3 let debug_print s = if debug then prerr_endline (Lazy.force s);;
6 let print_metasenv metasenv =
7 String.concat "\n--------------------------\n"
8 (List.map (fun (i, context, term) ->
9 (string_of_int i) ^ " [\n" ^ (CicPp.ppcontext context) ^
10 "\n] " ^ (CicPp.ppterm term))
15 let print_subst ?(prefix="\n") subst =
18 (fun (i, (c, t, ty)) ->
19 Printf.sprintf "?%d -> %s : %s" i
20 (CicPp.ppterm t) (CicPp.ppterm ty))
24 (* (weight of constants, [(meta, weight_of_meta)]) *)
25 type weight = int * (int * int) list;;
27 let string_of_weight (cw, mw) =
30 (List.map (function (m, w) -> Printf.sprintf "(%d,%d)" m w) mw)
32 Printf.sprintf "[%d; %s]" cw s
35 let weight_of_term ?(consider_metas=true) term =
36 (* ALB: what to consider as a variable? I think "variables" in our case are
37 Metas and maybe Rels... *)
39 let vars_dict = Hashtbl.create 5 in
40 let rec aux = function
41 | C.Meta (metano, _) when consider_metas ->
43 let oldw = Hashtbl.find vars_dict metano in
44 Hashtbl.replace vars_dict metano (oldw+1)
46 Hashtbl.add vars_dict metano 1);
48 | C.Meta _ -> 0 (* "variables" are lighter than constants and functions...*)
52 | C.MutInd (_, _, ens)
53 | C.MutConstruct (_, _, _, ens) ->
54 List.fold_left (fun w (u, t) -> (aux t) + w) 1 ens
57 | C.Lambda (_, t1, t2)
59 | C.LetIn (_, t1, t2) ->
64 | C.Appl l -> List.fold_left (+) 0 (List.map aux l)
66 | C.MutCase (_, _, outt, t, pl) ->
69 let w3 = List.fold_left (+) 0 (List.map aux pl) in
73 List.fold_left (fun w (n, i, t1, t2) -> (aux t1) + (aux t2) + w) 1 fl
76 List.fold_left (fun w (n, t1, t2) -> (aux t1) + (aux t2) + w) 1 fl
82 Hashtbl.fold (fun meta metaw resw -> (meta, metaw)::resw) vars_dict [] in
85 | (m1, _), (m2, _) -> m2 - m1
87 (w, List.sort compare l) (* from the biggest meta to the smallest (0) *)
91 module OrderedInt = struct
94 let compare = Pervasives.compare
97 module IntSet = Set.Make(OrderedInt)
99 let compute_equality_weight ty left right =
100 (* let metasw = ref IntSet.empty in *)
101 let metasw = ref 0 in
103 let w, m = (weight_of_term ~consider_metas:true(* false *) t) in
104 (* let mw = List.fold_left (fun mw (_, c) -> mw + 2 * c) 0 m in *)
105 (* metasw := !metasw + mw; *)
106 metasw := !metasw + (2 * (List.length m));
107 (* metasw := List.fold_left (fun s (i, _) -> IntSet.add i s) !metasw m; *)
110 (* Warning: the following let cannot be expanded since it forces the
111 right evaluation order!!!! *)
112 let w = (weight_of ty) + (weight_of left) + (weight_of right) in
114 (* (4 * IntSet.cardinal !metasw) *)
118 (* returns a "normalized" version of the polynomial weight wl (with type
119 * weight list), i.e. a list sorted ascending by meta number,
120 * from 0 to maxmeta. wl must be sorted descending by meta number. Example:
121 * normalize_weight 5 (3, [(3, 2); (1, 1)]) ->
122 * (3, [(1, 1); (2, 0); (3, 2); (4, 0); (5, 0)]) *)
123 let normalize_weight maxmeta (cw, wl) =
124 (* Printf.printf "normalize_weight: %d, %s\n" maxmeta *)
125 (* (string_of_weight (cw, wl)); *)
126 let rec aux = function
128 | m -> (m, 0)::(aux (m-1))
130 let tmpl = aux maxmeta in
133 (fun (m, _) (n, _) -> Pervasives.compare m n)
135 (fun res (m, w) -> (m, w)::(List.remove_assoc m res)) tmpl wl)
141 let normalize_weights (cw1, wl1) (cw2, wl2) =
142 let rec aux wl1 wl2 =
145 | (m, w)::tl1, (n, w')::tl2 when m = n ->
146 let res1, res2 = aux tl1 tl2 in
