+open Utils;;
+
+
+exception NotMetaConvertible;;
+
+let meta_convertibility_aux table t1 t2 =
+ let module C = Cic in
+ let rec aux table t1 t2 =
+ match t1, t2 with
+ | t1, t2 when t1 = t2 -> table
+ | C.Meta (m1, tl1), C.Meta (m2, tl2) ->
+ let m1_binding, table =
+ try List.assoc m1 table, table
+ with Not_found -> m2, (m1, m2)::table
+ in
+ if m1_binding <> m2 then
+ raise NotMetaConvertible
+ else (
+ try
+ List.fold_left2
+ (fun res t1 t2 ->
+ match t1, t2 with
+ | None, Some _ | Some _, None -> raise NotMetaConvertible
+ | None, None -> res
+ | Some t1, Some t2 -> (aux res t1 t2))
+ table tl1 tl2
+ with Invalid_argument _ ->
+ raise NotMetaConvertible
+ )
+ | 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)
+ | C.LetIn (_, s1, t1), C.LetIn (_, s2, t2) ->
+ let table = aux table s1 s2 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
+ )
+ | _, _ -> raise NotMetaConvertible
+
+ and aux_ens table ens1 ens2 =
+ let cmp (u1, t1) (u2, t2) =
+ 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), _, _ = eq1
+ and _, (ty', left', right'), _, _ = eq2 in
+ if ty <> ty' then
+ false
+ else
+ let print_table t w =
+ Printf.printf "table %s is:\n" w;
+ List.iter
+ (fun (k, v) -> Printf.printf "?%d: ?%d\n" k v)
+ t;
+ print_newline ();
+ in
+ try
+ let table = meta_convertibility_aux [] left left' in
+(* print_table table "before"; *)
+ let table = meta_convertibility_aux table right right' in
+(* print_table table "after"; *)
+ true
+ with NotMetaConvertible ->
+(* Printf.printf "NotMetaConvertible:\n%s = %s\n%s = %s\n\n" *)
+(* (CicPp.ppterm left) (CicPp.ppterm right) *)
+(* (CicPp.ppterm left') (CicPp.ppterm right'); *)
+ false
+;;
+
+
+let meta_convertibility t1 t2 =
+ try
+ let _ = meta_convertibility_aux [] t1 t2 in
+ true
+ with NotMetaConvertible ->
+ false
+;;
+
+
+let beta_expand ?(metas_ok=true) ?(match_only=false)
+ what type_of_what where context metasenv ugraph =
+ let module S = CicSubstitution in
+ let module C = Cic in
+ (*
+ return value:
+ ((list of all possible beta expansions, subst, metasenv, ugraph),
+ lifted term)
+ *)
+ let rec aux lift_amount term context metasenv subst ugraph =
+(* Printf.printf "enter aux %s\n" (CicPp.ppterm term); *)
+ let res, lifted_term =
+ match term with
+ | C.Rel m ->
+ [], if m <= lift_amount then C.Rel m else C.Rel (m+1)
+
+ | C.Var (uri, exp_named_subst) ->
+ let ens', lifted_ens =
+ aux_ens lift_amount exp_named_subst context metasenv subst ugraph
+ in
+ let expansions =
+ List.map
+ (fun (e, s, m, ug) ->
+ (C.Var (uri, e), s, m, ug)) ens'
+ in
+ expansions, C.Var (uri, lifted_ens)
+
+ | C.Meta (i, l) ->
+ let l', lifted_l =
+ List.fold_right
+ (fun arg (res, lifted_tl) ->
+ match arg with
+ | Some arg ->
+ let arg_res, lifted_arg =
