--- /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/.
+ *)
+
+(* let _profiler = <:profiler<_profiler>>;; *)
+
+(* $Id: inference.ml 6245 2006-04-05 12:07:51Z tassi $ *)
+
+type rule = SuperpositionRight | SuperpositionLeft | Demodulation
+type uncomparable = int -> int
+
+type equality =
+ uncomparable * (* trick to break structural equality *)
+ int * (* weight *)
+ proof *
+ (Cic.term * (* type *)
+ Cic.term * (* left side *)
+ Cic.term * (* right side *)
+ Utils.comparison) * (* ordering *)
+ Cic.metasenv * (* environment for metas *)
+ int (* id *)
+and proof =
+ | Exact of Cic.term
+ | Step of Subst.substitution * (rule * int*(Utils.pos*int)* Cic.term)
+ (* subst, (rule,eq1, eq2,predicate) *)
+and goal_proof = (rule * Utils.pos * int * Subst.substitution * Cic.term) list
+;;
+(* the hashtbl eq_id -> proof, max_eq_id *)
+type equality_bag = (int,equality) Hashtbl.t * int ref
+
+type goal = goal_proof * Cic.metasenv * Cic.term
+
+(* globals *)
+let mk_equality_bag () =
+ Hashtbl.create 1024, ref 0
+;;
+
+let freshid (_,i) =
+ incr i; !i
+;;
+
+let add_to_bag (id_to_eq,_) id eq =
+ Hashtbl.add id_to_eq id eq
+;;
+
+let uncomparable = fun _ -> 0
+
+let mk_equality bag (weight,p,(ty,l,r,o),m) =
+ let id = freshid bag in
+ let eq = (uncomparable,weight,p,(ty,l,r,o),m,id) in
+ add_to_bag bag id eq;
+ eq
+;;
+
+let mk_tmp_equality (weight,(ty,l,r,o),m) =
+ let id = -1 in
+ uncomparable,weight,Exact (Cic.Implicit None),(ty,l,r,o),m,id
+;;
+
+
+let open_equality (_,weight,proof,(ty,l,r,o),m,id) =
+ (weight,proof,(ty,l,r,o),m,id)
+
+let string_of_rule = function
+ | SuperpositionRight -> "SupR"
+ | SuperpositionLeft -> "SupL"
+ | Demodulation -> "Demod"
+;;
+
+let string_of_equality ?env eq =
+ match env with
+ | None ->
+ let w, _, (ty, left, right, o), m , id = open_equality eq in
+ Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s [%s]"
+ id w (CicPp.ppterm ty)
+ (CicPp.ppterm left)
+ (Utils.string_of_comparison o) (CicPp.ppterm right)
+ (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
+(* "..." *)
+ | Some (_, context, _) ->
+ let names = Utils.names_of_context context in
+ let w, _, (ty, left, right, o), m , id = open_equality eq in
+ Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s [%s]"
+ id w (CicPp.pp ty names)
+ (CicPp.pp left names) (Utils.string_of_comparison o)
+ (CicPp.pp right names)
+ (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
+(* "..." *)
+;;
+
+let compare (_,_,_,s1,_,_) (_,_,_,s2,_,_) =
+ Pervasives.compare s1 s2
+;;
+
+let rec max_weight_in_proof ((id_to_eq,_) as bag) current =
+ function
+ | Exact _ -> current
+ | Step (_, (_,id1,(_,id2),_)) ->
+ let eq1 = Hashtbl.find id_to_eq id1 in
+ let eq2 = Hashtbl.find id_to_eq id2 in
+ let (w1,p1,(_,_,_,_),_,_) = open_equality eq1 in
+ let (w2,p2,(_,_,_,_),_,_) = open_equality eq2 in
+ let current = max current w1 in
+ let current = max_weight_in_proof bag current p1 in
+ let current = max current w2 in
+ max_weight_in_proof bag current p2
+
+let max_weight_in_goal_proof ((id_to_eq,_) as bag) =
+ List.fold_left
+ (fun current (_,_,id,_,_) ->
+ let eq = Hashtbl.find id_to_eq id in
+ let (w,p,(_,_,_,_),_,_) = open_equality eq in
+ let current = max current w in
+ max_weight_in_proof bag current p)
+
+let max_weight bag goal_proof proof =
+ let current = max_weight_in_proof bag 0 proof in
+ max_weight_in_goal_proof bag current goal_proof
+
+let proof_of_id (id_to_eq,_) id =
+ try
+ let (_,p,(_,l,r,_),_,_) = open_equality (Hashtbl.find id_to_eq id) in
+ p,l,r
+ with
+ Not_found -> assert false
+
+
+let string_of_proof ?(names=[]) bag p gp =
+ let str_of_pos = function
+ | Utils.Left -> "left"
+ | Utils.Right -> "right"
+ in
+ let fst3 (x,_,_) = x in
+ let rec aux margin name =
+ let prefix = String.make margin ' ' ^ name ^ ": " in function
+ | Exact t ->
+ Printf.sprintf "%sExact (%s)\n"
+ prefix (CicPp.pp t names)
+ | Step (subst,(rule,eq1,(pos,eq2),pred)) ->
+ Printf.sprintf "%s%s(%s|%d with %d dir %s pred %s))\n"
+ prefix (string_of_rule rule) (Subst.ppsubst ~names subst) eq1 eq2 (str_of_pos pos)
+ (CicPp.pp pred names)^
+ aux (margin+1) (Printf.sprintf "%d" eq1) (fst3 (proof_of_id bag eq1)) ^
+ aux (margin+1) (Printf.sprintf "%d" eq2) (fst3 (proof_of_id bag eq2))
+ in
+ aux 0 "" p ^
+ String.concat "\n"
+ (List.map
+ (fun (r,pos,i,s,t) ->
+ (Printf.sprintf
+ "GOAL: %s %s %d %s %s\n" (string_of_rule r)
+ (str_of_pos pos) i (Subst.ppsubst ~names s) (CicPp.pp t names)) ^
+ aux 1 (Printf.sprintf "%d " i) (fst3 (proof_of_id bag i)))
+ gp)
+;;
+
+let rec depend ((id_to_eq,_) as bag) eq id seen =
+ let (_,p,(_,_,_,_),_,ideq) = open_equality eq in
+ if List.mem ideq seen then
+ false,seen
+ else
+ if id = ideq then
+ true,seen
+ else
+ match p with
+ | Exact _ -> false,seen
+ | Step (_,(_,id1,(_,id2),_)) ->
+ let seen = ideq::seen in
+ let eq1 = Hashtbl.find id_to_eq id1 in
+ let eq2 = Hashtbl.find id_to_eq id2 in
+ let b1,seen = depend bag eq1 id seen in
+ if b1 then b1,seen else depend bag eq2 id seen
+;;
+
+let depend bag eq id = fst (depend bag eq id []);;
+
+let ppsubst = Subst.ppsubst ~names:[];;
+
