+++ /dev/null
-(* Copyright (C) 2005, HELM Team.
- *
- * This file is part of HELM, an Hypertextual, Electronic
- * Library of Mathematics, developed at the Computer Science
- * Department, University of Bologna, Italy.
- *
- * HELM is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License
- * as published by the Free Software Foundation; either version 2
- * of the License, or (at your option) any later version.
- *
- * HELM is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with HELM; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- *
- * For details, see the HELM World-Wide-Web page,
- * http://cs.unibo.it/helm/.
- *)
-
-(* $Id$ *)
-
-let debug = true;;
-
-let debug_print s = if debug then prerr_endline (Lazy.force s);;
-
-let print_metasenv metasenv =
- String.concat "\n--------------------------\n"
- (List.map (fun (i, context, term) ->
- (string_of_int i) ^ " [\n" ^ (CicPp.ppcontext context) ^
- "\n] " ^ (CicPp.ppterm term))
- metasenv)
-;;
-
-
-
-
-let print_subst ?(prefix="\n") subst =
- String.concat prefix
- (List.map
- (fun (i, (c, t, ty)) ->
- Printf.sprintf "?%d -> %s : %s" i
- (CicPp.ppterm t) (CicPp.ppterm ty))
- subst)
-;;
-
-type comparison = Lt | Le | Eq | Ge | Gt | Incomparable;;
-
-let string_of_comparison = function
- | Lt -> "<"
- | Le -> "<="
- | Gt -> ">"
- | Ge -> ">="
- | Eq -> "="
- | Incomparable -> "I"
-
-module OrderedTerm =
-struct
- type t = Cic.term
-
- let compare = Pervasives.compare
-end
-
-module TermSet = Set.Make(OrderedTerm);;
-module TermMap = Map.Make(OrderedTerm);;
-
-let symbols_of_term term =
- let module C = Cic in
- let rec aux map = function
- | C.Meta _ -> map
- | C.Appl l ->
- List.fold_left (fun res t -> (aux res t)) map l
- | t ->
- let map =
- try
- let c = TermMap.find t map in
- TermMap.add t (c+1) map
- with Not_found ->
- TermMap.add t 1 map
- in
- map
- in
- aux TermMap.empty term
-;;
-
-
-let metas_of_term term =
- let module C = Cic in
- let rec aux = function
- | C.Meta _ as t -> TermSet.singleton t
- | C.Appl l ->
- List.fold_left (fun res t -> TermSet.union res (aux t)) TermSet.empty l
- | t -> TermSet.empty (* TODO: maybe add other cases? *)
- in
- aux term
-;;
-
-
-(************************* rpo ********************************)
-let number = [
- UriManager.uri_of_string "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)",3;
- UriManager.uri_of_string "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/1)",6;
- UriManager.uri_of_string "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)",9;
- HelmLibraryObjects.Peano.pred_URI, 12;
- HelmLibraryObjects.Peano.plus_URI, 15;
- HelmLibraryObjects.Peano.minus_URI, 18;
- HelmLibraryObjects.Peano.mult_URI, 21;
- UriManager.uri_of_string "cic:/matita/nat/nat/nat.ind#xpointer(1/1)",103;
- UriManager.uri_of_string "cic:/matita/nat/nat/nat.ind#xpointer(1/1/1)",106;
- UriManager.uri_of_string "cic:/matita/nat/nat/nat.ind#xpointer(1/1/2)",109;
- UriManager.uri_of_string "cic:/matita/nat/nat/pred.con",112;
