Amb

Amb

[oleg]

Andrej Bauer wrote:
> let me point out that amb is supposed to work as an _angelic_
> nondeterministic choice operator. This means it must choose a value
> that, if at all possible, leads to successful completion of the
> computation.... The scheme implementation involves callcc magic. 
> If anyone knows a reasonable implementation of amb, I'd be
> interested to know.

Here it is. Ocaml has something better than call/cc: delimited
continuations. So, amb is trivially implementable, in two lines of
code. We also need a `toplevel function', to tell us if the overall
computation succeeded. One may think of it as St.Peter at the
gate. For now, we take a computation that raises no exception as
successful. In general, even non-termination within a branch can be
dealt with intelligently (cf. `cooperative' threading which must yield
from time to time).

Regarding effects incurred while evaluating branches: one deal with
them as one deal with effects when implementing any transactional
mechanism: you prohibit them, you log the updates, you log the state
before the beginning so to undo, you use zipper for functional
`mutations' (which can be done with delimited continuations, too), you
operate in a sandbox, etc. The ZFS talk gives an example:
 http://pobox.com/~oleg/ftp/Computation/Continuations.html#zipper-fs

Here are the tests. The second one requires a three-step clairvoyance:

let test1 () =
  let v = 
    if (amb [(fun _ -> false); (fun _ -> true)]) then
      7
    else failwith "Sinner!"
  in Printf.printf "got the result %d\n" v;;
let test1r = toplevel test1;;
(* got the result 7 *)

(* Test that invokes the Pythagorean spirit *)
let numbers = List.map (fun n -> (fun () -> n)) [1;2;3;4;5];;
let pyth () = 
  let (v1,v2,v3) =
    let i = amb numbers in
    let j = amb numbers in
    let k = amb numbers in
    if i*i + j*j = k*k then (i,j,k) else failwith "too bad"
  in Printf.printf "got the result (%d,%d,%d)\n" v1 v2 v3;;

let pythr = toplevel pyth;;
(* got the result (3,4,5) *)

(* Open the DelimCC library
  http://pobox.com/~oleg/ftp/Computation/Continuations.html#caml-shift
*)
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 c)))))
;;

(* How evaluation has finished *)
type res = 
    Done                             (* Finished with the result *)
  | Exc     of exn                   (* Got an exception -- no good *)
  | Choices of (unit -> res) list    (* Alternative universes *)

exception Amb		             (* Raise when all choices are bad *)
;;

let topprompt = new_prompt ();;

(* If it looks like an OS scheduler, it's because it is *)
let toplevel thunk =
  let rec loop queue = function 
  | Done (* evaluation of a branch finished successfully *)
     -> ()
  | Exc _ -> try_another queue
  | Choices more  -> (* OK, add them to the end: breadth-first *)
      try_another (queue @ more)
  and try_another = function
  |  [] -> raise Amb (* No more choices *)
  |  h::t -> loop t (try h () with e -> Exc e)
  in
  loop [] (push_prompt topprompt 
	     (fun () -> try let _ = thunk () in Done with e -> Exc e))
;;

(* Split the universe. Something like `fork (2)' *)
let amb choices = shift topprompt (fun sk -> 
  Choices (List.map (fun choice -> (fun () -> sk choice)) choices));;

Amb

[Jonathan Bryant]

All,

I'm having to learn Scheme for a class, and I ran across a simple but  
really useful predicate: amb.  More info on this can be found here:  
http://www.ccs.neu.edu/home/dorai/t-y-scheme/t-y-scheme-Z- 
H-16.html#node_chap_14

Since OCaml doesn't seem to have this, I implemented it:

exception Amb
let rec amb l = match l with
| [] -> raise Amb
| h::t -> try h () with Amb -> amb t

let amb l = try Some (amb l) with Amb -> None

(* val amb : (unit -> 'a) list -> 'a option *)

I know things are not added to the standard library lightly, but it  
seems that this one function doesn't really need it's own library and  
could be easily added somewhere.  It just seems that this would be a  
small but convenient addition.

--Jonathan Bryant