+(* returns an explicit named subst and a list of arguments for sym_eq_URI *)
+let build_ens uri termlist =
+ let obj, _ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ match obj with
+ | Cic.Constant (_, _, _, uris, _) ->
+ (* assert (List.length uris <= List.length termlist); *)
+ let rec aux = function
+ | [], tl -> [], tl
+ | (uri::uris), (term::tl) ->
+ let ens, args = aux (uris, tl) in
+ (uri, term)::ens, args
+ | _, _ -> assert false
+ in
+ aux (uris, termlist)
+ | _ -> assert false
+;;
+
+let mk_sym uri ty t1 t2 p =
+ let ens, args = build_ens uri [ty;t1;t2;p] in
+ Cic.Appl (Cic.Const(uri, ens) :: args)
+;;
+
+let mk_trans uri ty t1 t2 t3 p12 p23 =
+ let ens, args = build_ens uri [ty;t1;t2;t3;p12;p23] in
+ Cic.Appl (Cic.Const (uri, ens) :: args)
+;;
+
+let mk_eq_ind uri ty what pred p1 other p2 =
+ let ens, args = build_ens uri [ty; what; pred; p1; other; p2] in
+ Cic.Appl (Cic.Const (uri, ens) :: args)
+;;
+
+let p_of_sym ens tl =
+ let args = List.map snd ens @ tl in
+ match args with
+ | [_;_;_;p] -> p
+ | _ -> assert false
+;;
+
+let open_trans ens tl =
+ let args = List.map snd ens @ tl in
+ match args with
+ | [ty;l;m;r;p1;p2] -> ty,l,m,r,p1,p2
+ | _ -> assert false
+;;
+
+let open_sym ens tl =
+ let args = List.map snd ens @ tl in
+ match args with
+ | [ty;l;r;p] -> ty,l,r,p
+ | _ -> assert false
+;;
+
+let open_eq_ind args =
+ match args with
+ | [ty;l;pred;pl;r;pleqr] -> ty,l,pred,pl,r,pleqr
+ | _ -> assert false
+;;
+
+let open_pred pred =
+ match pred with
+ | Cic.Lambda (_,_,(Cic.Appl [Cic.MutInd (uri, 0,_);ty;l;r]))
+ when LibraryObjects.is_eq_URI uri -> ty,uri,l,r
+ | _ -> Utils.debug_print (lazy (CicPp.ppterm pred)); assert false
+;;
+
+let is_not_fixed t =
+ CicSubstitution.subst (Cic.Implicit None) t <>
+ CicSubstitution.subst (Cic.Rel 1) t
+;;
+
+let canonical t context menv =
+ let remove_cycles t =
+ let is_transitive =
+ function
+ Cic.Appl (Cic.Const (uri_trans,_)::_)
+ when LibraryObjects.is_trans_eq_URI uri_trans ->
+ true
+ | _ -> false in
+ let rec collect =
+ function
+ Cic.Appl (Cic.Const (uri_trans,ens)::tl)
+ when LibraryObjects.is_trans_eq_URI uri_trans ->
+ let ty,l,m,r,p1,p2 = open_trans ens tl in
+ (if is_transitive p1 then fst (collect p1) else [l,p1]) @
+ (if is_transitive p2 then fst (collect p2) else [m,p2]),
+ (r, uri_trans, ty)
+ | t -> assert false in
+ let rec cut_to_last_duplicate l acc =
+ function
+ [] -> List.rev acc
+ | (l',p)::tl when l=l' ->
+if acc <> [] then
+Utils.debug_print (lazy ("!!! RISPARMIO " ^ string_of_int (List.length acc) ^ " PASSI"));
+ cut_to_last_duplicate l [l',p] tl
+ | (l',p)::tl ->
+ cut_to_last_duplicate l ((l',p)::acc) tl
+ in
+ let rec rebuild =
+ function
+ (l,_)::_::_ as steps, ((r,uri_trans,ty) as last) ->
+ (match cut_to_last_duplicate l [] steps with
+ (l,p1)::((m,_)::_::_ as tl) ->
+ mk_trans uri_trans ty l m r p1 (rebuild (tl,last))
+ | [l,p1 ; m,p2] -> mk_trans uri_trans ty l m r p1 p2
+ | [l,p1] -> p1
+ | [] -> assert false)
+ | _ -> assert false
+ in
+ if is_transitive t then
+ rebuild (collect t)
+ else
+ t
+ in
+ let rec remove_refl t =
+ match t with
+ | Cic.Appl (((Cic.Const(uri_trans,ens))::tl) as args)
+ when LibraryObjects.is_trans_eq_URI uri_trans ->
+ let ty,l,m,r,p1,p2 = open_trans ens tl in
+ (match p1,p2 with
+ | Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_],p2 ->
+ remove_refl p2
+ | p1,Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_] ->
+ remove_refl p1
+ | _ -> Cic.Appl (List.map remove_refl args))
+ | Cic.Appl l -> Cic.Appl (List.map remove_refl l)
+ | Cic.LetIn (name,bo,ty,rest) ->
+ Cic.LetIn (name,remove_refl bo,remove_refl ty,remove_refl rest)
+ | _ -> t
+ in
+ let rec canonical_trough_lambda context = function
+ | Cic.Lambda(name,ty,bo) ->
+ let context' = (Some (name,Cic.Decl ty))::context in
+ Cic.Lambda(name,ty,canonical_trough_lambda context' bo)
+ | t -> canonical context t
+
+ and canonical context t =
+ match t with
+ | Cic.LetIn(name,bo,ty,rest) ->
+ let bo = canonical_trough_lambda context bo in
+ let ty = canonical_trough_lambda context ty in
+ let context' = (Some (name,Cic.Def (bo,ty)))::context in
+ Cic.LetIn(name,bo,ty,canonical context' rest)
+ | Cic.Appl (((Cic.Const(uri_sym,ens))::tl) as args)
+ when LibraryObjects.is_sym_eq_URI uri_sym ->
+ (match p_of_sym ens tl with
+ | Cic.Appl ((Cic.Const(uri,ens))::tl)
+ when LibraryObjects.is_sym_eq_URI uri ->
+ canonical context (p_of_sym ens tl)
+ | Cic.Appl ((Cic.Const(uri_trans,ens))::tl)
+ when LibraryObjects.is_trans_eq_URI uri_trans ->
+ let ty,l,m,r,p1,p2 = open_trans ens tl in
+ mk_trans uri_trans ty r m l
+ (canonical context (mk_sym uri_sym ty m r p2))
+ (canonical context (mk_sym uri_sym ty l m p1))
+ | Cic.Appl (([Cic.Const(uri_feq,ens);ty1;ty2;f;x;y;p]))
+ when LibraryObjects.is_eq_f_URI uri_feq ->
+ let eq = LibraryObjects.eq_URI_of_eq_f_URI uri_feq in
+ let eq_f_sym =
+ Cic.Const (LibraryObjects.eq_f_sym_URI ~eq, [])
+ in
+ let rc = Cic.Appl [eq_f_sym;ty1;ty2;f;x;y;p] in
+ Utils.debug_print (lazy ("CANONICAL " ^ CicPp.ppterm rc));
+ rc
+ | Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_] as t
