to put the “object” or “handle” first. base itself is ripe with examples, and packages like network hold many more:

-- From System.IO
  :: Handle -> BufferMode -> IO ()
  :: Handle -> Ptr a -> Int -> IO Int

-- From Control.Concurrent.Chan
  :: Chan a -> a -> IO ()

-- From Control.Concurrent.MVar
  :: MVar a -> (a -> IO (a, b)) -> IO b

This allows us to easily partially apply functions to a specific “object”, which comes in useful in where clauses:

writeSomeStuff :: Chan String -> IO ()
writeSomeStuff c = do
  write "Tuca"
  write "Bertie"
  write "Speckle"
  write = writeChan c

In addition to that, it allows us to replace the type by a record of functions – as I went over in the handle pattern explanation.

Specializing top-level handle functions

However, we end up in a bit of a bind when we want to write succinct top-level definitions, like we did with increaseCount. Imagine we have a Handle to our database:

data Handle = Handle

Some mock utility types:

data Tier = Free | Premium
type MemberId = String

And a top-level function to change a member’s plan:

  :: Handle
  -> Tier       -- ^ New plan
  -> String     -- ^ Comment
  -> MemberId   -- ^ Member to upgrade
  -> IO ()
changePlan = undefined

If we want a specialized version of this, we need to explicitly name and bind h, which sometimes feels a bit awkward:

halloweenPromo1 :: Handle -> MemberId -> IO ()
halloweenPromo1 h = changePlan h Premium "Halloween 2018 promo"

We sometimes would like to be able to write succinct definitions, such as:

halloweenPromo2 :: Handle -> MemberId -> IO ()
halloweenPromo2 = specialize changePlan Premium "Halloween 2018 promo"

But is this possible? And what would specialize look like?

Since this is a feature that relates to the type system, it is probably unsurprising that, yes, this is possible in Haskell. The concept can be represented as changing a function f to a function g:

class Specialize f g where
  specialize :: f -> g

Of course, a function can be converted to itself:

instance Specialize (a -> b) (a -> b) where
  specialize = id

Furthermore, if a Handle (a below) is the first argument, we can skip that it the converted version and first supply the second argument, namely b. This leads us to the following definition:

instance Specialize (a -> c) f => Specialize (a -> b -> c) (b -> f) where
  specialize f = \b -> specialize (\a -> f a b)

This is a somewhat acceptable solution, but it’s not great:

Again, not show stoppers, but not pleasant either.

Flippin’ partial application

The unpleasantness around specialize is mainly caused by the fact that we need a typeclass to make this work for multiple arguments. Maybe using some sort of combinator can give us a simpler solution?

Because we’re lazy, let’s see if GHC has any ideas – we’ll use Typed holes to get a bit more info rather than doing the work ourselves:

halloweenPromo3 :: Handle -> MemberId -> IO ()
halloweenPromo3 =
  changePlan `_` Premium `_` "Halloween 2018 promo"

We get an error, and some suggestions:

posts/2019-10-15-flip-specialize.lhs:152:18: error:
 • Found hole:
     _ :: (Handle -> Tier -> String -> MemberId -> IO ()) -> Tier -> t0
   Where: ‘t0’ is an ambiguous type variable
 • In the expression: _
   In the first argument of ‘_’, namely ‘changePlan `_` Premium’
   In the expression:
     changePlan `_` Premium `_` "Halloween 2018 promo"
 • Relevant bindings include
     halloweenPromo3 :: Handle -> MemberId -> IO ()
       (bound at posts/2019-10-15-flip-specialize.lhs:151:3)
   Valid hole fits include
     flip :: forall a b c. (a -> b -> c) -> b -> a -> c
       with flip @Handle @Tier @(String -> MemberId -> IO ())
       (imported from ‘Prelude’ at posts/2019-10-15-flip-specialize.lhs:1:1
        (and originally defined in ‘GHC.Base’))
     seq :: forall a b. a -> b -> b
       with seq @(Handle -> Tier -> String -> MemberId -> IO ()) @Tier
       (imported from ‘Prelude’ at posts/2019-10-15-flip-specialize.lhs:1:1
        (and originally defined in ‘GHC.Prim’))
     const :: forall a b. a -> b -> a
       with const @(Handle -> Tier -> String -> MemberId -> IO ()) @Tier
       (imported from ‘Prelude’ at posts/2019-10-15-flip-specialize.lhs:1:1
        (and originally defined in ‘GHC.Base’))

Wait a minute! flip looks kind of like what we want: it’s type really converts a function to another function which “skips” the first argument. Is it possible that what we were looking for was really just… the basic function flip?

  :: Handle -> MemberId -> IO ()
halloweenPromo4 =
  changePlan `flip` Premium `flip` "Halloween 2018 promo"

We can make the above pattern a bit cleaner by introducing a new operator:

(/$) :: (a -> b -> c) -> (b -> a -> c)
(/$) = flip
halloweenPromo5 :: Handle -> MemberId -> IO ()
halloweenPromo5 =
  changePlan /$ Premium /$ "Halloween 2018 promo"

Fascinating! I was aware of using flip in this way to skip a single argument (e.g. foldr (flip M.increaseCount 1)), but, in all the time I’ve been writing Haskell, I hadn’t realized this chained in a usable and nice way.

In a way, it comes down to reading the type signature of flip in two ways:

  1. flip :: (a -> b -> c) -> (b -> a -> c)

    Convert a function to another function that has the two first arguments flipped. This is the way I am used to reading flip – and also what the name refers to.

  2. flip :: (a -> b -> c) -> b -> (a -> c)

    Partially apply a function to the second argument. After supplying a second argument, we can once again supply a second argument, and so on – yielding an intuitive explanation of the chaining.

It’s also possible to define sibling operators //$, ///$, etc., to “skip” the first N arguments rather than just the first one in a composable way.

Update: Dan Dart pointed out to me that the sibling operators actually exist under the names of -$, --$, etc. in the composition-extra package.

Should I use this everywhere?

… probably not? While it is a mildly interesting trick, unless it becomes a real pain point for you, I see nothing wrong with just writing:

halloweenPromo6 :: Handle -> MemberId -> IO ()
halloweenPromo6 h = changePlan h Premium "Halloween 2018 promo"