let debug = ref false
let debug_print s = if !debug then prerr_endline (Lazy.force s) else ()
+let debug_do f = if !debug then f () else ()
open Continuationals.Stack
open NTacStatus
]
type sort = T | P
-type goal = int * int * sort (* goal, depth, sort *)
+type goal = int * sort (* goal, depth, sort *)
type fail = goal * cic_term
type candidate = int * Ast.term (* unique candidate number, candidate *)
-type op =
+type 'a op =
(* goal has to be proved *)
| D of goal
(* goal has to be cached as a success obtained using candidate as the first
* step *)
- | S of goal * cic_term * candidate (* int was minsize *)
-type 'a elem =
- (* menv, subst, size, operations done (only S), operations to do,
- * failures to cache if any op fails *)
- (#tac_status as 'a) * int * op list * op list * fail list
+ | S of goal * (#tac_status as 'a)
+ (* * cic_term * candidate (* int was minsize *) *)
-type 'a auto_status =
- (* list of computations that may lead to the solution: all op list will
- * end with the same (S(g,_)) *)
- 'a elem list * th_cache
-
-type 'a auto_result =
- | Gaveup
- | Proved of (#tac_status as 'a) * 'a auto_status (* alt. proofs *)
+let pp_goal (g,_) = string_of_int g
+let pp_item = function
+ | D g -> "D" ^ pp_goal g
+ | S (g,_) -> "S" ^ pp_goal g
type flags = {
do_types : bool; (* solve goals in Type *)
maxwidth : int;
maxsize : int;
+ maxdepth : int;
timeout : float;
}
+type 'a tree_status = #tac_status as 'a * int * int
+type 'a tree_item = 'a op
+
+type 'a and_pos =
+ (AndOrTree.andT, 'a tree_status, 'a tree_item) AndOrTree.position
+type 'a or_pos =
+ (AndOrTree.orT, 'a tree_status, 'a tree_item) AndOrTree.position
+
+type 'a auto_status = 'a and_pos * th_cache
+
+type 'a auto_result =
+ | Gaveup
+ | Proved of (#tac_status as 'a) * 'a auto_status option (* alt. proofs *)
+
let close_failures _ c = c;;
let prunable _ _ _ = false;;
let cache_examine cache gty = `Notfound;;
let candidate_no = ref 0;;
let sort_new_elems l =
- List.sort (fun (_,_,l1) (_,_,l2) -> List.length l1 - List.length l2) l
+ List.sort (fun (_,_,_,l1) (_,_,_,l2) -> List.length l1 - List.length l2) l
;;
let try_candidate status t g =
in
let elems =
(* XXX calculate the sort *)
- List.map (fun c,s,gl -> c,s,List.map (fun i -> i,depth-1,P) gl) elems
+ List.map (fun c,s,gl -> c,1,s,List.map (fun i -> i,P) gl) elems
in
let elems = sort_new_elems elems in
elems, cache
;;
-let calculate_goal_ty (goalno,_,_) status =
+let calculate_goal_ty (goalno,_) status =
try Some (get_goalty status goalno)
with Error _ -> None
;;
let prop_only l =
List.filter (function (_,_,P) -> true | _ -> false) l
;;
-let remove_s_from_fl (id,_,_) (fl : fail list) =
- let rec aux = function
- | [] -> []
- | ((id1,_,_),_)::tl when id = id1 -> tl
- | hd::tl -> hd :: aux tl
- in
- aux fl
-;;
let rec guess_name name ctx =
if name = "_" then guess_name "auto" ctx else
(* pp_th status cache; *)
incr candidate_no;
(* XXX calculate the sort *)
- [(!candidate_no,Ast.Implicit `JustOne),status,[open_goal,depth,P]],
+ [(!candidate_no,Ast.Implicit `JustOne),0,status,[open_goal,P]],
cache
;;
equational_and_applicative_case signature flags s gno depth gty cache
;;
-let auto_main flags signature elems cache =
- let rec aux (elems, cache : 'a auto_status) =
-(* processa le hint dell'utente *)
-(* let cache, elems = filter_prune_hint cache elems in *)
- match elems with
-(* USER HINT
- | (m, s, size, don, todo, fl)::orlist when !hint <> None ->
- debug_print (lazy "skip");
- (match !hint with
- | Some i when condition_for_hint i todo ->
