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If so, you append the appropriate escape sequence to the string already accumulated and advance the current position. Upon encountering the closing character, you return the overall string. An imperative System.Text.StringBuffer object could also have been used to accumulate the string, which is more efficient if strings get very long.
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Note Because lexer rules can pass arguments, there is little need to use mutable state in a lexer simply
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pass additional arguments.
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Recursive-Descent Parsing
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You can now turn your attention to parsing. Let s assume for the moment you are writing an application that performs simple symbolic differentiation, say on polynomials only. Let s say you want to read polynomials such as x^5-2x^3+20 as input from your users, which in turn will be converted to your internal polynomial representation so that you can perform symbolic differentiation and pretty-print the result to the screen. One way to represent polynomials is as a list of terms that are added or subtracted to form the polynomial: type term = | Term of int * string * int | Const of int type polynomial = term list For instance, the polynomial in this example is as follows: [Term (1,"x",5); Term (-2,"x",3); Const 20] In Listing 16-3 we built a lexer and a token type suitable for generating a token stream for the input text (shown as a list of tokens here): [ID "x"; HAT; INT 5; MINUS; INT 2; ID "x"; HAT; INT 3; PLUS; INT 20] Listing 16-4 shows a recursive-decent parser that consumes this token stream and converts it into the internal representation of polynomials. The parser works by generating a lazy list for the token stream. Lazy lists are a data structure in the F# library module Microsoft.FSharp. Collections.LazyList, and they are a lot like sequences with one major addition lazy lists effectively allow you to pattern match on a sequence and return a residue lazy list for the tail of the sequence. Listing 16-4. Recursive-Descent Parser for Polynomials #light open SimpleTokensLex open Lexing
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CHAPTER 16 LEXING A ND PARS ING
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type term = | Term of int * string * int | Const of int type polynomial = term list type tokenStream = LazyList<token * position * position> let tryToken (src: tokenStream) = match src with | LazyList.Cons ((tok, startPos, endPos), rest) -> Some(tok, rest) | _ -> None let parseIndex src = match tryToken src with | Some (HAT, src) -> match tryToken src with | Some (INT num2, src) -> num2, src | _ -> failwith "expected an integer after '^'" | _ -> 1, src let parseTerm src = match tryToken src with | Some (INT num, src) -> match tryToken src with | Some (ID id, src) -> let idx, src = parseIndex src Term (num, id, idx), src | _ -> Const num, src | Some (ID id, src) -> let idx, src = parseIndex src Term(1, id, idx), src | _ -> failwith "end of token stream in term" let rec parsePolynomial src = let t1, src = parseTerm src match tryToken src with | Some (PLUS, src) -> let p2, src = parsePolynomial src (t1 :: p2), src | _ -> [t1], src The functions here have the following types:
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val val val val
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tryToken parseIndex parseTerm parsePolynomial
: : : :
tokenStream tokenStream tokenStream tokenStream
-> -> -> ->
(token * tokenStream) option int * tokenStream term * tokenStream polynomial * tokenStream
You can turn the fslex-generated lexer for the lexer specification in Listing 16-3 into a tokenStream using the following code: let tokenStream inp : tokenStream = // Generate the token stream as a seq<token> seq { let lexbuf = Lexing.from_string inp while not lexbuf.IsPastEndOfStream do match SimpleTokensLex.token lexbuf with | EOF -> yield! [] | token -> yield (token, lexbuf.StartPos, lexbuf.EndPos) } // Convert to a lazy list |> LazyList.of_seq let parse input = let src = tokenStream input let result, src = parsePolynomial src match tryToken src with | Some _ -> failwith "unexpected input at end of token stream!" | None -> result These functions have the following types: val tokenStream: string -> tokenStream val parse: string -> polynomial Note in the previous examples that you can successfully parse either constants or complete terms, but once you locate a HAT symbol you insist on having a number following. This sort of parsing, when you look only at the next token to guide the parsing process is referred to as LL(1), which stands for Left-to-right, Leftmost derivation parsing, where 1 means that only one look-ahead symbol is used. The parser approach we used earlier is called recursive-descent. This has various advantages and disadvantages, and we will be discussing those in a bit. To conclude here, you can look at the parse function in action: > parse "1+3";; val it : polynomial = [Const 1; Const 3] > parse "2x^2+3x+5";; val it : polynomial = [Term (2,"x",2); Term (3,"x",1); Const 5]
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