+ when LibraryObjects.is_eq_URI uri -> t
+ | _ -> Cic.Appl (List.map (canonical context) args))
+ | Cic.Appl l -> Cic.Appl (List.map (canonical context) l)
+ | _ -> t
+ in
+ remove_cycles (remove_refl (canonical context t))
+;;
+
+let compose_contexts ctx1 ctx2 =
+ ProofEngineReduction.replace_lifting
+ ~equality:(fun _ ->(=)) ~context:[] ~what:[Cic.Implicit(Some `Hole)] ~with_what:[ctx2] ~where:ctx1
+;;
+
+let put_in_ctx ctx t =
+ ProofEngineReduction.replace_lifting
+ ~equality:(fun _ -> (=)) ~context:[] ~what:[Cic.Implicit (Some `Hole)] ~with_what:[t] ~where:ctx
+;;
+
+let mk_eq uri ty l r =
+ let ens, args = build_ens uri [ty; l; r] in
+ Cic.Appl (Cic.MutInd(uri,0,ens) :: args)
+;;
+
+let mk_refl uri ty t =
+ let ens, args = build_ens uri [ty; t] in
+ Cic.Appl (Cic.MutConstruct(uri,0,1,ens) :: args)
+;;
+
+let open_eq = function
+ | Cic.Appl [Cic.MutInd(uri,0,[]);ty;l;r] when LibraryObjects.is_eq_URI uri ->
+ uri, ty, l ,r
+ | _ -> assert false
+;;
+
+let mk_feq uri_feq ty ty1 left pred right t =
+ let ens, args = build_ens uri_feq [ty;ty1;pred;left;right;t] in
+ Cic.Appl (Cic.Const(uri_feq,ens) :: args)
+;;
+
+let rec look_ahead aux = function
+ | Cic.Appl ((Cic.Const(uri_ind,ens))::tl) as t
+ when LibraryObjects.is_eq_ind_URI uri_ind ||
+ LibraryObjects.is_eq_ind_r_URI uri_ind ->
+ let ty1,what,pred,p1,other,p2 = open_eq_ind tl in
+ let ty2,eq,lp,rp = open_pred pred in
+ let hole = Cic.Implicit (Some `Hole) in
+ let ty2 = CicSubstitution.subst hole ty2 in
+ aux ty1 (CicSubstitution.subst other lp) (CicSubstitution.subst other rp) hole ty2 t
+ | Cic.Lambda (n,s,t) -> Cic.Lambda (n,s,look_ahead aux t)
+ | t -> t
+;;
+
+let contextualize uri ty left right t =
+ let hole = Cic.Implicit (Some `Hole) in
+ (* aux [uri] [ty] [left] [right] [ctx] [ctx_ty] [t]
+ *
+ * the parameters validate this invariant
+ * t: eq(uri) ty left right
+ * that is used only by the base case
+ *
+ * ctx is a term with an hole. Cic.Implicit(Some `Hole) is the empty context
+ * ctx_ty is the type of ctx
+ *)
+ let rec aux uri ty left right ctx_d ctx_ty t =
+ match t with
+ | Cic.Appl ((Cic.Const(uri_sym,ens))::tl)
+ when LibraryObjects.is_sym_eq_URI uri_sym ->
+ let ty,l,r,p = open_sym ens tl in
+ mk_sym uri_sym ty l r (aux uri ty l r ctx_d ctx_ty p)
+ | Cic.LetIn (name,body,bodyty,rest) ->
+ Cic.LetIn
+ (name,look_ahead (aux uri) body, bodyty,
+ aux uri ty left right ctx_d ctx_ty rest)
+ | Cic.Appl ((Cic.Const(uri_ind,ens))::tl)
+ when LibraryObjects.is_eq_ind_URI uri_ind ||
+ LibraryObjects.is_eq_ind_r_URI uri_ind ->
+ let ty1,what,pred,p1,other,p2 = open_eq_ind tl in
+ let ty2,eq,lp,rp = open_pred pred in
+ let uri_trans = LibraryObjects.trans_eq_URI ~eq:uri in
+ let uri_sym = LibraryObjects.sym_eq_URI ~eq:uri in
+ let is_not_fixed_lp = is_not_fixed lp in
+ let avoid_eq_ind = LibraryObjects.is_eq_ind_URI uri_ind in
+ (* extract the context and the fixed term from the predicate *)
+ let m, ctx_c, ty2 =
+ let m, ctx_c = if is_not_fixed_lp then rp,lp else lp,rp in
+ (* they were under a lambda *)
+ let m = CicSubstitution.subst hole m in
+ let ctx_c = CicSubstitution.subst hole ctx_c in
+ let ty2 = CicSubstitution.subst hole ty2 in
+ m, ctx_c, ty2
+ in
+ (* create the compound context and put the terms under it *)
+ let ctx_dc = compose_contexts ctx_d ctx_c in
+ let dc_what = put_in_ctx ctx_dc what in
+ let dc_other = put_in_ctx ctx_dc other in
+ (* m is already in ctx_c so it is put in ctx_d only *)
+ let d_m = put_in_ctx ctx_d m in
+ (* we also need what in ctx_c *)
+ let c_what = put_in_ctx ctx_c what in
+ (* now put the proofs in the compound context *)
+ let p1 = (* p1: dc_what = d_m *)
+ if is_not_fixed_lp then
+ aux uri ty2 c_what m ctx_d ctx_ty p1
+ else
+ mk_sym uri_sym ctx_ty d_m dc_what
+ (aux uri ty2 m c_what ctx_d ctx_ty p1)
+ in
+ let p2 = (* p2: dc_other = dc_what *)
+ if avoid_eq_ind then
+ mk_sym uri_sym ctx_ty dc_what dc_other
+ (aux uri ty1 what other ctx_dc ctx_ty p2)
+ else
+ aux uri ty1 other what ctx_dc ctx_ty p2
+ in
+ (* if pred = \x.C[x]=m --> t : C[other]=m --> trans other what m
+ if pred = \x.m=C[x] --> t : m=C[other] --> trans m what other *)
+ let a,b,c,paeqb,pbeqc =
+ if is_not_fixed_lp then
+ dc_other,dc_what,d_m,p2,p1
+ else
+ d_m,dc_what,dc_other,
+ (mk_sym uri_sym ctx_ty dc_what d_m p1),
+ (mk_sym uri_sym ctx_ty dc_other dc_what p2)
+ in
+ mk_trans uri_trans ctx_ty a b c paeqb pbeqc
+ | t when ctx_d = hole -> t
+ | t ->
+(* let uri_sym = LibraryObjects.sym_eq_URI ~eq:uri in *)
+(* let uri_ind = LibraryObjects.eq_ind_URI ~eq:uri in *)
+
+ let uri_feq = LibraryObjects.eq_f_URI ~eq:uri in
+ let pred =
+(* let r = CicSubstitution.lift 1 (put_in_ctx ctx_d left) in *)
+ let l =
+ let ctx_d = CicSubstitution.lift 1 ctx_d in
+ put_in_ctx ctx_d (Cic.Rel 1)
+ in
+(* let lty = CicSubstitution.lift 1 ctx_ty in *)
+(* Cic.Lambda (Cic.Name "foo",ty,(mk_eq uri lty l r)) *)
+ Cic.Lambda (Cic.Name "foo",ty,l)
+ in
+(* let d_left = put_in_ctx ctx_d left in *)
+(* let d_right = put_in_ctx ctx_d right in *)
+(* let refl_eq = mk_refl uri ctx_ty d_left in *)
+(* mk_sym uri_sym ctx_ty d_right d_left *)