- UriManager.uri_of_string "cic:/matita/nat/plus/plus.con",115;
- UriManager.uri_of_string "cic:/matita/nat/minus/minus.con",118;
- UriManager.uri_of_string "cic:/matita/nat/times/times.con",121;
- ]
-;;
-
-let atomic t =
- match t with
- Cic.Const _
- | Cic.MutInd _
- | Cic.MutConstruct _
- | Cic.Rel _ -> true
- | _ -> false
-
-let sig_order_const t1 t2 =
- try
- let u1 = CicUtil.uri_of_term t1 in
- let u2 = CicUtil.uri_of_term t2 in
- let n1 = List.assoc u1 number in
- let n2 = List.assoc u2 number in
- if n1 < n2 then Lt
- else if n1 > n2 then Gt
- else
- begin
- prerr_endline ("t1 = "^(CicPp.ppterm t1));
- prerr_endline ("t2 = "^(CicPp.ppterm t2));
- assert false
- end
- with
- Invalid_argument _
- | Not_found -> Incomparable
-
-let sig_order t1 t2 =
- match t1, t2 with
- Cic.Rel n, Cic.Rel m when n < m -> Gt (* inverted order *)
- | Cic.Rel n, Cic.Rel m when n = m -> Incomparable
- | Cic.Rel n, Cic.Rel m when n > m -> Lt
- | Cic.Rel _, _ -> Gt
- | _, Cic.Rel _ -> Lt
- | _,_ -> sig_order_const t1 t2
-
-let rec rpo_lt t1 t2 =
- let module C = Cic in
- let first_trie =
- match t1,t2 with
- C.Meta (_, _), C.Meta (_,_) -> false
- | C.Meta (_,_) , t2 -> TermSet.mem t1 (metas_of_term t2)
- | t1, C.Meta (_,_) -> false
- | C.Appl [h1;a1],C.Appl [h2;a2] when h1=h2 ->
- rpo_lt a1 a2
- | C.Appl (h1::arg1),C.Appl (h2::arg2) when h1=h2 ->
- if lex_lt arg1 arg2 then
- check_lt arg1 t2
- else false
- | C.Appl (h1::arg1),C.Appl (h2::arg2) ->
- (match sig_order h1 h2 with
- | Lt -> check_lt arg1 t2
- | _ -> false)
- | C.Appl (h1::arg1), t2 when atomic t2 ->
- (match sig_order h1 t2 with
- | Lt -> check_lt arg1 t2
- | _ -> false)
- | t1 , C.Appl (h2::arg2) when atomic t1 ->
- (match sig_order t1 h2 with
- | Lt -> true
- | _ -> false )
- | C.Appl [] , _ -> assert false
- | _ , C.Appl [] -> assert false
- | t1, t2 when (atomic t1 && atomic t2 && t1<>t2) ->
- (match sig_order t1 t2 with
- | Lt -> true
- | _ -> false)
- | _,_ -> false
- in
- if first_trie then true else
- match t2 with
- C.Appl (_::args) ->
- List.exists (fun a -> t1 = a || rpo_lt t1 a) args
- | _ -> false
-
-and lex_lt l1 l2 =
- match l1,l2 with
- [],[] -> false
- | [],_ -> assert false
- | _, [] -> assert false
- | a1::l1, a2::l2 when a1 = a2 -> lex_lt l1 l2
- | a1::_, a2::_ -> rpo_lt a1 a2
-
-and check_lt l t =
- List.fold_left
- (fun b a -> b && (rpo_lt a t))
- true l
-;;
-
-let rpo t1 t2 =
- if rpo_lt t2 t1 then Gt
- else if rpo_lt t1 t2 then Lt
- else Incomparable
-
-
-(*********************** fine rpo *****************************)
-
-(* (weight of constants, [(meta, weight_of_meta)]) *)
-type weight = int * (int * int) list;;
-
-let string_of_weight (cw, mw) =
- let s =
- String.concat ", "
- (List.map (function (m, w) -> Printf.sprintf "(%d,%d)" m w) mw)
- in
- Printf.sprintf "[%d; %s]" cw s
-
-
-let weight_of_term ?(consider_metas=true) term =
- let module C = Cic in
- let vars_dict = Hashtbl.create 5 in
- let rec aux = function
- | C.Meta (metano, _) when consider_metas ->