- aux tables flags cache orlist
- | _ ->
- hint := None;
- aux tables flags cache elems)
-*)
- | [] ->
- debug_print (lazy "gave up");
- Gaveup
- | (s, _, _, [],_)::orlist ->
- debug_print (lazy "success");
- Proved (s, (orlist, cache))
- | (s, size, don, (D (_,_,T))::todo, fl)::orlist
- when not flags.do_types ->
- debug_print (lazy "skip goal in Type");
- aux ((s, size, don, todo, fl)::orlist, cache)
- | (s, size, don, (S(g, key, c) as op)::todo, fl)::orlist ->
- let cache, orlist, fl, sibling_pruned =
- add_to_cache_and_del_from_orlist_if_green_cut
- g s cache key todo orlist fl size
- in
- let fl = remove_s_from_fl g fl in
- let don = if sibling_pruned then don else op::don in
- let s = NTactics.unfocus_tac s in
- aux ((s, size, don, todo, fl)::orlist, cache)
- | (s, size, don, todo, fl)::orlist
- when List.length(prop_only (d_goals todo)) > flags.maxwidth ->
- debug_print (lazy ("FAIL: WIDTH: " ^
- String.concat ", "
- (List.map (fun (x,_,_) -> string_of_int x) (d_goals todo))));
- aux (orlist, cache)
- | (s, size, don, todo, fl)::orlist when size > flags.maxsize ->
- debug_print (lazy ("FAIL: SIZE: "^string_of_int size ^
- " > " ^ string_of_int flags.maxsize ^ ": " ^
- String.concat ", "
- (List.map (fun (x,_,_) -> string_of_int x) (d_goals todo))));
- aux (orlist, cache)
- | _ when Unix.gettimeofday () > flags.timeout ->
- debug_print (lazy ("FAIL: TIMEOUT"));
- Gaveup
- | (s, size, don, (D (gno,depth,_ as g))::todo, fl)::orlist ->
- debug_print (lazy "attack goal");
- match calculate_goal_ty g s with
+module T = ZipTree
+module Z = AndOrTree
+
+let show pos =
+ debug_print (lazy("generating a.dot"));
+ debug_do (fun () ->
+ let oc = open_out "/tmp/a.dot" in
+ let fmt = Format.formatter_of_out_channel oc in
+ GraphvizPp.Dot.header fmt;
+ Z.dump pp_item pos fmt;
+ GraphvizPp.Dot.trailer fmt;
+ Format.fprintf fmt "@?";
+ close_out oc;
+ ignore(Sys.command ("dot -Tpng /tmp/a.dot > /tmp/a.png"));
+ ignore(Sys.command ("gnome-open /tmp/a.png")))
+;;
+
+let rightmost_bro pred =
+ let rec fst pos =
+ match Z.right pos with
+ | None -> None
+ | Some pos ->
+ if pred pos then Some pos else fst pos
+ in
+ fst
+;;
+
+let is_not_S pos =
+ match Z.getO pos with
+ | S _ -> false
+ | D _ -> true
+;;
+
+let rec next_choice_point (pos : 'a and_pos) : 'a or_pos option =
+ let rec giveup_right_giveup_up_backtrack_left (pos : 'a and_pos) =
+ match Z.upA pos with
+ | None -> None
+ | Some alts ->
+ match rightmost_bro is_not_S alts with
+ | None ->
+ let upalts = Z.upO alts in
+ let upalts = Z.inject T.Nil upalts in
+ backtrack_left_giveup_right_giveup_up upalts
+ | Some _ as x -> x
+ and backtrack_left_giveup_right_giveup_up (pos : 'a and_pos) =
+ let pos = Z.inject T.Nil pos in
+ let pos = match Z.getA pos with s,D g | s, S (g,_) -> Z.setA s (D g) pos in
+ match Z.left pos with
+ | None -> giveup_right_giveup_up_backtrack_left pos
+ | Some (pos as left_bro) ->
+ match Z.downA pos with
+ | Z.Unexplored -> assert false (* we explore left2right *)
+ | Z.Alternatives alts ->
+ match rightmost_bro is_not_S alts with
+ | None -> backtrack_left_giveup_right_giveup_up left_bro
+ | Some _ as x -> x
+ in
+ backtrack_left_giveup_right_giveup_up pos
+;;
+
+let auto_main flags signature (pos : 'a and_pos) cache =
+ let solved g depth size s pos =
+ Z.inject (T.Node(`Or,[D g,T.Node(`And(s,depth,size),[])])) pos
+ in
+ let failed pos =
+ Z.inject (T.Node(`Or,[])) pos
+ in
+
+ let rec next ~unfocus (pos : 'a and_pos) cache =
+ (* USER HINT *)
+ match Z.downA pos with