+(* (mk_eq_ind uri_ind ty left pred refl_eq right t) *)
+ (mk_feq uri_feq ty ctx_ty left pred right t)
+ in
+ aux uri ty left right hole ty t
+;;
+
+let contextualize_rewrites t ty =
+ let eq,ty,l,r = open_eq ty in
+ contextualize eq ty l r t
+;;
+
+let add_subst subst =
+ function
+ | Exact t -> Exact (Subst.apply_subst subst t)
+ | Step (s,(rule, id1, (pos,id2), pred)) ->
+ Step (Subst.concat subst s,(rule, id1, (pos,id2), pred))
+;;
+
+let build_proof_step eq lift subst p1 p2 pos l r pred =
+ let p1 = Subst.apply_subst_lift lift subst p1 in
+ let p2 = Subst.apply_subst_lift lift subst p2 in
+ let l = CicSubstitution.lift lift l in
+ let l = Subst.apply_subst_lift lift subst l in
+ let r = CicSubstitution.lift lift r in
+ let r = Subst.apply_subst_lift lift subst r in
+ let pred = CicSubstitution.lift lift pred in
+ let pred = Subst.apply_subst_lift lift subst pred in
+ let ty,body =
+ match pred with
+ | Cic.Lambda (_,ty,body) -> ty,body
+ | _ -> assert false
+ in
+ let what, other =
+ if pos = Utils.Left then l,r else r,l
+ in
+ let p =
+ match pos with
+ | Utils.Left ->
+ mk_eq_ind (LibraryObjects.eq_ind_URI ~eq) ty what pred p1 other p2
+ | Utils.Right ->
+ mk_eq_ind (LibraryObjects.eq_ind_r_URI ~eq) ty what pred p1 other p2
+ in
+ p
+;;
+
+let parametrize_proof p l r =
+ let uniq l = HExtlib.list_uniq (List.sort (fun (i,_) (j,_) -> Pervasives.compare i j) l) in
+ let mot = CicUtil.metas_of_term_set in
+ let parameters = uniq (mot p @ mot l @ mot r) in
+ (* ?if they are under a lambda? *)
+(*
+ let parameters =
+ HExtlib.list_uniq (List.sort Pervasives.compare parameters)
+ in
+*)
+ (* resorts l such that *hopefully* dependencies can be inferred *)
+ let guess_dependency p l =
+ match p with
+ | Cic.Appl ((Cic.Const(uri_ind,ens))::tl)
+ when LibraryObjects.is_eq_ind_URI uri_ind ||
+ LibraryObjects.is_eq_ind_r_URI uri_ind ->
+ let ty,_,_,_,_,_ = open_eq_ind tl in
+ let metas = CicUtil.metas_of_term ty in
+ let nondep, dep =
+ List.partition (fun (i,_) -> List.exists (fun (j,_) -> j=i) metas) l
+ in
+ nondep@dep
+ | _ -> l
+ in
+ let parameters = guess_dependency p parameters in
+ let what = List.map (fun (i,l) -> Cic.Meta (i,l)) parameters in
+ let with_what, lift_no =
+ List.fold_right (fun _ (acc,n) -> ((Cic.Rel n)::acc),n+1) what ([],1)
+ in
+ let p = CicSubstitution.lift (lift_no-1) p in
+ let p =
+ ProofEngineReduction.replace_lifting
+ ~equality:(fun _ t1 t2 ->
+ match t1,t2 with Cic.Meta (i,_),Cic.Meta(j,_) -> i=j | _ -> false)
+ ~context:[]
+ ~what ~with_what ~where:p
+ in
+ let ty_of_m _ = Cic.Implicit (Some `Type) in
+ let args, proof,_ =
+ List.fold_left
+ (fun (instance,p,n) m ->
+ (instance@[m],
+ Cic.Lambda
+ (Cic.Name ("X"^string_of_int n),
+ CicSubstitution.lift (lift_no - n - 1) (ty_of_m m),
+ p),
+ n+1))
+ ([Cic.Rel 1],p,1)
+ what
+ in
+ let instance = match args with | [x] -> x | _ -> Cic.Appl args in
+ proof, instance
+;;
+
+let wfo bag goalproof proof id =
+ let rec aux acc id =
+ let p,_,_ = proof_of_id bag id in
+ match p with
+ | Exact _ -> if (List.mem id acc) then acc else id :: acc
+ | Step (_,(_,id1, (_,id2), _)) ->
+ let acc = if not (List.mem id1 acc) then aux acc id1 else acc in
+ let acc = if not (List.mem id2 acc) then aux acc id2 else acc in
+ id :: acc
+ in
+ let acc =
+ match proof with
+ | Exact _ -> [id]
+ | Step (_,(_,id1, (_,id2), _)) -> aux (aux [id] id1) id2
+ in
+ List.fold_left (fun acc (_,_,id,_,_) -> aux acc id) acc goalproof
+;;
+
+let string_of_id (id_to_eq,_) names id =
+ if id = 0 then "" else
+ try
+ let (_,p,(t,l,r,_),m,_) = open_equality (Hashtbl.find id_to_eq id) in
+ match p with
+ | Exact t ->
+ Printf.sprintf "%d = %s: %s = %s [%s]" id
+ (CicPp.pp t names) (CicPp.pp l names) (CicPp.pp r names)
+(* "..." *)
+ (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
+ | Step (_,(step,id1, (dir,id2), p) ) ->
+ Printf.sprintf "%6d: %s %6d %6d %s =(%s) %s [%s]" id
+ (string_of_rule step)
+ id1 id2 (CicPp.pp l names) (CicPp.pp t names) (CicPp.pp r names)
+ (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
+ (*"..."*)
+ with
+ Not_found -> assert false
+
+let pp_proof bag names goalproof proof subst id initial_goal =
+ String.concat "\n" (List.map (string_of_id bag names) (wfo bag goalproof proof id)) ^
+ "\ngoal:\n " ^
+ (String.concat "\n "
+ (fst (List.fold_right
+ (fun (r,pos,i,s,pred) (acc,g) ->
+ let _,_,left,right = open_eq g in
+ let ty =
+ match pos with
+ | Utils.Left -> CicReduction.head_beta_reduce (Cic.Appl[pred;right])
+ | Utils.Right -> CicReduction.head_beta_reduce (Cic.Appl[pred;left])
+ in
+ let ty = Subst.apply_subst s ty in
+ ("("^ string_of_rule r ^ " " ^ string_of_int i^") -> "
+ ^ CicPp.pp ty names) :: acc,ty) goalproof ([],initial_goal)))) ^
+ "\nand then subsumed by " ^ string_of_int id ^ " when " ^ Subst.ppsubst subst
+;;
+
+module OT =
+ struct
+ type t = int
+ let compare = Pervasives.compare
+ end
+
+module M = Map.Make(OT)
+
+let rec find_deps bag m i =
+ if M.mem i m then m
+ else
+ let p,_,_ = proof_of_id bag i in
+ match p with
+ | Exact _ -> M.add i [] m
+ | Step (_,(_,id1,(_,id2),_)) ->
+ let m = find_deps bag m id1 in
