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Incremental, undoable parsing in OCaml as the general parser inversion
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Date: -- (:)
From: oleg@p...
Subject: Incremental, undoable parsing in OCaml as the general parser inversion

This message is to show that the incremental parsing in OCaml is a
solved problem -- essentially for any parser. Moreover, the procedure
to convert from a regular parser to an incremental one is independent
of the parser implementation. The incremental parsing lets us parse
from a stream that is only partially known. The parser may
report what it can and will ask for more input. When more input is
supplied, the parsing resumes. No OS threads are required. The
solution to control inversion is to use delimited continuations --
which are designed for the purpose of giving fine control over
continuations in direct-style programs.

skaller wrote:
> This problem is not restricted to parsers .. it's a general
> problem with Ocaml and also C, C++, and most other languages.
> My language Felix solves this problem for procedures with
> user space threading .. but it doesn't work with functions.
> [And the builtin GLR parser is purely functional:]

The solution below works especially well with functions. That is, if
the parser maintains no visible state, the parsing is not only
incremental but is also undoable and restartable. If, after ingesting
the current chunk of input the parser reported a problem, we can `go
back' and supply a different.

> Other languages like Scheme and I think Haskell and MLton
> have more general solutions because they're not restricted
> to the archaic concept of a linear stack.

Linear or segmented stack is an implementation detail. The central
issue is delimited continuations. In fact, OCaml has a rare
distinction of being the first system with widely available native
delimited continuations (the native implementation of `control' was
announced for Scheme48 back at ICFP02, but it was not included in the
Scheme48 distribution). So, OCaml is well ahead of the pack.

The solution is illustrated below. For simplicity, we'll be using
Genlex.make_lexer of OCaml 3.09 as our parser (it is quite
inconvenient for me at the moment to upgrade to OCaml 3.10).  Code
fragments (cut and pasted from the eshell buffer) are given below
within [[ ... ]] brackets.

First, preliminaries:


(* Open the DelimCC library
open Delimcc;;
let shift p f = take_subcont p (fun sk () ->
  push_prompt p (fun () -> (f (fun c -> 
    push_prompt p (fun () -> push_subcont sk (fun () -> c))))))

open Stream;;
open Printf;;

First, we define the lexer and demonstrate non-incremental parsing. We
apply the lexer to a sample stream and print out the produced tokens.
We use the standard library Stream.iter function.

let lexer = Genlex.make_lexer ["+";"-";"*";"/";"let";"="; "("; ")"];;

let stream_fn1 str = fun pos ->
  (* printf "stream_fn1: asked for char #%d\n" pos; *)
  if pos < String.length str then Some str.[pos] else None;;

let show_token_stream = Stream.iter (function 
  | Genlex.Kwd s    -> printf "Stream elem: Kwd %s\n" s
  | Genlex.Ident s  -> printf "Stream elem: Ident %s\n" s
  | Genlex.Int d    -> printf "Stream elem: int %d\n" d
  | Genlex.Float f  -> printf "Stream elem: float %g\n" f
  | Genlex.String s -> printf "Stream elem: \"%s\"\n" s
  | Genlex.Char c   -> printf "Stream elem: '%c'\n" c

let test1 = show_token_stream (lexer (Stream.from (stream_fn1 
   "let x = 1 + 2 in (* comment *) \"xxx\" ^ x")));;

produces the expected result

	Stream elem: Kwd let
	Stream elem: Ident x
	Stream elem: Kwd =
	Stream elem: int 1
	Stream elem: Kwd +
	Stream elem: int 2
	Stream elem: Ident in
	Stream elem: "xxx"
	Stream elem: Ident ^
	Stream elem: Ident x
	val test1 : unit = ()

We now invert the parser, in the following two lines:
type stream_req = ReqDone | ReqChar of int * (char option -> stream_req);;
let stream_inv p = fun pos -> shift p (fun sk -> ReqChar (pos,sk));;

That is it. If we wish to ask the user for chunks (rather than
characters) of data, we need a simple buffering layer.

let rec filler buffer buffer_pos = function ReqDone -> ReqDone
  | ReqChar (pos,k) as req ->
  let pos_rel = pos - buffer_pos in
  let _ = 
    (* we don't accumulate already emptied buffers. We could. *)
    assert (pos_rel >= 0) in
  if pos_rel < String.length buffer then
    (* desired char is already in buffer *)
    filler buffer buffer_pos (k (Some buffer.[pos_rel])) 
    (* buffer underflow. Ask the user to fill the buffer *)

let cont str (ReqChar (pos,k) as req) = filler str pos req;;
let finish (ReqChar (pos,k)) = filler "" pos (k None);;


We are all set. Please compare the iterator below with test1 above.
The composition "show_token_stream (lexer (Stream.from" is exactly as
before. We merely replaced the stream function stream_fn with
stream_inv. In calculus terms, we replaced "x" with "x+dx".

let test2c0 = 
  let p = new_prompt () in
  push_prompt p (fun () ->
    filler "" 0 (
    show_token_stream (lexer (Stream.from (stream_inv p))); ReqDone));;

Now, the result is 
          val test2c0 : stream_req = ReqChar (0, <fun>)

That is, the parser is suspended, awaiting the character number 0. We
now feed the parser chunks of input. The chunks do
not have to contain complete lexems. For example, a comment may start
in one chunk and end in another. 

let test2c1 = cont "let x = 1 + 2 " test2c0;;
	Stream elem: Kwd let
	Stream elem: Ident x
	Stream elem: Kwd =
	Stream elem: int 1
	Stream elem: Kwd +
	Stream elem: int 2
	val test2c1 : stream_req = ReqChar (14, <fun>)

The parser ate the chunk, produced some tokens, and waits for more

let test2c2 = cont "in (* com " test2c1;;

	Stream elem: Ident in
	val test2c2 : stream_req = ReqChar (24, <fun>)

Here, the chunk contains a non-terminating comment.

let test2c3 = cont "ment *) " test2c2;;
	val test2c3 : stream_req = ReqChar (32, <fun>)

let test2c4 = cont "\"xx" test2c3;;
	val test2c4 : stream_req = ReqChar (35, <fun>)

let test2c5 = cont "x\" " test2c4;;
	Stream elem: "xxx"
	val test2c5 : stream_req = ReqChar (38, <fun>)

Finally the parser produced something, because it got the matching
double quote.

let test2c6 = cont " ^ x" test2c5;;

	Stream elem: Ident ^
	val test2c6 : stream_req = ReqChar (42, <fun>)
let test2c7 = finish test2c6;;

	Stream elem: Ident x
	val test2c7 : stream_req = ReqDone

And we are finished. As we said earlier, the parser can be
restartable and undoable. Suppose, we have changed our mind and
decided to continue parsing after the checkpoint test2c6:

let test2c71 = cont "yx * 10" test2c6;;
let test2c8  = finish test2c71;;

	Stream elem: Ident xyx
	Stream elem: Kwd *
	val test2c71 : stream_req = ReqChar (49, <fun>)
	Stream elem: int 10
	val test2c8 : stream_req = ReqDone

and so we get an `alternative' parse, of an alternative stream. We can go
back to any checkpoint test2c1, test2c2, etc. and continue parsing
from that point.