How do I organize my pure functions with my monadic actions idiomatically

Question

I've decided today is the day I fix some of my pure functions that are unnecessarily running in a monadic action. Here's what I have.

flagWorkDays :: [C.Day] -> Handler [WorkDay] 
flagWorkDays dayList =
   flagWeekEnds dayList >>=
   flagHolidays >>=
   flagScheduled >>=
   flagASAP >>=
   toWorkDays

Here is flagWeekEnds, as of now.

flagWeekEnds :: [C.Day] -> Handler [(C.Day,Availability)]
flagWeekEnds dayList = do
   let yepNope = Prelude.map isWorkDay dayList
       availability = Prelude.map flagAvailability yepNope
   return $ Prelude.zip dayList availability

flagHolidays follows a similar pattern. toWorkDays just changes one type to another, and is a pure function.

flagScheduled, and flagASAP are monadic actions. I am not sure how to combine the monadic actions with the pure functions idiomatically in flagWorkDays. Could someone help me fix flagWorkDays, assuming flagWeekEnds and flagHolidays have been made pure?

Answer 1

Let's take a step back for a moment. You have two types of functions, some pure with types of the form a -> b, and some monadic of type a -> m b.

To avoid confusion, let's also stick with right-to-left composition. If you prefer to read left-to-right, just reverse the order of the functions and replace (<=<) with (>=>), and (.) with (>>>) from Control.Arrow.

There are then four possibilities for how these can be composed.

1. Pure then pure. Use regular function composition (.).

    g :: a -> b
    f :: b -> c
    f . g :: a -> c
   

2. Pure then monadic. Also use (.).

    g :: a -> b
    f :: b -> m c
    f . g :: a -> m c
   

3. Monadic then monadic. Use kleisli composition (<=<).

    g :: a -> m b
    f :: b -> m c
    f <=< g :: a -> m c
   

4. Monadic then pure. Use fmap on the pure function and (.) to compose.

    g :: a -> m b
    f :: b -> c
    fmap f . g :: a -> m c
   

Ignoring the specifics of the types involved, your functions are:

flagWeekEnds :: a -> b
flagHolidays :: b -> c
flagScheduled :: c -> m d
flagASAP :: d -> m e
toWorkDays :: e -> f

Let's go from the top. flagWeekEnds and flagHolidays are both pure. Case 1.

flagHolidays . flagWeekEnds
  :: a -> c

This is pure. Next up is flagScheduled, which is monadic. Case 2.

flagScheduled . flagHolidays . flagWeekEnds
  :: a -> m d

Next is flagASAP, now we have two monadic functions. Case 3.

flagASAP <=< flagScheduled . flagHolidays . flagWeekEnds
  :: a -> m e

And finally, we have the pure function toWorkDays. Case 4.

fmap toWorkDays . flagASAP <=< flagScheduled . flagHolidays . flagWeekEnds
  :: a -> m f

And we're done.