+ let m = find_deps bag m id2 in
+ (* without the uniq there is a stack overflow doing concatenation *)
+ let xxx = [id1;id2] @ M.find id1 m @ M.find id2 m in
+ let xxx = HExtlib.list_uniq (List.sort Pervasives.compare xxx) in
+ M.add i xxx m
+;;
+
+let topological_sort bag l =
+ (* build the partial order relation *)
+ let m = List.fold_left (fun m i -> find_deps bag m i) M.empty l in
+ let m = (* keep only deps inside l *)
+ List.fold_left
+ (fun m' i ->
+ M.add i (List.filter (fun x -> List.mem x l) (M.find i m)) m')
+ M.empty l
+ in
+ let m = M.map (fun x -> Some x) m in
+ (* utils *)
+ let keys m = M.fold (fun i _ acc -> i::acc) m [] in
+ let split l m = List.filter (fun i -> M.find i m = Some []) l in
+ let purge l m =
+ M.mapi
+ (fun k v -> if List.mem k l then None else
+ match v with
+ | None -> None
+ | Some ll -> Some (List.filter (fun i -> not (List.mem i l)) ll))
+ m
+ in
+ let rec aux m res =
+ let keys = keys m in
+ let ok = split keys m in
+ let m = purge ok m in
+ let res = ok @ res in
+ if ok = [] then res else aux m res
+ in
+ let rc = List.rev (aux m []) in
+ rc
+;;
+
+
+(* returns the list of ids that should be factorized *)
+let get_duplicate_step_in_wfo bag l p =
+ let ol = List.rev l in
+ let h = Hashtbl.create 13 in
+ (* NOTE: here the n parameter is an approximation of the dependency
+ between equations. To do things seriously we should maintain a
+ dependency graph. This approximation is not perfect. *)
+ let add i =
+ let p,_,_ = proof_of_id bag i in
+ match p with
+ | Exact _ -> true
+ | _ ->
+ try
+ let no = Hashtbl.find h i in
+ Hashtbl.replace h i (no+1);
+ false
+ with Not_found -> Hashtbl.add h i 1;true
+ in
+ let rec aux = function
+ | Exact _ -> ()
+ | Step (_,(_,i1,(_,i2),_)) ->
+ let go_on_1 = add i1 in
+ let go_on_2 = add i2 in
+ if go_on_1 then aux (let p,_,_ = proof_of_id bag i1 in p);
+ if go_on_2 then aux (let p,_,_ = proof_of_id bag i2 in p)
+ in
+ aux p;
+ List.iter
+ (fun (_,_,id,_,_) -> aux (let p,_,_ = proof_of_id bag id in p))
+ ol;
+ (* now h is complete *)
+ let proofs = Hashtbl.fold (fun k count acc-> (k,count)::acc) h [] in
+ let proofs = List.filter (fun (_,c) -> c > 1) proofs in
+ let res = topological_sort bag (List.map (fun (i,_) -> i) proofs) in
+ res
+;;
+
+let build_proof_term bag eq h lift proof =
+ let proof_of_id aux id =
+ let p,l,r = proof_of_id bag id in
+ try List.assoc id h,l,r with Not_found -> aux p, l, r
+ in
+ let rec aux = function
+ | Exact term ->
+ CicSubstitution.lift lift term
+ | Step (subst,(rule, id1, (pos,id2), pred)) ->
+ let p1,_,_ = proof_of_id aux id1 in
+ let p2,l,r = proof_of_id aux id2 in
+ let varname =
+ match rule with
+ | SuperpositionRight -> Cic.Name ("SupR" ^ Utils.string_of_pos pos)
+ | Demodulation -> Cic.Name ("DemEq"^ Utils.string_of_pos pos)
+ | _ -> assert false
+ in
+ let pred =
+ match pred with
+ | Cic.Lambda (_,a,b) -> Cic.Lambda (varname,a,b)
+ | _ -> assert false
+ in
+ let p = build_proof_step eq lift subst p1 p2 pos l r pred in
+(* let cond = (not (List.mem 302 (Utils.metas_of_term p)) || id1 = 8 || id1 = 132) in
+ if not cond then
+ prerr_endline ("ERROR " ^ string_of_int id1 ^ " " ^ string_of_int id2);
+ assert cond;*)
+ p
+ in
+ aux proof
+;;
+
+let build_goal_proof bag eq l initial ty se context menv =
+ let se = List.map (fun i -> Cic.Meta (i,[])) se in
+ let lets = get_duplicate_step_in_wfo bag l initial in
+ let letsno = List.length lets in
+ let lift_list l = List.map (fun (i,t) -> i,CicSubstitution.lift 1 t) l in
+ let lets,_,h =
+ List.fold_left
+ (fun (acc,n,h) id ->
+ let p,l,r = proof_of_id bag id in
+ let cic = build_proof_term bag eq h n p in
+ let real_cic,instance =
+ parametrize_proof cic l r
+ in
+ let h = (id, instance)::lift_list h in
+ acc@[id,real_cic],n+1,h)
+ ([],0,[]) lets
+ in
+ let lets =
+ List.map (fun (id,cic) -> id,cic,Cic.Implicit (Some `Type)) lets
+ in
+ let proof,se =
+ let rec aux se current_proof = function
+ | [] -> current_proof,se
+ | (rule,pos,id,subst,pred)::tl ->
+ let p,l,r = proof_of_id bag id in
+ let p = build_proof_term bag eq h letsno p in
+ let pos = if pos = Utils.Left then Utils.Right else Utils.Left in
+ let varname =
+ match rule with
+ | SuperpositionLeft -> Cic.Name ("SupL" ^ Utils.string_of_pos pos)
+ | Demodulation -> Cic.Name ("DemG"^ Utils.string_of_pos pos)
+ | _ -> assert false
+ in
+ let pred =
+ match pred with
+ | Cic.Lambda (_,a,b) -> Cic.Lambda (varname,a,b)
+ | _ -> assert false
+ in
+ let proof =
+ build_proof_step eq letsno subst current_proof p pos l r pred
+ in
+ let proof,se = aux se proof tl in
+ Subst.apply_subst_lift letsno subst proof,
+ List.map (fun x -> Subst.apply_subst(*_lift letsno*) subst x) se
+ in
+ aux se (build_proof_term bag eq h letsno initial) l
+ in
+ let n,proof =
+ let initial = proof in
+ List.fold_right
+ (fun (id,cic,ty) (n,p) ->
+ n-1,
+ Cic.LetIn (
+ Cic.Name ("H"^string_of_int id),
+ cic,
+ ty,
+ p))
+ lets (letsno-1,initial)
+ in
+ canonical
+ (contextualize_rewrites proof (CicSubstitution.lift letsno ty))
+ context menv,
+ se
+;;
+
+let refl_proof eq_uri ty term =
+ Cic.Appl [Cic.MutConstruct (eq_uri, 0, 1, []); ty; term]
