11 July 2013

The Polar Game in Haskell, Day 5 1/2: Refactoring with a Monad

The job search has eaten my brain for the last few days -- have I mentioned yet that I need a job? Oh, yes, I believe I may have -- but I'm taking some time to press on with my Haskell larnin', especially since I've been getting great, helpful feedback.

The first thing I did was make some minor fixes to the list implementation, as suggested by Jeff. It's working now and my version looks like this:

next_board_list :: BoardList -> Pos -> Dir ->
    ( Bool, BoardList )
next_board_list board pos dir =
    let ( penguin_moved, updated_view_list ) =
        step_list $ view_list board pos dir
    in ( penguin_moved, update_board_from_view_list 
         board pos dir updated_view_list )

apply_view_list_to_row :: [ Tile ] -> Int -> Bool -> [ Tile ] -> [Tile]
apply_view_list_to_row orig pos True update =
    take ( pos + 1 ) orig ++ update
apply_view_list_to_row orig pos False update =
    ( reverse update ) ++ ( drop pos orig )

apply_view_list_to_rows :: BoardList -> Int -> Int -> Bool -> [ Tile ]
    -> BoardList
apply_view_list_to_rows orig row pos is_forward update =
    take row orig ++
    nest ( apply_view_list_to_row ( orig !! row ) pos
           is_forward update ) ++
    drop ( row + 1 ) orig
    where nest xs = [xs]

update_board_from_view_list :: BoardList -> Pos -> Dir -> [ Tile ]
    -> BoardList
update_board_from_view_list board pos dir updated_view_list
    | is_eastwest = apply_view_list_to_rows board
                        ( posY pos ) ( posX pos )
                        is_forward updated_view_list
    | otherwise = transpose ( apply_view_list_to_rows ( transpose board )
                         ( posX pos ) ( posY pos ) 
                         is_forward updated_view_list )
    where is_forward = elem dir [ East, South ]
          is_eastwest = elem dir [ East, West ]

This code is on GitHub here.

Now, it turns out that Jeff did more than suggest a refactoring -- he actually did something I haven't quite gotten my head around yet, which is to refactor my code to use a monad for managing some of this task. He forked my code in his own GitHub repo here and sent me some notes to share on my blog. Here's part of what he said:

The way I got my head wrapped around monads was to think of them as "important stuff to do, but not the point". You need to do some housekeeping that's important, but it's not the reason you're writing this function. The classic example is division. You're writing a math library, and you need to implement division. Division by zero is something you need to deal with sanely, but it's not the point; you're writing the function because you want to divide by things that aren't zero. So, to handle the zero case, you return a Maybe instead of a simple number. Only now you can't just add numbers together with division, because you're dealing with Maybes, not numbers. So you end up implementing addition with Maybes, except that makes no sense, as adding never fails, and people using your math library get annoyed because now *they* have to deal with division-by-zero errors even when they're not dividing, and it's a mess. Except -- Maybe is a monad. So you skip all that mess, implement division with a Maybe, everything else without, and use the cool monad and functor features of the language to bridge the gaps. The same pattern exists with scorekeeping. A lot of the functions in your code need to keep track of the score and occasionally award points, but scores aren't "the point" of, say, collide. And when you start thinking about all the places you need to worry about scores, you start seeing scorekeeping infect all kinds of weird places in your code. I think you even mentioned having to "uglify" your code with scorekeeping in your blog post.

Yes, yes, yes -- mainly the chain of function invocations that handle generating the next board, down to the collide calls. Because it's only at the point where a heart disappears that we can decrement the heart count. Without state, I can't make this a global state. In a purely function form, I have to "thread" the indication that the heart count should be decreased through the whole chain of function signatures, which now all have to return an extra thing.

So, minimize the ugly with monads. Just do what you need to do to pass around the score, and deal with it when it's appropriate. (In my implementation, that was in next_world). The Writer monad is perfect for the job. It uses a monoid, which is a fancy ways of saying "something that knows how to grow". Lists are monoids, because you can append to them. Numbers are monoids, because you can add and multiply them. And so on. What the Writer monad does is take care of the adding part. You just return the thing you're working with, and the monad tacks it on using the monoid. Specifically, with scorekeeping, you just note how many points each individual action takes, and the monad does the adding together. When you finally deal with the score in next_world, you get all the accumulated points in one tidy variable.

