3 let debug_print = if debug then prerr_endline else ignore;;
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 let w = (weight_of ty) + (weight_of left) + (weight_of right) in
112 (* (4 * IntSet.cardinal !metasw) *)
116 (* returns a "normalized" version of the polynomial weight wl (with type
117 * weight list), i.e. a list sorted ascending by meta number,
118 * from 0 to maxmeta. wl must be sorted descending by meta number. Example:
119 * normalize_weight 5 (3, [(3, 2); (1, 1)]) ->
120 * (3, [(1, 1); (2, 0); (3, 2); (4, 0); (5, 0)]) *)
121 let normalize_weight maxmeta (cw, wl) =
122 (* Printf.printf "normalize_weight: %d, %s\n" maxmeta *)
123 (* (string_of_weight (cw, wl)); *)
124 let rec aux = function
126 | m -> (m, 0)::(aux (m-1))
128 let tmpl = aux maxmeta in
131 (fun (m, _) (n, _) -> Pervasives.compare m n)
133 (fun res (m, w) -> (m, w)::(List.remove_assoc m res)) tmpl wl)
139 let normalize_weights (cw1, wl1) (cw2, wl2) =
140 let rec aux wl1 wl2 =
143 | (m, w)::tl1, (n, w')::tl2 when m = n ->
144 let res1, res2 = aux tl1 tl2 in
145 (m, w)::res1, (n, w')::res2
146 | (m, w)::tl1, ((n, w')::_ as wl2) when m < n ->
147 let res1, res2 = aux tl1 wl2 in
148 (m, w)::res1, (m, 0)::res2
149 | ((m, w)::_ as wl1), (n, w')::tl2 when m > n ->
150 let res1, res2 = aux wl1 tl2 in
151 (n, 0)::res1, (n, w')::res2
153 let res1, res2 = aux [] tl2 in
154 (n, 0)::res1, (n, w)::res2
156 let res1, res2 = aux tl1 [] in
157 (m, w)::res1, (m, 0)::res2
158 | _, _ -> assert false
160 let cmp (m, _) (n, _) = compare m n in
161 let wl1, wl2 = aux (List.sort cmp wl1) (List.sort cmp wl2) in
162 (cw1, wl1), (cw2, wl2)
166 type comparison = Lt | Le | Eq | Ge | Gt | Incomparable;;
168 let string_of_comparison = function
174 | Incomparable -> "I"
177 let compare_weights ?(normalize=false)
178 ((h1, w1) as weight1) ((h2, w2) as weight2)=
179 let (h1, w1), (h2, w2) =
182 (* let maxmeta l = *)
184 (* match List.hd l with *)
186 (* with Failure _ -> 0 *)
188 (* max (maxmeta w1) (maxmeta w2) *)
190 (* (normalize_weight maxmeta (h1, w1)), (normalize_weight maxmeta (h2, w2)) *)
191 normalize_weights weight1 weight2
198 (fun ((lt, eq, gt), diffs) w1 w2 ->
200 | (meta1, w1), (meta2, w2) when meta1 = meta2 ->
201 let diffs = (w1 - w2) + diffs in
202 let r = compare w1 w2 in
203 if r < 0 then (lt+1, eq, gt), diffs
204 else if r = 0 then (lt, eq+1, gt), diffs
205 else (lt, eq, gt+1), diffs
206 | (meta1, w1), (meta2, w2) ->
207 Printf.printf "HMMM!!!! %s, %s\n"
208 (string_of_weight weight1) (string_of_weight weight2);
211 with Invalid_argument _ ->
212 Printf.printf "Invalid_argument: %s{%s}, %s{%s}, normalize = %s\n"
213 (string_of_weight (h1, w1)) (string_of_weight weight1)
214 (string_of_weight (h2, w2)) (string_of_weight weight2)
215 (string_of_bool normalize);
218 let hdiff = h1 - h2 in
222 else if hdiff > 0 then Gt
223 else Eq (* Incomparable *)
226 if m > 0 || hdiff < 0 then Lt
227 else if diffs >= (- hdiff) then Le else Incomparable
229 if diffs >= (- hdiff) then Le else Incomparable
232 if m > 0 || hdiff > 0 then Gt
233 else if (- diffs) >= hdiff then Ge else Incomparable
235 if (- diffs) >= hdiff then Ge else Incomparable
236 | (m, _, n) when m > 0 && n > 0 ->
242 let rec aux_ordering ?(recursion=true) t1 t2 =
243 let module C = Cic in
244 let compare_uris u1 u2 =
246 compare (UriManager.string_of_uri u1) (UriManager.string_of_uri u2) in
248 else if res = 0 then Eq
253 | _, C.Meta _ -> Incomparable
255 | t1, t2 when t1 = t2 -> Eq
257 | C.Rel n, C.Rel m -> if n > m then Lt else Gt
261 | C.Const (u1, _), C.Const (u2, _) -> compare_uris u1 u2
265 | C.MutInd (u1, _, _), C.MutInd (u2, _, _) -> compare_uris u1 u2
266 | C.MutInd _, _ -> Lt
267 | _, C.MutInd _ -> Gt
269 | C.MutConstruct (u1, _, _, _), C.MutConstruct (u2, _, _, _) ->
271 | C.MutConstruct _, _ -> Lt
272 | _, C.MutConstruct _ -> Gt