+ | Z.Unexplored -> attack pos cache (Z.getA pos)
+ | Z.Alternatives pos -> nextO ~unfocus pos cache
+
+ and nextO ~unfocus (pos : 'a or_pos) cache =
+ match Z.getO pos with
+ | S _ -> assert false (* XXX set to Nil when backtracking *)
+ | D g ->
+ match Z.downO pos with
+ | Z.Solution (s,_,_) -> move_solution_up ~unfocus s pos cache
+ | Z.Todo pos -> next ~unfocus:true pos cache
+
+ and next_choice (pos : 'a and_pos) cache =
+ match next_choice_point pos with
+ | None -> Gaveup
+ | Some pos -> nextO ~unfocus:true pos cache
+
+ and move_solution_up
+ ~unfocus (status : #tac_status as 'a) (pos : 'a or_pos) cache
+ =
+ let pos = (* mark as solved *)
+ match Z.getO pos with
+ | S _ -> assert false (* XXX *)
+ | D g -> Z.setO (S (g,status)) pos
+ in
+ let pos = Z.upO pos in
+ match Z.getA pos with
+ | (_, size, depth), S (g,_)
+ (* S if already solved and then solved again because of a backtrack *)
+ | (_, size, depth), D g ->
+ let newg = S (g,status) in(* TODO: cache success g *)
+ let status = if unfocus then NTactics.unfocus_tac status else status in
+ let news = status,size,depth in
+ let pos = Z.setA news newg pos in
+ match Z.right pos with
+ | Some pos -> next ~unfocus:true pos cache
| None ->
- debug_print (lazy ("SUCCESS: SIDE EFFECT: " ^ string_of_int gno));
- aux ((s,size,don,todo, fl)::orlist, cache)
- | Some gty ->
- let s, gty = apply_subst s (ctx_of gty) gty in
- debug_print (lazy ("EXAMINE: "^ ppterm s gty));
- match cache_examine cache gty with
- | `Failed_in d when d >= depth ->
- debug_print (lazy ("FAIL: DEPTH (cache): "^string_of_int gno));
- let cache = close_failures fl cache in
- aux (orlist, cache)
- | `UnderInspection ->
- debug_print (lazy ("FAIL: LOOP: " ^ string_of_int gno));
- let cache = close_failures fl cache in
- aux (orlist,cache)
- | `Succeded t ->
- debug_print (lazy ("SUCCESS: CACHE HIT: " ^ string_of_int gno));
- let s = put_in_subst s g t gty in
- aux ((s, size, don,todo, fl)::orlist, cache)
- | `Notfound
- | `Failed_in _ when depth > 0 ->
- ( (* more depth or is the first time we see the goal *)
- if prunable s gty todo then
- (debug_print (lazy( "FAIL: LOOP: one father is equal"));
- let cache = close_failures fl cache in
- aux (orlist,cache))
- else
- let cache = cache_add_underinspection cache gty depth in
- debug_print (lazy ("INSPECTING: " ^
- string_of_int gno ^ "("^ string_of_int size ^ "): "^
- ppterm s gty));
- (* elems are possible computations for proving gty *)
- let elems, cache =
- do_something signature flags s gno depth gty cache
+ match Z.upA pos with
+ | None -> Proved (status, Some (pos,cache))
+ | Some pos -> move_solution_up ~unfocus:true status pos cache
+
+ and attack pos cache and_item =
+ show pos;
+ match and_item with
+ | _, S _ -> assert false (* next would close the proof or give a D *)
+ | _ when Unix.gettimeofday () > flags.timeout ->
+ debug_print (lazy ("fail timeout"));
+ Gaveup
+ | (s, depth, width), D (_, T as g) when not flags.do_types ->
+ debug_print (lazy "skip goal in Type");
+ next ~unfocus:true (solved g depth width s pos) cache
+ | (_,depth,_), D _ when depth > flags.maxdepth ->
+ debug_print (lazy "fail depth");
+ next_choice (failed pos) cache
+ | (_,_,size), D _ when size > flags.maxsize ->
+ debug_print (lazy "fail size");
+ next_choice (failed pos) cache
+ | (s,depth,size), D (gno,_ as g) ->
+ (* assert unexplored *)
+ assert (Z.eject pos = ZipTree.Nil);
+ match calculate_goal_ty g s with
+ | None ->
+ debug_print (lazy ("success side effect: " ^ string_of_int gno));
