Bowling kata as a zipper

A few days ago I have practiced the bowling kata with one of the members of the Software Crafters Lyon.

It's a kata I've only tried two times before that (and I've never played a real world bowling game, though, there is a bowling 10 minutes away from my home).

Let's dive in with some basic tests:

it "A game with no pins down should be 0" $
  bowlingScore (replicate 20 0) `shouldBe` 0
it "A game with two pins down on each try should be 40" $
  bowlingScore (replicate 20 2) `shouldBe` 40

Note: I have choosen to represent tries and not frames for simplicity, which is not a safe representation, but we aim to trust our inputs.

A trivial implementation is to simply sum tries:

bowlingScore :: [Int] -> Int
bowlingScore = sum

Then, we should handle spares (when it takes two tries to knock them all down):

it "A game with all 5-spares frames should be 150" $
  bowlingScore (replicate 21 5) `shouldBe` 150

In order to do that show somehow model the frame.

An easy way to have arbitrary list traversal is to use unfoldr which iterate while having a valid output:

bowlingScore :: [Int] -> Int
bowlingScore = sum . take 10 . unfoldr go
  where
    go =
      \case
        (x : y : z : nexts)
          | x + y == 10 -> Just (10 + z, z : nexts)
          | otherwise -> Just (x + y, z : nexts)
        (x : y : nexts) -> Just (x + y, nexts)
        [] -> Nothing

There is a design tension here:

• go is partial (i.e. we do not handle 1-element list [_]), in production code, warning would make it fail
• take 10 emphasis the number of frames

Finally we have to handle strikes (10 pins down in one try):

it "A game with all strike frames should be 300" $
  bowlingScore (replicate 12 10) `shouldBe` 300

All we have to do it add one line for this case:

bowlingScore :: [Int] -> Int
bowlingScore = sum . take 10 . unfoldr go
  where
    go =
      \case
        (x : y : z : nexts)
          | x == 10 -> Just (10 + y + z, y : z : nexts)
          | x + y == 10 -> Just (10 + z, z : nexts)
          | otherwise -> Just (x + y, z : nexts)
        (x : y : nexts) -> Just (x + y, nexts)
        [] -> Nothing

There is something quite annoying: in each of our cases we look for two or three elements which looks like a good use case for a Zipper.

It could be as simple as:

data BowlingZipper a = Z a a [a]

We can rewrite our function adding a local smart constructor:

bowlingScore :: [Int] -> Int
bowlingScore = sum . take 10 . unfoldr go . toBowlingZipper
  where
    go =
      \case
        Z x y (z : nexts)
          | x == 10 -> Just (10 + y + z, Z y z nexts)
          | x + y == 10 -> Just (10 + z, toBowlingZipper (z : nexts))
          | otherwise -> Just (x + y, toBowlingZipper (z : nexts))
        Z x y nexts -> Just (x + y, toBowlingZipper nexts)
    toBowlingZipper (x : y : nexts) = Z x y nexts

go is now a total function (i.e. all branches are covered), only toBowlingZipper (the smart constructor) is partial, which is better, we could push it to the boundaries in more complex project, letting our core domain work only with sound values.

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