+;;
+
+let metas_of_proof bag p =
+ let eq =
+ match LibraryObjects.eq_URI () with
+ | Some u -> u
+ | None ->
+ raise
+ (ProofEngineTypes.Fail
+ (lazy "No default equality defined when calling metas_of_proof"))
+ in
+ let p = build_proof_term bag eq [] 0 p in
+ Utils.metas_of_term p
+;;
+
+let remove_local_context eq =
+ let w, p, (ty, left, right, o), menv,id = open_equality eq in
+ let p = Utils.remove_local_context p in
+ let ty = Utils.remove_local_context ty in
+ let left = Utils.remove_local_context left in
+ let right = Utils.remove_local_context right in
+ w, p, (ty, left, right, o), menv, id
+;;
+
+let relocate newmeta menv to_be_relocated =
+ let subst, newmetasenv, newmeta =
+ List.fold_right
+ (fun i (subst, metasenv, maxmeta) ->
+ let _,context,ty = CicUtil.lookup_meta i menv in
+ let irl = [] in
+ let newmeta = Cic.Meta(maxmeta,irl) in
+ let newsubst = Subst.buildsubst i context newmeta ty subst in
+ newsubst, (maxmeta,context,ty)::metasenv, maxmeta+1)
+ to_be_relocated (Subst.empty_subst, [], newmeta+1)
+ in
+ let menv = Subst.apply_subst_metasenv subst menv @ newmetasenv in
+ subst, menv, newmeta
+
+let fix_metas_goal newmeta goal =
+ let (proof, menv, ty) = goal in
+ let to_be_relocated =
+ HExtlib.list_uniq (List.sort Pervasives.compare (Utils.metas_of_term ty))
+ in
+ let subst, menv, newmeta = relocate newmeta menv to_be_relocated in
+ let ty = Subst.apply_subst subst ty in
+ let proof =
+ match proof with
+ | [] -> assert false (* is a nonsense to relocate the initial goal *)
+ | (r,pos,id,s,p) :: tl -> (r,pos,id,Subst.concat subst s,p) :: tl
+ in
+ newmeta+1,(proof, menv, ty)
+;;
+
+let fix_metas bag newmeta eq =
+ let w, p, (ty, left, right, o), menv,_ = open_equality eq in
+ let to_be_relocated =
+(* List.map (fun i ,_,_ -> i) menv *)
+ HExtlib.list_uniq
+ (List.sort Pervasives.compare
+ (Utils.metas_of_term left @ Utils.metas_of_term right @
+ Utils.metas_of_term ty))
+ in
+ let subst, metasenv, newmeta = relocate newmeta menv to_be_relocated in
+ let ty = Subst.apply_subst subst ty in
+ let left = Subst.apply_subst subst left in
+ let right = Subst.apply_subst subst right in
+ let fix_proof = function
+ | Exact p -> Exact (Subst.apply_subst subst p)
+ | Step (s,(r,id1,(pos,id2),pred)) ->
+ Step (Subst.concat s subst,(r,id1,(pos,id2), pred))
+ in
+ let p = fix_proof p in
+ let eq' = mk_equality bag (w, p, (ty, left, right, o), metasenv) in
+ newmeta+1, eq'
+
+exception NotMetaConvertible;;
+
+let meta_convertibility_aux table t1 t2 =
+ let module C = Cic in
+ let rec aux ((table_l,table_r) as table) t1 t2 =
+ match t1, t2 with
+ | C.Meta (m1, tl1), C.Meta (m2, tl2) when m1 = m2 -> table
+ | C.Meta (m1, tl1), C.Meta (m2, tl2) when m1 < m2 -> aux table t2 t1
+ | C.Meta (m1, tl1), C.Meta (m2, tl2) ->
+ let m1_binding, table_l =
+ try List.assoc m1 table_l, table_l
+ with Not_found -> m2, (m1, m2)::table_l
+ and m2_binding, table_r =
+ try List.assoc m2 table_r, table_r
+ with Not_found -> m1, (m2, m1)::table_r
+ in
+ if (m1_binding <> m2) || (m2_binding <> m1) then
+ raise NotMetaConvertible
+ else table_l,table_r
+ | C.Var (u1, ens1), C.Var (u2, ens2)
+ | C.Const (u1, ens1), C.Const (u2, ens2) when (UriManager.eq u1 u2) ->
+ aux_ens table ens1 ens2
+ | C.Cast (s1, t1), C.Cast (s2, t2)
+ | C.Prod (_, s1, t1), C.Prod (_, s2, t2)
+ | C.Lambda (_, s1, t1), C.Lambda (_, s2, t2) ->
+ let table = aux table s1 s2 in
+ aux table t1 t2
+ | C.LetIn (_, s1, ty1, t1), C.LetIn (_, s2, ty2, t2) ->
+ let table = aux table s1 s2 in
+ let table = aux table ty1 ty2 in
+ aux table t1 t2
+ | C.Appl l1, C.Appl l2 -> (
+ try List.fold_left2 (fun res t1 t2 -> (aux res t1 t2)) table l1 l2
+ with Invalid_argument _ -> raise NotMetaConvertible
+ )
+ | C.MutInd (u1, i1, ens1), C.MutInd (u2, i2, ens2)
+ when (UriManager.eq u1 u2) && i1 = i2 -> aux_ens table ens1 ens2
+ | C.MutConstruct (u1, i1, j1, ens1), C.MutConstruct (u2, i2, j2, ens2)
+ when (UriManager.eq u1 u2) && i1 = i2 && j1 = j2 ->
+ aux_ens table ens1 ens2
+ | C.MutCase (u1, i1, s1, t1, l1), C.MutCase (u2, i2, s2, t2, l2)
+ when (UriManager.eq u1 u2) && i1 = i2 ->
+ let table = aux table s1 s2 in
+ let table = aux table t1 t2 in (
+ try List.fold_left2 (fun res t1 t2 -> (aux res t1 t2)) table l1 l2
+ with Invalid_argument _ -> raise NotMetaConvertible
+ )
+ | C.Fix (i1, il1), C.Fix (i2, il2) when i1 = i2 -> (
+ try
+ List.fold_left2
+ (fun res (n1, i1, s1, t1) (n2, i2, s2, t2) ->
+ if i1 <> i2 then raise NotMetaConvertible
+ else
+ let res = (aux res s1 s2) in aux res t1 t2)
+ table il1 il2
+ with Invalid_argument _ -> raise NotMetaConvertible
+ )
+ | C.CoFix (i1, il1), C.CoFix (i2, il2) when i1 = i2 -> (
+ try
+ List.fold_left2
+ (fun res (n1, s1, t1) (n2, s2, t2) ->
+ let res = aux res s1 s2 in aux res t1 t2)
+ table il1 il2
+ with Invalid_argument _ -> raise NotMetaConvertible
+ )
+ | t1, t2 when t1 = t2 -> table
+ | _, _ -> raise NotMetaConvertible
+
+ and aux_ens table ens1 ens2 =
+ let cmp (u1, t1) (u2, t2) =
+ Pervasives.compare (UriManager.string_of_uri u1) (UriManager.string_of_uri u2)
+ in
+ let ens1 = List.sort cmp ens1
