问题描述
是否有任何常用的方法，甚至是一个库，用于漂亮地打印(和解析)带有(二元)运算符的语法树，这些运算符具有关联性和优先级，以便结果使用尽可能少的括号?
Is there any commonly used method or even a library for pretty printing (and parsing) a syntax tree with (binary) operators that have an associativity and a precedence level assigned, so that the result uses as few brackets as possible?
以命题演算的公式为例:
Take the formulas of propositional calculus as an example:
data Formula
= Atom String
| Not (Formula)
| And (Formula) (Formula)
| Or (Formula) (Formula)
| Imp (Formula) (Formula)
假设优先级是 Imp Imp或 <和 <Not(所以 Not 绑定最多)并且 And、Or 和 Imp应该关联到右边；所以例如 Imp (And (Imp (Atom "A") (Atom "B")) (Atom "A")) (Atom "B") 应该打印类似 (A-> B)/ A ->B.
Assume that the precedence is Imp < Or < And < Not (so Not binds the most) and that And, Or and Imp should associate to the right; so for example Imp (And (Imp (Atom "A") (Atom "B")) (Atom "A")) (Atom "B") should print something like (A -> B) / A -> B.
当然这可以通过模式匹配来实现，但这既乏味又令人不快；我正在从 Coq 证明助手中寻找与此符号类似的简单内容:
Of course this could be achieved by pattern matching but this is tedious and very unpleasant; I'm looking for something similarly simple to this notation from the Coq proof assistant:
Notation "A / B" := (and A B) (at level 80, right associativity).
它生成一个解析器和一个漂亮的打印机.
which generates a parser and a pretty printer.
推荐答案
Formula 的 Show 实例可能如下所示:
A Show instance for Formula might look like this:
instance Show Formula where
showsPrec _ (Atom name) = showString name
showsPrec p (Not formula) = showParen (p > 3) $
showString "\+ " . showsPrec 3 formula
showsPrec p (And lhs rhs) = showParen (p > 2) $
showsPrec 3 lhs . showString " /\ " . showsPrec 2 rhs
showsPrec p (Or lhs rhs) = showParen (p > 1) $
showsPrec 2 lhs . showString " \/ " . showsPrec 1 rhs
showsPrec p (Imp lhs rhs) = showParen (p > 0) $
showsPrec 1 lhs . showString " -> " . showsPrec 0 rhs
这将允许任何 Formula 使用适当的括号 shown :
Which will allow any Formula to be shown with appropriate parens:
main = print $ Imp (And (Imp (Atom "A") (Atom "B")) (Atom "A")) (Atom "B")
打印(print 是 putStrLn .show):
(A -> B) / A -> B
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