- (try
- let oldw = Hashtbl.find vars_dict metano in
- Hashtbl.replace vars_dict metano (oldw+1)
- with Not_found ->
- Hashtbl.add vars_dict metano 1);
- 0
- | C.Meta _ -> 0 (* "variables" are lighter than constants and functions...*)
-
- | C.Var (_, ens)
- | C.Const (_, ens)
- | C.MutInd (_, _, ens)
- | C.MutConstruct (_, _, _, ens) ->
- List.fold_left (fun w (u, t) -> (aux t) + w) 1 ens
-
- | C.Cast (t1, t2)
- | C.Lambda (_, t1, t2)
- | C.Prod (_, t1, t2)
- | C.LetIn (_, t1, t2) ->
- let w1 = aux t1 in
- let w2 = aux t2 in
- w1 + w2 + 1
-
- | C.Appl l -> List.fold_left (+) 0 (List.map aux l)
-
- | C.MutCase (_, _, outt, t, pl) ->
- let w1 = aux outt in
- let w2 = aux t in
- let w3 = List.fold_left (+) 0 (List.map aux pl) in
- w1 + w2 + w3 + 1
-
- | C.Fix (_, fl) ->
- List.fold_left (fun w (n, i, t1, t2) -> (aux t1) + (aux t2) + w) 1 fl
-
- | C.CoFix (_, fl) ->
- List.fold_left (fun w (n, t1, t2) -> (aux t1) + (aux t2) + w) 1 fl
-
- | _ -> 1
- in
- let w = aux term in
- let l =
- Hashtbl.fold (fun meta metaw resw -> (meta, metaw)::resw) vars_dict [] in
- let compare w1 w2 =
- match w1, w2 with
- | (m1, _), (m2, _) -> m2 - m1
- in
- (w, List.sort compare l) (* from the biggest meta to the smallest (0) *)
-;;
-
-
-module OrderedInt = struct
- type t = int
-
- let compare = Pervasives.compare
-end
-
-module IntSet = Set.Make(OrderedInt)
-
-let compute_equality_weight ty left right =
- let metasw = ref 0 in
- let weight_of t =
- let w, m = (weight_of_term ~consider_metas:true t) in
- metasw := !metasw + (2 * (List.length m));
- w
- in
- (* Warning: the following let cannot be expanded since it forces the
- right evaluation order!!!! *)
- let w = (weight_of ty) + (weight_of left) + (weight_of right) in
- w + !metasw
-;;
-
-
-(* returns a "normalized" version of the polynomial weight wl (with type
- * weight list), i.e. a list sorted ascending by meta number,
- * from 0 to maxmeta. wl must be sorted descending by meta number. Example:
- * normalize_weight 5 (3, [(3, 2); (1, 1)]) ->
- * (3, [(1, 1); (2, 0); (3, 2); (4, 0); (5, 0)]) *)
-let normalize_weight maxmeta (cw, wl) =
- let rec aux = function
- | 0 -> []
- | m -> (m, 0)::(aux (m-1))
- in
- let tmpl = aux maxmeta in
- let wl =
- List.sort
- (fun (m, _) (n, _) -> Pervasives.compare m n)
- (List.fold_left
- (fun res (m, w) -> (m, w)::(List.remove_assoc m res)) tmpl wl)
- in
- (cw, wl)
-;;
-
-
-let normalize_weights (cw1, wl1) (cw2, wl2) =
- let rec aux wl1 wl2 =
- match wl1, wl2 with
- | [], [] -> [], []
- | (m, w)::tl1, (n, w')::tl2 when m = n ->
- let res1, res2 = aux tl1 tl2 in
- (m, w)::res1, (n, w')::res2
- | (m, w)::tl1, ((n, w')::_ as wl2) when m < n ->
- let res1, res2 = aux tl1 wl2 in
- (m, w)::res1, (m, 0)::res2
- | ((m, w)::_ as wl1), (n, w')::tl2 when m > n ->
- let res1, res2 = aux wl1 tl2 in
- (n, 0)::res1, (n, w')::res2
- | [], (n, w)::tl2 ->
- let res1, res2 = aux [] tl2 in
- (n, 0)::res1, (n, w)::res2
- | (m, w)::tl1, [] ->
- let res1, res2 = aux tl1 [] in