OK, cool... let's see what he came up with!

import Control.Monad.Writer


-- Keep track of the score with a writer monad
type ScoreTracker = Writer ( Sum Int )

OK, let me pause there and see if I can make sense of that. Learn You a Haskell says

Whereas Maybe is for values with an added context of failure and the list is for non-deterministic values, the Writer monad is for values that have another value attached that acts as a sort of log value. Writer allows us to do computations while making sure that all the log values are combined into one log value that then gets attached to the result.

OK, I think I get that -- in Learn You it is used for implementing logging, not scoring of a game, but it seems like it could be generalizable. The example given does this just kind of thing I was mentioning -- makes a simple function return a tuple to pass both the actual interesting return value and the log string, or in our case I think we want a score. Learn You continues:

When we were exploring the Maybe monad, we made a function applyMaybe, which took a Maybe a value and a function of type a -> Maybe b and fed that Maybe a value into the function, even though the function takes a normal a instead of a Maybe a. It did this by minding the context that comes with Maybe a values, which is that they are values with possible failure. But inside the a -> Maybe b function, we were able to treat that value as just a normal value, because applyMaybe (which later became >>=) took care of checking if it was a Nothing or a Just value. In the same vein, let's make a function that takes a value with an attached log, that is, an (a,String) value and a function of type a -> (b,String) and feeds that value into the function. We'll call it applyLog. But because an (a,String) value doesn't carry with it a context of possible failure, but rather a context of an additional log value, applyLog is going to make sure that the log of the original value isn't lost, but is joined together with the log of the value that results from the function.

Oooh, again, that sounds very promising. So I'm convinced that Writer is the right abstraction here. The values that Writer gets are Sum and Int -- Sum is our monoid, Int is a type we're going to use to accumulate the updated score. (To go along with the Polar game logic, I think there really should ultimately be two scores -- one should be the heart count for a given board, which decrements, and gets tested against zero to indicate board completion, and the other should be a level, which increments as the player moves through the levels, but never mind that for now).

Jeff then came up with:

noscore :: a -> ScoreTracker a
noscore x = writer (x, Sum 0)

score :: a -> ScoreTracker a
score x = writer (x, Sum 1)

Two functions, noscore and score. I think these are both monadic return -- injecting a value, passing it to the next step while applying the sum operation. So let's see how he uses it. here's my slide function:

slide :: [ Tile ] -> [ Tile ]
slide ( Ice_Block : ts ) | ( null ts ) || ( blocking $ head ts ) = 
    ( Ice_Block : ts )
slide ( t : Empty : ts ) =
    ( Empty : ( slide ( t : ts ) ) )
slide ( t : ts ) | ( null ts ) || ( blocking $ head ts ) =
    collide ( t : ts )

I'm not going to take Jeff's current version, because he's restructured it a bit using guards, which obscures just the differences due to the use of the ScoreTracker, but here's a version that does the same thing. We don't have to explictly construct the return tuples:

slide' :: [ Tile ] -> ScoreTracker [ Tile ]
slide' ( Ice_Block : ts ) | ( null ts ) || ( blocking $ head ts ) =
    noscore ( Ice_Block : ts )
slide' ( t : Empty : ts ) =
    noscore ( Empty : ( slide ( t : ts ) ) )
slide' ( t : ts ) | ( null ts ) || ( blocking $ head ts ) =
    collide ( t : ts )

And this doesn't actually compile. Note that collide doesn't handle the monad -- the compiler warns us as Jeff described:

    Couldn't match expected type `ScoreTracker [Tile]'
                with actual type `[Tile]'
    In the return type of a call of `collide'
    In the expression: collide (t : ts)
    In an equation for slide':
        slide' (t : ts)
          | (null ts) || (blocking $ head ts) = collide (t : ts)

That seems pretty clear -- so I have to fix it up the same way:

collide' :: [ Tile ] -> ScoreTracker [ Tile ]
collide' [] = noscore []
collide' ( t : ts ) | fixed t = 
    noscore ( t : ts )
collide' ( Bomb : Mountain : ts) = 
    noscore ( [ Empty, Empty ] ++ ts )
collide' ( Heart : House : ts ) = score ( [ Empty, House ] ++ ts )
collide' ( Ice_Block : ts ) | ( null ts ) || ( blocking $ head ts ) = 
    noscore ( Empty : ts )
collide' ( t : ts ) | ( movable t ) && ( ( null ts ) ||
    ( blocking $ head ts ) ) = noscore ( t : ts )
collide' ( t : Empty : ts ) | movable t = 
    noscore ( Empty : ( slide( t : ts ) ) )