+ aux lift_amount arg context metasenv subst ugraph in
+ let l1 =
+ List.map
+ (fun (a, s, m, ug) -> (Some a)::lifted_tl, s, m, ug)
+ arg_res
+ in
+ (l1 @
+ (List.map
+ (fun (r, s, m, ug) -> (Some lifted_arg)::r, s, m, ug)
+ res),
+ (Some lifted_arg)::lifted_tl)
+ | None ->
+ (List.map
+ (fun (r, s, m, ug) -> None::r, s, m, ug)
+ res,
+ None::lifted_tl)
+ ) l ([], [])
+ in
+ let e =
+ List.map
+ (fun (l, s, m, ug) ->
+ (C.Meta (i, l), s, m, ug)) l'
+ in
+ e, C.Meta (i, lifted_l)
+
+ | C.Sort _
+ | C.Implicit _ as t -> [], t
+
+ | C.Cast (s, t) ->
+ let l1, lifted_s =
+ aux lift_amount s context metasenv subst ugraph in
+ let l2, lifted_t =
+ aux lift_amount t context metasenv subst ugraph
+ in
+ let l1' =
+ List.map
+ (fun (t, s, m, ug) ->
+ C.Cast (t, lifted_t), s, m, ug) l1 in
+ let l2' =
+ List.map
+ (fun (t, s, m, ug) ->
+ C.Cast (lifted_s, t), s, m, ug) l2 in
+ l1'@l2', C.Cast (lifted_s, lifted_t)
+
+ | C.Prod (nn, s, t) ->
+ let l1, lifted_s =
+ aux lift_amount s context metasenv subst ugraph in
+ let l2, lifted_t =
+ aux (lift_amount+1) t ((Some (nn, C.Decl s))::context)
+ metasenv subst ugraph
+ in
+ let l1' =
+ List.map
+ (fun (t, s, m, ug) ->
+ C.Prod (nn, t, lifted_t), s, m, ug) l1 in
+ let l2' =
+ List.map
+ (fun (t, s, m, ug) ->
+ C.Prod (nn, lifted_s, t), s, m, ug) l2 in
+ l1'@l2', C.Prod (nn, lifted_s, lifted_t)
+
+ | C.Lambda (nn, s, t) ->
+ let l1, lifted_s =
+ aux lift_amount s context metasenv subst ugraph in
+ let l2, lifted_t =
+ aux (lift_amount+1) t ((Some (nn, C.Decl s))::context)
+ metasenv subst ugraph
+ in
+ let l1' =
+ List.map
+ (fun (t, s, m, ug) ->
+ C.Lambda (nn, t, lifted_t), s, m, ug) l1 in
+ let l2' =
+ List.map
+ (fun (t, s, m, ug) ->
+ C.Lambda (nn, lifted_s, t), s, m, ug) l2 in
+ l1'@l2', C.Lambda (nn, lifted_s, lifted_t)
+
+ | C.LetIn (nn, s, t) ->
+ let l1, lifted_s =
+ aux lift_amount s context metasenv subst ugraph in
+ let l2, lifted_t =
+ aux (lift_amount+1) t ((Some (nn, C.Def (s, None)))::context)
+ metasenv subst ugraph
+ in
+ let l1' =
+ List.map
+ (fun (t, s, m, ug) ->
+ C.LetIn (nn, t, lifted_t), s, m, ug) l1 in
+ let l2' =
+ List.map
+ (fun (t, s, m, ug) ->
+ C.LetIn (nn, lifted_s, t), s, m, ug) l2 in
+ l1'@l2', C.LetIn (nn, lifted_s, lifted_t)
+
+ | C.Appl l ->
+ let l', lifted_l =
+ aux_list lift_amount l context metasenv subst ugraph
+ in
+ (List.map (fun (l, s, m, ug) -> (C.Appl l, s, m, ug)) l',
+ C.Appl lifted_l)
+
+ | C.Const (uri, exp_named_subst) ->
+ let ens', lifted_ens =
+ aux_ens lift_amount exp_named_subst context metasenv subst ugraph
+ in
+ let expansions =
+ List.map
+ (fun (e, s, m, ug) ->
+ (C.Const (uri, e), s, m, ug)) ens'
+ in
+ (expansions, C.Const (uri, lifted_ens))
+
+ | C.MutInd (uri, i ,exp_named_subst) ->
+ let ens', lifted_ens =
