解析数学表达式 [英] Parsing a mathematical expression

问题描述

给定一个包含数学表达式的字符串，给定一组函数/命令并给定一组分配的变量，.NET是否提供工具来快速构建解析器？

Given a string containing a mathematical expression, given a set of functions/commands and given a set of assigned variables, are there tools that .NET provides to quickly build a parser?

我想构建一个简单的解析器，用于分析表达式并将其分解为最简单的组件，例如：

I would like to build a simple parser that analyzes an expression and breaks it into its simplest components, for example:

d * （abs（ab）+ sqrt（c））

成为

1. f = abs（ab）和 g = sqrt（c）


2. e = f + g


3. d * e

1. f = abs(a-b) and g = sqrt(c)
2. e = f + g
3. d*e

推荐答案

查看蔬菜。这是一个示例代码，显示了如何构建表达式评估器（该代码分析表达式并直接计算输出）。可以修改此示例以存储评估树而不是运行它。

Check out veparser as well. Here is a sample code that shows how you can build an expression evaluator( the code parses the expression and directly calculates the output ). This sample can be modified to store the evaluation tree instead of running it.

using System;
using VeParser;

public class MathEvaluator : CharParser
{
    protected override Parser GetRootParser()
    {
        Func<double, double, double> productFunc = (value1, value2) => value1 * value2;
        Func<double, double, double> divideFunc = (value1, value2) => value1 / value2;
        Func<double, double, double> sumFunc = (value1, value2) => value1 + value2;
        Func<double, double, double> subtractFunc = (value1, value2) => value1 - value2;
        Func<double, double> negativeFunc = value => -value;
        Func<double, double> posititveFunc = value => value;


        var dot = token('.');
        var op = token('(');
        var cp = token(')');
        var sumOp = create(sumFunc, token('+'));
        var subtractOp = create(subtractFunc, token('-'));
        var positiveOp = create(posititveFunc, token('+'));
        var negativeOp = create(negativeFunc, token('-'));
        var productOp = create(productFunc, token('*'));
        var divideOp = create(divideFunc, token('/'));

        // Numbers
        var deciamlPlaceValue = 1M;
        var decimalDot = run(() => { deciamlPlaceValue = 1; }, dot);
        var digit = consume((n, d) => n * 10 + char.GetNumericValue(d), keep(Digit));
        var decimalDigit = consume((n, d) => { deciamlPlaceValue = deciamlPlaceValue * 10; return (double)((decimal)n + ((decimal)char.GetNumericValue(d)) / deciamlPlaceValue); }, keep(Digit));
        var number = any(
            /* float */  create(0, seq(zeroOrMore(digit), decimalDot, oneOrMore(decimalDigit))),
            /* int   */  create(0, oneOrMore(digit))
        );

        var expression = createReference();
        var simpleExpression = createReference();
        // Unary
        var unaryOp = any(positiveOp, negativeOp);
        var unaryExpression = update(d => d.action(d.value),
                    createNew(seq(set("action", unaryOp), set("value", expression))));
        // Binary
        var binaryOp = any(sumOp, subtractOp, productOp, divideOp);

        var binaryExpressinoTree = update(x => x.value1, createNew(
            seq(
                set("value1", simpleExpression),
                zeroOrMore(
                    update(d => { var r = base.CreateDynamicObject(); r.value1 = d.action(d.value1, d.value2); return r; },
                        seq(
                            set("action", binaryOp),
                            set("value2", simpleExpression))))
            )));


        var privilegedExpressoin = seq(op, expression, cp);

        setReference(simpleExpression, any(privilegedExpressoin, unaryExpression, number));

        setReference(expression, any(binaryExpressinoTree, simpleExpression));

        return seq(expression, endOfFile());
    }

    public static object Eval(string expression)
    {
        MathEvaluator me = new MathEvaluator();
        var result = me.Parse(expression.ToCharArray());
        return result;
    }
}

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