如何从头开始编写递归下降解析器？

Question

作为一个纯粹的学术练习,我从头开始编写一个递归下降解析器 - 不使用ANTLR或lex/yacc.

我正在写一个简单的函数,它将数学表达式转换为它们的等效AST.我有以下内容:

// grammar
type expr =
    | Lit of float
    | Add of expr * expr
    | Mul of expr * expr
    | Div of expr * expr
    | Sub of expr * expr

// tokens
type tokens =
    | Num of float
    | LParen | RParen
    | XPlus | XStar | XMinus | XSlash

let tokenize (input : string) =
    Regex.Matches(input.Replace(" ", ""), "\d+|[+/*\-()]")
    |> Seq.cast<Match>
    |> Seq.map (fun x -> x.Value)
    |> Seq.map (function
        | "+" -> XPlus
        | "-" -> XMinus
        | "/" -> XSlash
        | "*" -> XStar
        | "(" -> LParen
        | ")" -> RParen
        | num -> Num(float num))
    |> Seq.to_list

因此,tokenize "10 * (4 + 5) - 1"返回以下标记流:

[Num 10.0; XStar; LParen; Num 4.0; XPlus; Num 5.0; RParen; XMinus; Num 1.0]

此时,我想根据运算符优先级将令牌流映射到其AST:

Sub(
    Mul(
        Lit 10.0
        ,Add(Lit 4.0, Lit 5.0)
       )
    ,Lit 1.0
   )

但是,我正在画一个空白.我从来没有从头开始编写解析器,我甚至不知道如何开始.

如何将令牌流转换为代表性的AST？

Answer 1

你知道语言语法吗？

假设是的,你有一个规则的语法

...
addTerm := mulTerm addOp addTerm
         | mulTerm

addOp   := XPlus | XMinus

mulTerm := litOrParen mulOp mulTerm
         | litOrParen
...

最终变成代码(在浏览器中编写代码,从未编译)

let rec AddTerm() =
    let mulTerm = MulTerm() // will parse next mul term (error if fails to parse)
    match TryAddOp with  // peek ahead in token stream to try parse
    | None -> mulTerm    // next token was not prefix for addOp rule, stop here
    | Some(ao) ->        // did parse an addOp
         let rhsMulTerm = MulTerm()
         match ao with
         | XPlus -> Add(mulTerm, rhsMulTerm)
         | XMinus -> Sub(mulTerm, rhsMulTerm)
and TryAddOp() =
    let next = tokens.Peek() 
    match next with
    | XPlus | XMinus ->
        tokens.ConsumeNext()
        Some(next)
    | _ -> None
...

希望你看到基本的想法.这假设一个全局可变令牌流,允许"查看下一个令牌"和"消耗下一个令牌".