+ and ens2 = List.sort cmp ens2 in
+ try
+ List.fold_left2
+ (fun res (u1, t1) (u2, t2) ->
+ if not (UriManager.eq u1 u2) then raise NotMetaConvertible
+ else aux res t1 t2)
+ table ens1 ens2
+ with Invalid_argument _ -> raise NotMetaConvertible
+ in
+ aux table t1 t2
+;;
+
+
+let meta_convertibility_eq eq1 eq2 =
+ let _, _, (ty, left, right, _), _,_ = open_equality eq1 in
+ let _, _, (ty', left', right', _), _,_ = open_equality eq2 in
+ if ty <> ty' then
+ false
+ else if (left = left') && (right = right') then
+ true
+ else if (left = right') && (right = left') then
+ true
+ else
+ try
+ let table = meta_convertibility_aux ([],[]) left left' in
+ let _ = meta_convertibility_aux table right right' in
+ true
+ with NotMetaConvertible ->
+ try
+ let table = meta_convertibility_aux ([],[]) left right' in
+ let _ = meta_convertibility_aux table right left' in
+ true
+ with NotMetaConvertible ->
+ false
+;;
+
+let meta_convertibility t1 t2 =
+ if t1 = t2 then
+ true
+ else
+ try
+ ignore(meta_convertibility_aux ([],[]) t1 t2);
+ true
+ with NotMetaConvertible ->
+ false
+;;
+
+let meta_convertibility_subst t1 t2 menv =
+ if t1 = t2 then
+ Some([])
+ else
+ try
+ let (l,_) = meta_convertibility_aux ([],[]) t1 t2 in
+ let subst =
+ List.map
+ (fun (x,y) ->
+ try
+ let (_,c,t) = CicUtil.lookup_meta x menv in
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable c in
+ (y,(c,Cic.Meta(x,irl),t))
+ with CicUtil.Meta_not_found _ ->
+ try
+ let (_,c,t) = CicUtil.lookup_meta y menv in
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable c in
+ (x,(c,Cic.Meta(y,irl),t))
+ with CicUtil.Meta_not_found _ -> assert false) l in
+ Some subst
+ with NotMetaConvertible ->
+ None
+;;
+
+exception TermIsNotAnEquality;;
+
+let term_is_equality term =
+ match term with
+ | Cic.Appl [Cic.MutInd (uri, _, _); _; _; _]
+ when LibraryObjects.is_eq_URI uri -> true
+ | _ -> false
+;;
+
+let equality_of_term bag proof term =
+ match term with
+ | Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2]
+ when LibraryObjects.is_eq_URI uri ->
+ let o = !Utils.compare_terms t1 t2 in
+ let stat = (ty,t1,t2,o) in
+ let w = Utils.compute_equality_weight stat in
+ let e = mk_equality bag (w, Exact proof, stat,[]) in
+ e
+ | _ ->
+ raise TermIsNotAnEquality
+;;
+
+let is_weak_identity eq =
+ let _,_,(_,left, right,_),_,_ = open_equality eq in
+ left = right
+ (* doing metaconv here is meaningless *)
+;;
+
+let is_identity (_, context, ugraph) eq =
+ let _,_,(ty,left,right,_),menv,_ = open_equality eq in
+ (* doing metaconv here is meaningless *)
+ left = right
+(* fst (CicReduction.are_convertible ~metasenv:menv context left right ugraph)
+ * *)
+;;
+
+
+let term_of_equality eq_uri equality =
+ let _, _, (ty, left, right, _), menv, _= open_equality equality in
+ let eq i = function Cic.Meta (j, _) -> i = j | _ -> false in
+ let argsno = List.length menv in
+ let t =
+ CicSubstitution.lift argsno
+ (Cic.Appl [Cic.MutInd (eq_uri, 0, []); ty; left; right])
+ in
+ snd (
+ List.fold_right
+ (fun (i,_,ty) (n, t) ->
+ let name = Cic.Name ("X" ^ (string_of_int n)) in
+ let ty = CicSubstitution.lift (n-1) ty in
+ let t =
+ ProofEngineReduction.replace
+ ~equality:eq ~what:[i]
+ ~with_what:[Cic.Rel (argsno - (n - 1))] ~where:t
+ in
+ (n-1, Cic.Prod (name, ty, t)))
+ menv (argsno, t))
+;;
+
+let symmetric bag eq_ty l id uri m =
+ let eq = Cic.MutInd(uri,0,[]) in
+ let pred =
+ Cic.Lambda (Cic.Name "Sym",eq_ty,
+ Cic.Appl [CicSubstitution.lift 1 eq ;
+ CicSubstitution.lift 1 eq_ty;
+ Cic.Rel 1;CicSubstitution.lift 1 l])
+ in
+ let prefl =
+ Exact (Cic.Appl
+ [Cic.MutConstruct(uri,0,1,[]);eq_ty;l])
+ in
+ let id1 =
+ let eq = mk_equality bag (0,prefl,(eq_ty,l,l,Utils.Eq),m) in
+ let (_,_,_,_,id) = open_equality eq in
+ id
+ in
+ Step(Subst.empty_subst,
+ (Demodulation,id1,(Utils.Left,id),pred))
+;;
+
+module IntOT = struct
+ type t = int
+ let compare = Pervasives.compare
+end
+
+module IntSet = Set.Make(IntOT);;
+
+let n_purged = ref 0;;
+
+let collect ((id_to_eq,_) as bag) alive1 alive2 alive3 =
+(* let _ = <:start<collect>> in *)
+ let deps_of id =
+ let p,_,_ = proof_of_id bag id in
+ match p with
+ | Exact _ -> IntSet.empty
+ | Step (_,(_,id1,(_,id2),_)) ->
+ IntSet.add id1 (IntSet.add id2 IntSet.empty)
+ in
+ let rec close s =
+ let news = IntSet.fold (fun id s -> IntSet.union (deps_of id) s) s s in
+ if IntSet.equal news s then s else close news
+ in
+ let l_to_s s l = List.fold_left (fun s x -> IntSet.add x s) s l in
+ let alive_set = l_to_s (l_to_s (l_to_s IntSet.empty alive2) alive1) alive3 in
+ let closed_alive_set = close alive_set in
+ let to_purge =
+ Hashtbl.fold
+ (fun k _ s ->
+ if not (IntSet.mem k closed_alive_set) then
+ k::s else s) id_to_eq []
+ in
+ n_purged := !n_purged + List.length to_purge;
+ List.iter (Hashtbl.remove id_to_eq) to_purge;
+(* let _ = <:stop<collect>> in () *)
+;;
+
+let id_of e =
+ let _,_,_,_,id = open_equality e in id
+;;
+
+let get_stats () = ""
+(*
+ <:show<Equality.>> ^
+ "# of purged eq by the collector: " ^ string_of_int !n_purged ^ "\n"
+*)
+;;
+
+let rec pp_proofterm name t context =