- (m, w)::res1, (m, 0)::res2
- | _, _ -> assert false
- in
- let cmp (m, _) (n, _) = compare m n in
- let wl1, wl2 = aux (List.sort cmp wl1) (List.sort cmp wl2) in
- (cw1, wl1), (cw2, wl2)
-;;
-
-
-let compare_weights ?(normalize=false)
- ((h1, w1) as weight1) ((h2, w2) as weight2)=
- let (h1, w1), (h2, w2) =
- if normalize then
- normalize_weights weight1 weight2
- else
- (h1, w1), (h2, w2)
- in
- let res, diffs =
- try
- List.fold_left2
- (fun ((lt, eq, gt), diffs) w1 w2 ->
- match w1, w2 with
- | (meta1, w1), (meta2, w2) when meta1 = meta2 ->
- let diffs = (w1 - w2) + diffs in
- let r = compare w1 w2 in
- if r < 0 then (lt+1, eq, gt), diffs
- else if r = 0 then (lt, eq+1, gt), diffs
- else (lt, eq, gt+1), diffs
- | (meta1, w1), (meta2, w2) ->
- debug_print
- (lazy
- (Printf.sprintf "HMMM!!!! %s, %s\n"
- (string_of_weight weight1) (string_of_weight weight2)));
- assert false)
- ((0, 0, 0), 0) w1 w2
- with Invalid_argument _ ->
- debug_print
- (lazy
- (Printf.sprintf "Invalid_argument: %s{%s}, %s{%s}, normalize = %s\n"
- (string_of_weight (h1, w1)) (string_of_weight weight1)
- (string_of_weight (h2, w2)) (string_of_weight weight2)
- (string_of_bool normalize)));
- assert false
- in
- let hdiff = h1 - h2 in
- match res with
- | (0, _, 0) ->
- if hdiff < 0 then Lt
- else if hdiff > 0 then Gt
- else Eq (* Incomparable *)
- | (m, _, 0) ->
- if hdiff <= 0 then Lt
- else if (- diffs) >= hdiff then Le else Incomparable
- | (0, _, m) ->
- if hdiff >= 0 then Gt
- else if diffs >= (- hdiff) then Ge else Incomparable
- | (m, _, n) when m > 0 && n > 0 ->
- Incomparable
- | _ -> assert false
-
-;;
-
-
-let rec aux_ordering ?(recursion=true) t1 t2 =
- let module C = Cic in
- let compare_uris u1 u2 =
- let res =
- compare (UriManager.string_of_uri u1) (UriManager.string_of_uri u2) in
- if res < 0 then Lt
- else if res = 0 then Eq
- else Gt
- in
- match t1, t2 with
- | C.Meta _, _
- | _, C.Meta _ -> Incomparable
-
- | t1, t2 when t1 = t2 -> Eq
-
- | C.Rel n, C.Rel m -> if n > m then Lt else Gt
- | C.Rel _, _ -> Lt
- | _, C.Rel _ -> Gt
-
- | C.Const (u1, _), C.Const (u2, _) -> compare_uris u1 u2
- | C.Const _, _ -> Lt
- | _, C.Const _ -> Gt
-
- | C.MutInd (u1, _, _), C.MutInd (u2, _, _) -> compare_uris u1 u2
- | C.MutInd _, _ -> Lt
- | _, C.MutInd _ -> Gt
-
- | C.MutConstruct (u1, _, _, _), C.MutConstruct (u2, _, _, _) ->
- compare_uris u1 u2
- | C.MutConstruct _, _ -> Lt
- | _, C.MutConstruct _ -> Gt
-
- | C.Appl l1, C.Appl l2 when recursion ->
- let rec cmp t1 t2 =
- match t1, t2 with
- | [], [] -> Eq
- | _, [] -> Gt
- | [], _ -> Lt
- | hd1::tl1, hd2::tl2 ->
- let o = aux_ordering hd1 hd2 in
- if o = Eq then cmp tl1 tl2
- else o
- in
- cmp l1 l2
- | C.Appl (h1::t1), C.Appl (h2::t2) when not recursion ->
- aux_ordering h1 h2
-
- | t1, t2 ->
- debug_print
- (lazy
- (Printf.sprintf "These two terms are not comparable:\n%s\n%s\n\n"
- (CicPp.ppterm t1) (CicPp.ppterm t2)));
- Incomparable
-;;
-
-
-(* w1, w2 are the weights, they should already be normalized... *)