+ aux_ens lift_amount exp_named_subst context metasenv subst ugraph
+ in
+ let expansions =
+ List.map
+ (fun (e, s, m, ug) ->
+ (C.MutInd (uri, i, e), s, m, ug)) ens'
+ in
+ (expansions, C.MutInd (uri, i, lifted_ens))
+
+ | C.MutConstruct (uri, i, j, exp_named_subst) ->
+ let ens', lifted_ens =
+ aux_ens lift_amount exp_named_subst context metasenv subst ugraph
+ in
+ let expansions =
+ List.map
+ (fun (e, s, m, ug) ->
+ (C.MutConstruct (uri, i, j, e), s, m, ug)) ens'
+ in
+ (expansions, C.MutConstruct (uri, i, j, lifted_ens))
+
+ | C.MutCase (sp, i, outt, t, pl) ->
+ let pl_res, lifted_pl =
+ aux_list lift_amount pl context metasenv subst ugraph
+ in
+ let l1, lifted_outt =
+ aux lift_amount outt context metasenv subst ugraph in
+ let l2, lifted_t =
+ aux lift_amount t context metasenv subst ugraph in
+
+ let l1' =
+ List.map
+ (fun (outt, s, m, ug) ->
+ C.MutCase (sp, i, outt, lifted_t, lifted_pl), s, m, ug) l1 in
+ let l2' =
+ List.map
+ (fun (t, s, m, ug) ->
+ C.MutCase (sp, i, lifted_outt, t, lifted_pl), s, m, ug) l2 in
+ let l3' =
+ List.map
+ (fun (pl, s, m, ug) ->
+ C.MutCase (sp, i, lifted_outt, lifted_t, pl), s, m, ug) pl_res
+ in
+ (l1'@l2'@l3', C.MutCase (sp, i, lifted_outt, lifted_t, lifted_pl))
+
+ | C.Fix (i, fl) ->
+ let len = List.length fl in
+ let fl', lifted_fl =
+ List.fold_right
+ (fun (nm, idx, ty, bo) (res, lifted_tl) ->
+ let lifted_ty = S.lift lift_amount ty in
+ let bo_res, lifted_bo =
+ aux (lift_amount+len) bo context metasenv subst ugraph in
+ let l1 =
+ List.map
+ (fun (a, s, m, ug) ->
+ (nm, idx, lifted_ty, a)::lifted_tl, s, m, ug)
+ bo_res
+ in
+ (l1 @
+ (List.map
+ (fun (r, s, m, ug) ->
+ (nm, idx, lifted_ty, lifted_bo)::r, s, m, ug) res),
+ (nm, idx, lifted_ty, lifted_bo)::lifted_tl)
+ ) fl ([], [])
+ in
+ (List.map
+ (fun (fl, s, m, ug) -> C.Fix (i, fl), s, m, ug) fl',
+ C.Fix (i, lifted_fl))
+
+ | C.CoFix (i, fl) ->
+ let len = List.length fl in
+ let fl', lifted_fl =
+ List.fold_right
+ (fun (nm, ty, bo) (res, lifted_tl) ->
+ let lifted_ty = S.lift lift_amount ty in
+ let bo_res, lifted_bo =
+ aux (lift_amount+len) bo context metasenv subst ugraph in
+ let l1 =
+ List.map
+ (fun (a, s, m, ug) ->
+ (nm, lifted_ty, a)::lifted_tl, s, m, ug)
+ bo_res
+ in
+ (l1 @
+ (List.map
+ (fun (r, s, m, ug) ->
+ (nm, lifted_ty, lifted_bo)::r, s, m, ug) res),
+ (nm, lifted_ty, lifted_bo)::lifted_tl)
+ ) fl ([], [])
+ in
+ (List.map
+ (fun (fl, s, m, ug) -> C.CoFix (i, fl), s, m, ug) fl',
+ C.CoFix (i, lifted_fl))
+ in
+ let retval =
+ match term with
+ | C.Meta _ when (not metas_ok) ->
+ res, lifted_term
+ | _ ->
+ try
+ let subst', metasenv', ugraph' =
+ CicUnification.fo_unif metasenv context
+ (S.lift lift_amount what) term ugraph
+ in
+ (* Printf.printf "Ok, trovato: %s\n\nwhat: %s" (CicPp.ppterm term) *)