+ next ~unfocus:false (solved g depth size s pos) cache
+ | Some gty ->
+ let s, gty = apply_subst s (ctx_of gty) gty in
+ debug_print (lazy ("EXAMINE: "^ ppterm s gty));
+ match cache_examine cache gty with
+ | `Failed_in d when d <= depth ->
+ debug_print (lazy ("fail depth (c): "^string_of_int gno));
+ next_choice (failed pos) cache
+ | `UnderInspection ->
+ debug_print (lazy ("fail loop: " ^ string_of_int gno));
+ next_choice (failed pos) cache
+ | `Succeded t ->
+ debug_print (lazy ("success (c): " ^ string_of_int gno));
+ let s = put_in_subst s g t gty in
+ next ~unfocus:true (solved g depth size s pos) cache
+ | `Notfound
+ | `Failed_in _ ->
+ (* more depth or is the first time we see the goal *)
+ if prunable s gty () then
+ (debug_print (lazy( "fail one father is equal"));
+ next_choice (failed pos) cache)
+ else
+ let cache = cache_add_underinspection cache gty depth in
+ debug_print (lazy ("INSPECTING: " ^
+ string_of_int gno ^ "("^ string_of_int size ^ ") "));
+ (* pos are possible computations for proving gty *)
+ let subgoals, cache =
+ do_something signature flags s gno depth gty cache
+ in
+ if subgoals = [] then (* this goal has failed *)
+ next_choice (failed pos) cache
+ else
+ let size_gl l = List.length
+ (List.filter (function (_,P) -> true | _ -> false) l)
+ in
+ let subtrees =
+ List.map (fun (_cand,depth_incr,s,gl) ->
+ D(gno,P),
+ ZipTree.Node (
+ `And (s,depth+depth_incr,size+size_gl gl),
+ List.map (fun g -> D g,ZipTree.Nil) gl))
+ subgoals
in
- if elems = [] then
- (* this goal has failed *)
- let cache = close_failures ((g,gty)::fl) cache in
- aux (orlist, cache)
- else
- let size_gl l = List.length
- (List.filter (function (_,_,P) -> true | _ -> false) l)
- in
- let elems =
- let inj_gl gl = List.map (fun g -> D g) gl in
- let rec map = function
- | [] -> assert false
- | (cand,s,gl)::[] ->
- let todo =
- inj_gl gl @ (S(g,gty,cand))::todo
- in
- (* we are the last in OR, we fail on g and
- * also on all failures implied by g *)
- (s, size + size_gl gl, don, todo, (g,gty)::fl)
- :: orlist
- | (cand,s,gl)::tl ->
- let todo =
- inj_gl gl @ (S(g,gty,cand))::todo
- in
- (s, size + size_gl gl, don, todo, []) :: map tl
- in
- map elems
- in
- aux (elems, cache))
- | _ ->
- debug_print (lazy ("FAIL: DEPTH: " ^ string_of_int gno));
- let cache = close_failures fl cache in
- aux (orlist, cache)
+ next ~unfocus:true
+ (Z.inject (ZipTree.Node (`Or,subtrees)) pos) cache
in
- (aux (elems, cache) : 'a auto_result)
+ (next ~unfocus:true pos cache : 'a auto_result)
;;
let int name l def =
let size = int "size" flags 10 in
let width = int "width" flags (3+List.length goals) in
(* XXX fix sort *)
- let goals depth = List.map (fun i -> D(i,depth,P)) goals in
- let elems depth = [status,0,[],goals depth,[]] in
+ let goals = List.map (fun i -> D(i,P), ZipTree.Nil) goals in
+ let elems = Z.start (ZipTree.Node (`And(status,0,0),goals)) in
let signature = () in
let flags = {
maxwidth = width;
maxsize = size;
+ maxdepth = depth;
timeout = Unix.gettimeofday() +. 3000.;
do_types = false;
} in
if x > y then raise (Error (lazy "auto gave up", None))
else
let _ = debug_print (lazy("\n\nRound "^string_of_int x^"\n")) in
- match auto_main flags signature (elems x) cache with
+ let flags = { flags with maxdepth = x } in
+ match auto_main flags signature elems cache with
| Gaveup -> up_to (x+1) y
- | Proved (s, (_orlist, _cache)) ->
+ | Proved (s, _) ->
HLog.debug ("proved at depth " ^ string_of_int x);
let stack =
match s#stack with
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