274 | C.Appl l1, C.Appl l2 when recursion ->
280 | hd1::tl1, hd2::tl2 ->
281 let o = aux_ordering hd1 hd2 in
282 if o = Eq then cmp tl1 tl2
286 | C.Appl (h1::t1), C.Appl (h2::t2) when not recursion ->
291 Printf.sprintf "These two terms are not comparable:\n%s\n%s\n\n"
292 (CicPp.ppterm t1) (CicPp.ppterm t2));
297 (* w1, w2 are the weights, they should already be normalized... *)
298 let nonrec_kbo_w (t1, w1) (t2, w2) =
299 match compare_weights w1 w2 with
300 | Le -> if aux_ordering t1 t2 = Lt then Lt else Incomparable
301 | Ge -> if aux_ordering t1 t2 = Gt then Gt else Incomparable
302 | Eq -> aux_ordering t1 t2
307 let nonrec_kbo t1 t2 =
308 let w1 = weight_of_term t1 in
309 let w2 = weight_of_term t2 in
310 match compare_weights ~normalize:true w1 w2 with
311 | Le -> if aux_ordering t1 t2 = Lt then Lt else Incomparable
312 | Ge -> if aux_ordering t1 t2 = Gt then Gt else Incomparable
313 | Eq -> aux_ordering t1 t2
320 (* Printf.sprintf "kbo %s %s" (CicPp.ppterm t1) (CicPp.ppterm t2)); *)
321 (* if t1 = t2 then *)
324 let aux = aux_ordering ~recursion:false in
325 let w1 = weight_of_term t1
326 and w2 = weight_of_term t2 in
332 | hd1::tl1, hd2::tl2 ->
335 (* Printf.sprintf "recursion kbo on %s %s" *)
336 (* (CicPp.ppterm hd1) (CicPp.ppterm hd2)); *)
339 if o = Eq then cmp tl1 tl2
342 let comparison = compare_weights ~normalize:true w1 w2 in
344 (* Printf.sprintf "Weights are: %s %s: %s" *)
345 (* (string_of_weight w1) (string_of_weight w2) *)
346 (* (string_of_comparison comparison)); *)
347 match comparison with
350 (* debug_print ("HERE! " ^ (string_of_comparison r)); *)
352 else if r = Eq then (
354 | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
355 if cmp tl1 tl2 = Lt then Lt else Incomparable
356 | _, _ -> Incomparable
361 else if r = Eq then (
363 | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
364 if cmp tl1 tl2 = Gt then Gt else Incomparable
365 | _, _ -> Incomparable
371 | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
372 (* if cmp tl1 tl2 = Gt then Gt else Incomparable *)
374 | _, _ -> Incomparable
380 let names_of_context context =
384 | Some (n, e) -> Some n)
393 let compare = Pervasives.compare
396 module TermSet = Set.Make(OrderedTerm);;
397 module TermMap = Map.Make(OrderedTerm);;
399 let symbols_of_term term =
400 let module C = Cic in
401 let rec aux map = function
404 List.fold_left (fun res t -> (aux res t)) map l
408 let c = TermMap.find t map in
409 TermMap.add t (c+1) map
415 aux TermMap.empty term
419 let metas_of_term term =
420 let module C = Cic in
421 let rec aux = function
422 | C.Meta _ as t -> TermSet.singleton t
424 List.fold_left (fun res t -> TermSet.union res (aux t)) TermSet.empty l
425 | t -> TermSet.empty (* TODO: maybe add other cases? *)
432 let module C = Cic in
434 | t1, t2 when t1 = t2 -> Eq
435 | t1, (C.Meta _ as m) ->
436 if TermSet.mem m (metas_of_term t1) then Gt else Incomparable
437 | (C.Meta _ as m), t2 ->
438 if TermSet.mem m (metas_of_term t2) then Lt else Incomparable
439 | C.Appl (hd1::tl1), C.Appl (hd2::tl2) -> (
447 let res1 = List.fold_left (f t2) false tl1 in
449 else let res2 = List.fold_left (f t1) false tl2 in
453 if res <> Incomparable then
457 if not r then false else
462 match aux_ordering hd1 hd2 with
464 let res = List.fold_left (f t1) false tl2 in
468 let res = List.fold_left (f t2) false tl1 in
475 (fun r t1 t2 -> if r <> Eq then r else lpo t1 t2)
477 with Invalid_argument _ ->
482 if List.fold_left (f t1) false tl2 then Gt
485 if List.fold_left (f t2) false tl1 then Lt
491 | t1, t2 -> aux_ordering t1 t2
495 (* settable by the user... *)
496 let compare_terms = ref nonrec_kbo;;
499 type equality_sign = Negative | Positive;;
501 let string_of_sign = function
502 | Negative -> "Negative"
503 | Positive -> "Positive"
507 type pos = Left | Right
509 let string_of_pos = function