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2013-12-05T18:24:42.697
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2013-12-06T14:09:55.057
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2013-12-06T14:09:55.057
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If you want to eliminate redundant parentheses, you will need to pass around some precedence information. For example, in Haskell, the <code>showsPrec</code> function embodies this pattern; it has type <pre><code>showsPrec :: Show a => Int -> a -> String -> String </code></pre> where the first <code>Int</code> argument is the precedence of the current printing context. The extra <code>String</code> argument is a trick to get efficient list appending. I'll demonstrate how to write a similar function for your type, though admittedly in Haskell (since I know that language best) and without using the extra efficiency trick. The idea is to first build a string that has no top-level parentheses -- but does have all the parentheses needed to disambiguate subterms -- then add parentheses only if necessary. The <code>unbracketed</code> computation below does the first step. Then the only question is: when should we put parentheses around our term? Well, the answer to that is that things should be parenthesized when a low-precedence term is an argument to a high-precedence operator. So we need to compare the precedence of our immediate "parent" -- called <code>dCntxt</code> in the code below -- to the precedence of the term we're currently rendering -- called <code>dHere</code> in the code below. The <code>bracket</code> function below either adds parentheses or leaves the string alone based on the result of this comparison. <pre><code>data Formula = Atom String | Neg Formula | Conj Formula Formula | Disj Formula Formula precedence :: Formula -> Int precedence Atom{} = 4 precedence Neg {} = 3 precedence Conj{} = 2 precedence Disj{} = 1 displayPrec :: Int -> Formula -> String displayPrec dCntxt f = bracket unbracketed where dHere = precedence f recurse = displayPrec dHere unbracketed = case f of Atom s -> s Neg p -> "~ " ++ recurse p Conj p q -> recurse p ++ " & " ++ recurse q Disj p q -> recurse p ++ " | " ++ recurse q bracket | dCntxt > dHere = \s -> "(" ++ s ++ ")" | otherwise = id display :: Formula -> String display = displayPrec 0 </code></pre> Here's how it looks in action. <pre><code>*Main> display (Neg (Conj (Disj (Conj (Atom "a") (Atom "b")) (Atom "c")) (Conj (Atom "d") (Atom "e")))) "~ ((a & b | c) & d & e)" </code></pre>
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1. POBetter display of boolean formulas
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1. USDaniel Wagner
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1. USDaniel Wagner
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