And slide' should call collide' instead of collide, of course. So once this is compiled and loaded into GHCI, we can play with it and compare it to the original collide:

*Main> :t collide'
collide' :: [Tile] -> ScoreTracker [Tile]
*Main> :t collide
collide :: [Tile] -> [Tile]
*Main> collide [ Bomb, Mountain ]
*Main> collide [ Heart, House ]
*Main> collide' [ Heart, House ]

    No instance for (Show (ScoreTracker [Tile]))
      arising from a use of `print'
    Possible fix:
      add an instance declaration for (Show (ScoreTracker [Tile]))
    In a stmt of an interactive GHCi command: print it

Er, yeah. The result is not printable, but can we see its type?

*Main> :t ( collide' [ Heart, House ] )
( collide' [ Heart, House ] ) :: ScoreTracker [Tile]

In fact, we can. So there might be an easy way to make the monadic type printable -- deriving ( Show ) doesn't work -- but first, how do we extract the values? Well, we get back the return value of the whole chain from runWriter:

*Main> runWriter $ collide' [Heart, House]
([Empty,House],Sum {getSum = 1})

What's the type? It's just a tuple:

*Main> :t ( runWriter $ collide' [Heart, House] )
( runWriter $ collide' [Heart, House] ) :: ([Tile], Sum Int)
*Main> fst $ runWriter $ collide' [Heart, House]
*Main> snd $ runWriter $ collide' [Heart, House]
Sum {getSum = 1}

Anyway, I think my mind is blown enough for today. I'm going to stop there. Jeff has made some other modifications to my code here and there -- modifications that improve the clarity -- but I'll have to get back to those. I'm off to read the monad tutorials again, and maybe understand them better this time!


Jeff Licquia said...

Good luck with the job search. I hope something pans out soon.

It occurs to me that I was a bit too clever in my code. When people talk about the Maybe monad, they usually talk about "Maybe a", where "a" is something else. Writer is like that, but it takes two things: the monoid, and the "something else" like what Maybe takes. So, defining ScoreTracker might make more sense defined like this:

type ScoreTracker a = Writer (Sum Int) a

That corresponds more closely to the "Maybe a" stuff that other tutorials talk about.

I think you got there eventually, but it's worth keeping consistent, and maybe someone else won't make the leap.

Ultimately, I think using runWriter is the best way to get the result at the ghci command line. In theory, we could use "instance" syntax to make ScoreTracker an instance of Show, but I couldn't get it to work, and for just doodling at the command line the runWriter form works fine.

I'm actually teaching myself the State monad now. It's got its own level of weird beyond all the monadic goodness. I think we can make Writer work for the heart counter, too, but you mentioning "state" made me think of how to do this with the State monad. But that just makes my brain hurt, so we'll skip it for now. :-)

Paul R. Potts said...

Jeff, State was the first one I tried to understand after how to use the basic IO monad and I had a lot of trouble. This one seems easier! I am going over functors and monoids in _Learn You a Haskell_. I'm thinking on tricks that would show the progress of the ScoreTracker better on the command line. Please keep me posted with what you learn about State. I'm getting there -- being able just about understand how Writer works was very encouraging!

Matt Walton said...

I always felt the State monad was a bit like cheating. "Oh we're in a language that doesn't have mutable state, let's just pretend that we have." You might as well run in IO and use actual mutables, says the part of my brain that conveniently ignores the real differences between pure monads and actual effects for the sake of being able to make dramatic statements.

I never figured out Writer, but that was probably because I didn't need to.

The last serious thing I wrote that used State was for my BSc dissertation and State seemed highly appropriate at the time because I was writing a compiler and needed to carry a symbol table and other such information around and State made that very convenient.

Thus, one then presumes that using State to model, well, game state, makes a lot of sense at some level, even if it's not perhaps the most... hmm... Haskelly thing to do. Whatever 'Haskelly' means.