如何简化基本算术表达式？

如何简化基本算术表达式？

例如

module ExprOps where 

simplify :: Expr -> Expr
simplify (Plus(Var"x") (Const 0)) = Var "x"

我需要做什么？

module Expr where

-- Variables are named by strings, assumed to be identifiers.
type Variable = String

-- Representation of expressions.
data Expr = Const Integer
          | Var Variable
          | Plus Expr Expr
          | Minus Expr Expr
          | Mult Expr Expr
          deriving (Eq, Show)

我想到的简化是:

0*e = e*0 = 0
1*e = e*1 = 0+e = e+0 = e-0 = e

并且简化常量子表达式,例如Plus(Const 1)(Const 2)将成为Const 3.我不希望连接变量(或变量和常量):Var"st"是Var"s"的不同变量.

我想要实现的是创建一个像上面那样使用被调用函数的模块 simplify :: Expr->Expr

那么,你有正确的通用模型.您只需要更多规则并递归应用简化过程.

simplify :: Expr -> Expr 
simplify (Mult (Const 0) x) = Const 0 
simplify (Mult x (Const 0)) = Const 0
simplify (Plus (Const 0) x) = simplify x
simplify (Plus x (Const 0)) = simplify x 
simplify (Mult (Const 1) x) = simplify x 
simplify (Mult x (Const 1)) = simplify x 
simplify (Minus x (Const 0)) = simpify x
simplify (Plus (Const x) (Const y)) = Const (x + y)
simplify (Minus (Const x) (Const y)) = Const (x - y)
simplify (Mult (Const x) (Const y)) = Const (x * y)
simplify x = x