Logic formula printing in Haskell

Question

I am dealing with some weird problem. I want to write a Haskell program, which will print given logical formulae, i.e.

print (showFormula (I (N (Z 'p')) (A (C (Z 'p') (Z 'q')) (Z 'r'))))

(where I is implication, A - alternative, N - negation, C - conjunction and Z - character)

should print something like that:

"(~p => ((p & q) | r))"

So far, my code looks like that:

data Formula
    = Z Char
    | V Bool
    | N Formula
    | C Formula Formula
    | A Formula Formula
    | I Formula Formula
    | Join Formula Formula

showFormula :: Formula -> String
showFormula (Z c) = [c]
showFormula (Join a b) = (showFormula a) ++ (showFormula b)

showFormula (N a) = '~':(showFormula a)
showFormula (C a b) = "("++(showFormula a)++" & "++(showFormula b)++")"
showFormula (A a b) = "("++(showFormula a)++" | "++(showFormula b)++")"
showFormula (I a b) = "("++(showFormula a)++" => "++(showFormula b)++")"

It does print proper string but only when you input simple formula like (C (Z 'a') (Z 'b')) and it crashes with some expanded formulae. I know that the problem is passing a Formula parameter instead of String to showFormula function, but I have no idea how to change that. Please give me some advices how to fix that.

You may also like [this question with a very similar goal](http://stackoverflow.com/q/20406722/791604). — Daniel Wagner, Jan 23 '14 at 18:20
Note, by the way, that you can write infix constructors if they begin with a `:`, so you could have `Formula :&: Formula`, `Formula :|: Formula`, and `Formula :=> Formula instead of `C`, `A`, and `I`. (You also may want fixity declarations then – perhaps `infixr 3 :&&:`, `infixr 2 :|:`, and `infixr 4 :=>`.) — Antal Spector-Zabusky, Jan 24 '14 at 06:58
Thank you @AntalS-Z, that's pretty handy, but C, A and I are required, because are generated by other program. — bartekmp, Jan 24 '14 at 12:24

score 4 · Accepted Answer · answered Jan 23 '14 at 17:02

4

If you compile your code with the -Wall flag it will show you the following warning:

fml.hs:4:1: Warning:
    Pattern match(es) are non-exhaustive
    In an equation for `showFormula': Patterns not matched: V _

You forgot to write the V case for showFormula so it will crash if it reaches that, similarly to how the head function crashes if you call it with an empty list.

answered Jan 23 '14 at 17:02

hugomg

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@user2342783: Thats not being dumb. Its just a beginner mistake. – hugomg Jan 23 '14 at 17:28

score 2 · Answer 2 · answered Jan 23 '14 at 17:05

Looks like you just missed the (V b) case in your pattern match.

data Formula
    = Z Char
    | V Bool
    | N Formula
    | C Formula Formula
    | A Formula Formula
    | I Formula Formula
    | Join Formula Formula

showFormula :: Formula -> String
showFormula (V b) = show b
showFormula (Z c) = [c]
showFormula (Join a b) = (showFormula a) ++ (showFormula b)

showFormula (N a) = '~':(showFormula a)
showFormula (C a b) = "("++(showFormula a)++" & "++(showFormula b)++")"
showFormula (A a b) = "("++(showFormula a)++" | "++(showFormula b)++")"
showFormula (I a b) = "("++(showFormula a)++" => "++(showFormula b)++")"

main :: IO ()
main = do
  print (showFormula (I (N (Z 'p')) (A (C (Z 'p') (Z 'q')) (Z 'r'))))
  -- "(~p => ((p & q) | r))"

Logic formula printing in Haskell

2 Answers2