+ let rec skip_lambda tys ctx = function
+ | Cic.Lambda (n,s,t) -> skip_lambda (s::tys) ((Some n)::ctx) t
+ | t -> ctx,tys,t
+ in
+ let rename s name =
+ match name with
+ | Cic.Name s1 -> Cic.Name (s ^ s1)
+ | _ -> assert false
+ in
+ let rec skip_letin ctx = function
+ | Cic.LetIn (n,b,_,t) ->
+ pp_proofterm (Some (rename "Lemma " n)) b ctx::
+ skip_letin ((Some n)::ctx) t
+ | t ->
+ let ppterm t = CicPp.pp t ctx in
+ let rec pp inner = function
+ | Cic.Appl [Cic.Const (uri,[]);_;l;m;r;p1;p2]
+ when Pcre.pmatch ~pat:"trans_eq" (UriManager.string_of_uri uri)->
+ if not inner then
+ (" " ^ ppterm l) :: pp true p1 @
+ [ " = " ^ ppterm m ] @ pp true p2 @
+ [ " = " ^ ppterm r ]
+ else
+ pp true p1 @
+ [ " = " ^ ppterm m ] @ pp true p2
+ | Cic.Appl [Cic.Const (uri,[]);_;l;m;p]
+ when Pcre.pmatch ~pat:"sym_eq" (UriManager.string_of_uri uri)->
+ pp true p
+ | Cic.Appl [Cic.Const (uri,[]);_;_;_;_;_;p]
+ when Pcre.pmatch ~pat:"eq_f" (UriManager.string_of_uri uri)->
+ pp true p
+ | Cic.Appl [Cic.Const (uri,[]);_;_;_;_;_;p]
+ when Pcre.pmatch ~pat:"eq_OF_eq" (UriManager.string_of_uri uri)->
+ pp true p
+ | Cic.Appl [Cic.MutConstruct (uri,_,_,[]);_;_;t;p]
+ when Pcre.pmatch ~pat:"ex.ind" (UriManager.string_of_uri uri)->
+ [ "witness " ^ ppterm t ] @ pp true p
+ | Cic.Appl (t::_) ->[ " [by " ^ ppterm t ^ "]"]
+ | t ->[ " [by " ^ ppterm t ^ "]"]
+ in
+ let rec compat = function
+ | a::b::tl -> (b ^ a) :: compat tl
+ | h::[] -> [h]
+ | [] -> []
+ in
+ let compat l = List.hd l :: compat (List.tl l) in
+ compat (pp false t) @ ["";""]
+ in
+ let names, tys, body = skip_lambda [] context t in
+ let ppname name = (match name with Some (Cic.Name s) -> s | _ -> "") in
+ ppname name ^ ":\n" ^
+ (if context = [] then
+ let rec pp_l ctx = function
+ | (t,name)::tl ->
+ " " ^ ppname name ^ ": " ^ CicPp.pp t ctx ^ "\n" ^
+ pp_l (name::ctx) tl
+ | [] -> "\n\n"
+ in
+ pp_l [] (List.rev (List.combine tys names))
+ else "")
+ ^
+ String.concat "\n" (skip_letin names body)
+;;
+
+let pp_proofterm t =
+ "\n\n" ^
+ pp_proofterm (Some (Cic.Name "Hypothesis")) t []
+;;
+
+let initial_nameset_list = [
+ "x"; "y"; "z"; "t"; "u"; "v"; "a"; "b"; "c"; "d";
+ "e"; "l"; "m"; "n"; "o"; "p"; "q"; "r";
+]
+
+module S = Set.Make(String)
+
+let initial_nameset = List.fold_right S.add initial_nameset_list S.empty, [];;
+
+let freshname (nameset, subst) term =
+ let m = CicUtil.metas_of_term term in
+ let nameset, subst =
+ List.fold_left
+ (fun (set,rc) (m,_) ->
+ if List.mem_assoc m rc then set,rc else
+ let name = S.choose set in
+ let set = S.remove name set in
+ set,
+ (m,Cic.Const(UriManager.uri_of_string
+ ("cic:/"^name^".con"),[]))::rc)
+ (nameset,subst) m
+ in
+ let term =
+ ProofEngineReduction.replace
+ ~equality:(fun i t -> match t with Cic.Meta (j,_) -> i=j| _ -> false)
+ ~what:(List.map fst subst)
+ ~with_what:(List.map snd subst) ~where:term
+ in
+ (nameset, subst), term
+;;
+
+let remove_names_in_context (set,subst) names =
+ List.fold_left
+ (fun s n ->
+ match n with Some (Cic.Name n) -> S.remove n s | _ -> s)
+ set names, subst
+;;
+
+let string_of_id2 (id_to_eq,_) names nameset id =
+ if id = 0 then "" else
+ try
+ let (_,_,(_,l,r,_),_,_) = open_equality (Hashtbl.find id_to_eq id) in
+ let nameset, l = freshname nameset l in
+ let nameset, r = freshname nameset r in
+ Printf.sprintf "%s = %s" (CicPp.pp l names) (CicPp.pp r names)
+ with
+ Not_found -> assert false
+;;
+
+let draw_proof bag names goal_proof proof id =
+ let b = Buffer.create 100 in
+ let fmt = Format.formatter_of_buffer b in
+ let sint = string_of_int in
+ let fst3 (x,_,_) = x in
+ let visited = ref [] in
+ let nameset = remove_names_in_context initial_nameset names in
+ let rec fact id = function
+ | Exact t ->
+ if not (List.mem id !visited) then
+ begin
+ visited := id :: !visited;
+ let nameset, t = freshname nameset t in
+ let t = CicPp.pp t names in
+ GraphvizPp.Dot.node (sint id)
+ ~attrs:["label",t^":"^string_of_id2 bag names nameset id;
+ "shape","rectangle"] fmt;
+ end
+ | Step (_,(_,id1,(_,id2),_)) ->
+ GraphvizPp.Dot.edge (sint id) (sint id1) fmt;
+ GraphvizPp.Dot.edge (sint id) (sint id2) fmt;
+ let p1,_,_ = proof_of_id bag id1 in
+ let p2,_,_ = proof_of_id bag id2 in
+ fact id1 p1;
+ fact id2 p2;
+ if not (List.mem id !visited); then
+ begin
+ visited := id :: !visited;
+ GraphvizPp.Dot.node (sint id)
+ ~attrs:["label",sint id^":"^string_of_id2 bag names nameset id;
+ "shape","ellipse"] fmt
+ end
+ in
+ let sleft acc (_,_,id,_,_) =
+ if acc != 0 then GraphvizPp.Dot.edge (sint acc) (sint id) fmt;
+ fact id (fst3 (proof_of_id bag id));
+ id
+ in
+ GraphvizPp.Dot.header ~node_attrs:["fontsize","10"; ] fmt;
+ ignore(List.fold_left sleft id goal_proof);
+ GraphvizPp.Dot.trailer fmt;
+ let oc = open_out "/tmp/matita_paramod.dot" in
+ Buffer.output_buffer oc b;
+ close_out oc;
+ Utils.debug_print (lazy "dot!");
+ ignore(Unix.system
+ "dot -Tps -o /tmp/matita_paramod.eps /tmp/matita_paramod.dot"
+(* "cat /tmp/matita_paramod.dot| tred | dot -Tps -o /tmp/matita_paramod.eps" *)
+ );
+ ignore(Unix.system "gv /tmp/matita_paramod.eps");
+;;
+
projects / helm.git / blobdiff