147 (m, w)::res1, (n, w')::res2
148 | (m, w)::tl1, ((n, w')::_ as wl2) when m < n ->
149 let res1, res2 = aux tl1 wl2 in
150 (m, w)::res1, (m, 0)::res2
151 | ((m, w)::_ as wl1), (n, w')::tl2 when m > n ->
152 let res1, res2 = aux wl1 tl2 in
153 (n, 0)::res1, (n, w')::res2
155 let res1, res2 = aux [] tl2 in
156 (n, 0)::res1, (n, w)::res2
158 let res1, res2 = aux tl1 [] in
159 (m, w)::res1, (m, 0)::res2
160 | _, _ -> assert false
162 let cmp (m, _) (n, _) = compare m n in
163 let wl1, wl2 = aux (List.sort cmp wl1) (List.sort cmp wl2) in
164 (cw1, wl1), (cw2, wl2)
168 type comparison = Lt | Le | Eq | Ge | Gt | Incomparable;;
170 let string_of_comparison = function
176 | Incomparable -> "I"
179 let compare_weights ?(normalize=false)
180 ((h1, w1) as weight1) ((h2, w2) as weight2)=
181 let (h1, w1), (h2, w2) =
184 (* let maxmeta l = *)
186 (* match List.hd l with *)
188 (* with Failure _ -> 0 *)
190 (* max (maxmeta w1) (maxmeta w2) *)
192 (* (normalize_weight maxmeta (h1, w1)), (normalize_weight maxmeta (h2, w2)) *)
193 normalize_weights weight1 weight2
200 (fun ((lt, eq, gt), diffs) w1 w2 ->
202 | (meta1, w1), (meta2, w2) when meta1 = meta2 ->
203 let diffs = (w1 - w2) + diffs in
204 let r = compare w1 w2 in
205 if r < 0 then (lt+1, eq, gt), diffs
206 else if r = 0 then (lt, eq+1, gt), diffs
207 else (lt, eq, gt+1), diffs
208 | (meta1, w1), (meta2, w2) ->
209 Printf.printf "HMMM!!!! %s, %s\n"
210 (string_of_weight weight1) (string_of_weight weight2);
213 with Invalid_argument _ ->
214 Printf.printf "Invalid_argument: %s{%s}, %s{%s}, normalize = %s\n"
215 (string_of_weight (h1, w1)) (string_of_weight weight1)
216 (string_of_weight (h2, w2)) (string_of_weight weight2)
217 (string_of_bool normalize);
220 let hdiff = h1 - h2 in
224 else if hdiff > 0 then Gt
225 else Eq (* Incomparable *)
228 if m > 0 || hdiff < 0 then Lt
229 else if diffs >= (- hdiff) then Le else Incomparable
231 if diffs >= (- hdiff) then Le else Incomparable
234 if m > 0 || hdiff > 0 then Gt
235 else if (- diffs) >= hdiff then Ge else Incomparable
237 if (- diffs) >= hdiff then Ge else Incomparable
238 | (m, _, n) when m > 0 && n > 0 ->
244 let rec aux_ordering ?(recursion=true) t1 t2 =
245 let module C = Cic in
246 let compare_uris u1 u2 =
248 compare (UriManager.string_of_uri u1) (UriManager.string_of_uri u2) in
250 else if res = 0 then Eq
255 | _, C.Meta _ -> Incomparable
257 | t1, t2 when t1 = t2 -> Eq
259 | C.Rel n, C.Rel m -> if n > m then Lt else Gt
263 | C.Const (u1, _), C.Const (u2, _) -> compare_uris u1 u2
267 | C.MutInd (u1, _, _), C.MutInd (u2, _, _) -> compare_uris u1 u2
268 | C.MutInd _, _ -> Lt
269 | _, C.MutInd _ -> Gt
271 | C.MutConstruct (u1, _, _, _), C.MutConstruct (u2, _, _, _) ->
273 | C.MutConstruct _, _ -> Lt
274 | _, C.MutConstruct _ -> Gt
276 | C.Appl l1, C.Appl l2 when recursion ->
282 | hd1::tl1, hd2::tl2 ->
283 let o = aux_ordering hd1 hd2 in
284 if o = Eq then cmp tl1 tl2
288 | C.Appl (h1::t1), C.Appl (h2::t2) when not recursion ->
293 Printf.sprintf "These two terms are not comparable:\n%s\n%s\n\n"
294 (CicPp.ppterm t1) (CicPp.ppterm t2)));
299 (* w1, w2 are the weights, they should already be normalized... *)
300 let nonrec_kbo_w (t1, w1) (t2, w2) =
301 match compare_weights w1 w2 with
302 | Le -> if aux_ordering t1 t2 = Lt then Lt else Incomparable
303 | Ge -> if aux_ordering t1 t2 = Gt then Gt else Incomparable