-let nonrec_kbo_w (t1, w1) (t2, w2) =
- match compare_weights w1 w2 with
- | Le -> if aux_ordering t1 t2 = Lt then Lt else Incomparable
- | Ge -> if aux_ordering t1 t2 = Gt then Gt else Incomparable
- | Eq -> aux_ordering t1 t2
- | res -> res
-;;
-
-
-let nonrec_kbo t1 t2 =
- let w1 = weight_of_term t1 in
- let w2 = weight_of_term t2 in
- (*
- prerr_endline ("weight1 :"^(string_of_weight w1));
- prerr_endline ("weight2 :"^(string_of_weight w2));
- *)
- match compare_weights ~normalize:true w1 w2 with
- | Le -> if aux_ordering t1 t2 = Lt then Lt else Incomparable
- | Ge -> if aux_ordering t1 t2 = Gt then Gt else Incomparable
- | Eq -> aux_ordering t1 t2
- | res -> res
-;;
-
-
-let rec kbo t1 t2 =
- let aux = aux_ordering ~recursion:false in
- let w1 = weight_of_term t1
- and w2 = weight_of_term t2 in
- let rec cmp t1 t2 =
- match t1, t2 with
- | [], [] -> Eq
- | _, [] -> Gt
- | [], _ -> Lt
- | hd1::tl1, hd2::tl2 ->
- let o =
- kbo hd1 hd2
- in
- if o = Eq then cmp tl1 tl2
- else o
- in
- let comparison = compare_weights ~normalize:true w1 w2 in
- match comparison with
- | Le ->
- let r = aux t1 t2 in
- if r = Lt then Lt
- else if r = Eq then (
- match t1, t2 with
- | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
- if cmp tl1 tl2 = Lt then Lt else Incomparable
- | _, _ -> Incomparable
- ) else Incomparable
- | Ge ->
- let r = aux t1 t2 in
- if r = Gt then Gt
- else if r = Eq then (
- match t1, t2 with
- | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
- if cmp tl1 tl2 = Gt then Gt else Incomparable
- | _, _ -> Incomparable
- ) else Incomparable
- | Eq ->
- let r = aux t1 t2 in
- if r = Eq then (
- match t1, t2 with
- | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
- cmp tl1 tl2
- | _, _ -> Incomparable
- ) else r
- | res -> res
-;;
-
-let rec ao t1 t2 =
- let get_hd t =
- match t with
- Cic.MutConstruct(uri,tyno,cno,_) -> Some(uri,tyno,cno)
- | Cic.Appl(Cic.MutConstruct(uri,tyno,cno,_)::_) ->
- Some(uri,tyno,cno)
- | _ -> None in
- let aux = aux_ordering ~recursion:false in
- let w1 = weight_of_term t1
- and w2 = weight_of_term t2 in
- let rec cmp t1 t2 =
- match t1, t2 with
- | [], [] -> Eq
- | _, [] -> Gt
- | [], _ -> Lt
- | hd1::tl1, hd2::tl2 ->
- let o =
- ao hd1 hd2
- in
- if o = Eq then cmp tl1 tl2
- else o
- in
- match get_hd t1, get_hd t2 with
- Some(_),None -> Lt
- | None,Some(_) -> Gt
- | _ ->
- let comparison = compare_weights ~normalize:true w1 w2 in
- match comparison with
- | Le ->
- let r = aux t1 t2 in
- if r = Lt then Lt
- else if r = Eq then (
- match t1, t2 with
- | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
- if cmp tl1 tl2 = Lt then Lt else Incomparable
- | _, _ -> Incomparable
- ) else Incomparable
- | Ge ->
- let r = aux t1 t2 in
- if r = Gt then Gt
- else if r = Eq then (
- match t1, t2 with
- | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
- if cmp tl1 tl2 = Gt then Gt else Incomparable
- | _, _ -> Incomparable
- ) else Incomparable
- | Eq ->
- let r = aux t1 t2 in
