Modified showPiece to use lookup table

[PatrickLerner]

showPiece now uses the same typeList lookup table that readPiece uses.

[paulcc]

Consider: where do the errors (or the possibility) come from?

Basically, from the potential for mismatch between the constructors in the type-map and the ones defined. We can simplify this by defining one function for converting Pieces to (lower-case) chars and then construct the type-map from this.

ie
letter_for King = 'k'
letter_for Queen = 'q'

type_map = map (\p -> (letter_for p, p)) [minBound .. maxBound]

NB you need to add "deriving (Enum, Bounded, ...)" somewhere

then, any missing char for a piece is a run-time error (missing case for letter_for) OR could even be caught at compile time if you have the right warnings turned on.

also it might help to push the colour handling elsewhere, eg with

color_fn White = id
color_fn Black = upcase

so you can then say

showPiece (Piece col thing) = color_fn col $ letter_for thing

You might call this "defensive programming" - ie anticipating where errors might occur and coding in a way to prevent them being an issue

[reinh]

@paulcc Thanks very much for your comments!

As a simple product type composed of sum types, it's trivial to prove that a function over Piece is total. One simply must ensure that each possible piece (the cartesian product colors x types ) in the domain is mapped. If the function from Piece is provably total then a runtime error based on a missing piece mapping is impossible. It should be possible, then, to prove both the totality and correctness of, say:

letterFor :: Piece -> Char
letterFor (Piece color ptype) = colorize letter
  where colorize = case color of
                     White -> toUpper
                     Black -> id
        letter = fromJust $ lookup ptype letterList
        letterList = map swap typeList

where colorize is a total function over PColor and letter is a total function over PType, and the two are composed into a total function over Piece.

In lieu of a formal proof, I think QuickCheck could do a great job exercising this code if Piece, PColor and PType are made instances of Arbitrary.

[reinh]

@benjaminfjones Yes, it would be better to do that at the top-level.