304 | Eq -> aux_ordering t1 t2
309 let nonrec_kbo t1 t2 =
310 let w1 = weight_of_term t1 in
311 let w2 = weight_of_term t2 in
312 match compare_weights ~normalize:true w1 w2 with
313 | Le -> if aux_ordering t1 t2 = Lt then Lt else Incomparable
314 | Ge -> if aux_ordering t1 t2 = Gt then Gt else Incomparable
315 | Eq -> aux_ordering t1 t2
321 (* debug_print (lazy ( *)
322 (* Printf.sprintf "kbo %s %s" (CicPp.ppterm t1) (CicPp.ppterm t2))); *)
323 (* if t1 = t2 then *)
326 let aux = aux_ordering ~recursion:false in
327 let w1 = weight_of_term t1
328 and w2 = weight_of_term t2 in
334 | hd1::tl1, hd2::tl2 ->
336 (* debug_print (lazy ( *)
337 (* Printf.sprintf "recursion kbo on %s %s" *)
338 (* (CicPp.ppterm hd1) (CicPp.ppterm hd2))); *)
341 if o = Eq then cmp tl1 tl2
344 let comparison = compare_weights ~normalize:true w1 w2 in
345 (* debug_print (lazy ( *)
346 (* Printf.sprintf "Weights are: %s %s: %s" *)
347 (* (string_of_weight w1) (string_of_weight w2) *)
348 (* (string_of_comparison comparison))); *)
349 match comparison with
352 (* debug_print (lazy ("HERE! " ^ (string_of_comparison r))); *)
354 else if r = Eq then (
356 | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
357 if cmp tl1 tl2 = Lt then Lt else Incomparable
358 | _, _ -> Incomparable
363 else if r = Eq then (
365 | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
366 if cmp tl1 tl2 = Gt then Gt else Incomparable
367 | _, _ -> Incomparable
373 | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
374 (* if cmp tl1 tl2 = Gt then Gt else Incomparable *)
376 | _, _ -> Incomparable
382 let names_of_context context =
386 | Some (n, e) -> Some n)
395 let compare = Pervasives.compare
398 module TermSet = Set.Make(OrderedTerm);;
399 module TermMap = Map.Make(OrderedTerm);;
401 let symbols_of_term term =
402 let module C = Cic in
403 let rec aux map = function
406 List.fold_left (fun res t -> (aux res t)) map l
410 let c = TermMap.find t map in
411 TermMap.add t (c+1) map
417 aux TermMap.empty term
421 let metas_of_term term =
422 let module C = Cic in
423 let rec aux = function
424 | C.Meta _ as t -> TermSet.singleton t
426 List.fold_left (fun res t -> TermSet.union res (aux t)) TermSet.empty l
427 | t -> TermSet.empty (* TODO: maybe add other cases? *)
434 let module C = Cic in
436 | t1, t2 when t1 = t2 -> Eq
437 | t1, (C.Meta _ as m) ->
438 if TermSet.mem m (metas_of_term t1) then Gt else Incomparable
439 | (C.Meta _ as m), t2 ->
440 if TermSet.mem m (metas_of_term t2) then Lt else Incomparable
441 | C.Appl (hd1::tl1), C.Appl (hd2::tl2) -> (
449 let res1 = List.fold_left (f t2) false tl1 in
451 else let res2 = List.fold_left (f t1) false tl2 in
455 if res <> Incomparable then
459 if not r then false else
464 match aux_ordering hd1 hd2 with
466 let res = List.fold_left (f t1) false tl2 in
470 let res = List.fold_left (f t2) false tl1 in
477 (fun r t1 t2 -> if r <> Eq then r else lpo t1 t2)
479 with Invalid_argument _ ->
484 if List.fold_left (f t1) false tl2 then Gt
487 if List.fold_left (f t2) false tl1 then Lt
493 | t1, t2 -> aux_ordering t1 t2
497 (* settable by the user... *)
498 let compare_terms = ref nonrec_kbo;;
501 type equality_sign = Negative | Positive;;
503 let string_of_sign = function
504 | Negative -> "Negative"
505 | Positive -> "Positive"
509 type pos = Left | Right
511 let string_of_pos = function