- if r = Eq then (
- match t1, t2 with
- | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
- cmp tl1 tl2
- | _, _ -> Incomparable
- ) else r
- | res -> res
-;;
-
-let names_of_context context =
- List.map
- (function
- | None -> None
- | Some (n, e) -> Some n)
- context
-;;
-
-
-let rec lpo t1 t2 =
- let module C = Cic in
- match t1, t2 with
- | t1, t2 when t1 = t2 -> Eq
- | t1, (C.Meta _ as m) ->
- if TermSet.mem m (metas_of_term t1) then Gt else Incomparable
- | (C.Meta _ as m), t2 ->
- if TermSet.mem m (metas_of_term t2) then Lt else Incomparable
- | C.Appl (hd1::tl1), C.Appl (hd2::tl2) -> (
- let res =
- let f o r t =
- if r then true else
- match lpo t o with
- | Gt | Eq -> true
- | _ -> false
- in
- let res1 = List.fold_left (f t2) false tl1 in
- if res1 then Gt
- else let res2 = List.fold_left (f t1) false tl2 in
- if res2 then Lt
- else Incomparable
- in
- if res <> Incomparable then
- res
- else
- let f o r t =
- if not r then false else
- match lpo o t with
- | Gt -> true
- | _ -> false
- in
- match aux_ordering hd1 hd2 with
- | Gt ->
- let res = List.fold_left (f t1) false tl2 in
- if res then Gt
- else Incomparable
- | Lt ->
- let res = List.fold_left (f t2) false tl1 in
- if res then Lt
- else Incomparable
- | Eq -> (
- let lex_res =
- try
- List.fold_left2
- (fun r t1 t2 -> if r <> Eq then r else lpo t1 t2)
- Eq tl1 tl2
- with Invalid_argument _ ->
- Incomparable
- in
- match lex_res with
- | Gt ->
- if List.fold_left (f t1) false tl2 then Gt
- else Incomparable
- | Lt ->
- if List.fold_left (f t2) false tl1 then Lt
- else Incomparable
- | _ -> Incomparable
- )
- | _ -> Incomparable
- )
- | t1, t2 -> aux_ordering t1 t2
-;;
-
-
-(* settable by the user... *)
-let compare_terms = ref nonrec_kbo;;
-(* let compare_terms = ref ao;; *)
-(* let compare_terms = ref rpo;; *)
-
-let guarded_simpl ?(debug=false) context t =
- if !compare_terms == nonrec_kbo then t
- else
- let t' = ProofEngineReduction.simpl context t in
- if t = t' then t else
- begin
- let simpl_order = !compare_terms t t' in
- if debug then
- prerr_endline ("comparing "^(CicPp.ppterm t)^(CicPp.ppterm t'));
- if simpl_order = Gt then (if debug then prerr_endline "GT";t')
- else (if debug then prerr_endline "NO_GT";t)
- end
-;;
-
-type equality_sign = Negative | Positive;;
-
-let string_of_sign = function
- | Negative -> "Negative"
- | Positive -> "Positive"
-;;
-
-
-type pos = Left | Right
-
-let string_of_pos = function
- | Left -> "Left"
- | Right -> "Right"
-;;
-
-
-let eq_ind_URI () = LibraryObjects.eq_ind_URI ~eq:(LibraryObjects.eq_URI ())
-let eq_ind_r_URI () = LibraryObjects.eq_ind_r_URI ~eq:(LibraryObjects.eq_URI ())
-let sym_eq_URI () = LibraryObjects.sym_eq_URI ~eq:(LibraryObjects.eq_URI ())
-let eq_XURI () =
- let s = UriManager.string_of_uri (LibraryObjects.eq_URI ()) in
- UriManager.uri_of_string (s ^ "#xpointer(1/1/1)")
-let trans_eq_URI () = LibraryObjects.trans_eq_URI ~eq:(LibraryObjects.eq_URI ())
projects / helm.git / blobdiff