+ (* (CicPp.ppterm (S.lift lift_amount what)); *)
+ (* Printf.printf "substitution:\n%s\n\n" (print_subst subst'); *)
+ (* Printf.printf "metasenv': %s\n" (print_metasenv metasenv'); *)
+ (* Printf.printf "metasenv: %s\n\n" (print_metasenv metasenv); *)
+ let term' = CicMetaSubst.apply_subst subst' term in (
+ if match_only && not (meta_convertibility term term') then (
+(* Printf.printf "term e term' sono diversi!:\n%s\n%s\n\n" *)
+(* (CicPp.ppterm term) (CicPp.ppterm term'); *)
+ res, lifted_term
+ )
+ else
+(* let _ = *)
+(* if match_only then *)
+(* Printf.printf "OK, trovato match con %s\n" *)
+(* (CicPp.ppterm term) *)
+(* in *)
+ ((C.Rel (1 + lift_amount), subst', metasenv', ugraph')::res,
+ lifted_term)
+ )
+ with _ ->
+ res, lifted_term
+ in
+(* Printf.printf "exit aux\n"; *)
+ retval
+
+ and aux_list lift_amount l context metasenv subst ugraph =
+ List.fold_right
+ (fun arg (res, lifted_tl) ->
+ let arg_res, lifted_arg =
+ aux lift_amount arg context metasenv subst ugraph in
+ let l1 = List.map
+ (fun (a, s, m, ug) -> a::lifted_tl, s, m, ug) arg_res
+ in
+ (l1 @ (List.map
+ (fun (r, s, m, ug) -> lifted_arg::r, s, m, ug) res),
+ lifted_arg::lifted_tl)
+ ) l ([], [])
+
+ and aux_ens lift_amount exp_named_subst context metasenv subst ugraph =
+ List.fold_right
+ (fun (u, arg) (res, lifted_tl) ->
+ let arg_res, lifted_arg =
+ aux lift_amount arg context metasenv subst ugraph in
+ let l1 =
+ List.map
+ (fun (a, s, m, ug) -> (u, a)::lifted_tl, s, m, ug) arg_res
+ in
+ (l1 @ (List.map (fun (r, s, m, ug) ->
+ (u, lifted_arg)::r, s, m, ug) res),
+ (u, lifted_arg)::lifted_tl)
+ ) exp_named_subst ([], [])
+
+ in
+ let expansions, _ = aux 0 where context metasenv [] ugraph in
+ List.map
+ (fun (term, subst, metasenv, ugraph) ->
+ let term' = C.Lambda (C.Anonymous, type_of_what, term) in
+(* Printf.printf "term is: %s\nsubst is:\n%s\n\n" *)
+(* (CicPp.ppterm term') (print_subst subst); *)
+ (term', subst, metasenv, ugraph))
+ expansions
+;;
+
+
+type equality =
+ Cic.term * (* proof *)
+ (Cic.term * (* type *)
+ Cic.term * (* left side *)
+ Cic.term) * (* right side *)
+ Cic.metasenv * (* environment for metas *)
+ Cic.term list (* arguments *)
+;;
+
+
+let find_equalities ?(eq_uri=HelmLibraryObjects.Logic.eq_URI) context proof =
+ let module C = Cic in
+ let module S = CicSubstitution in
+ let module T = CicTypeChecker in
+ let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
+ let rec aux index newmeta = function
+ | [] -> [], newmeta
+ | (Some (_, C.Decl (term)))::tl ->
+ let do_find context term =
+ match term with
+ | C.Prod (name, s, t) ->
+(* let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in *)
+ let (head, newmetas, args, _) =
+ PrimitiveTactics.new_metasenv_for_apply newmeta proof
+ context (S.lift index term)
+ in
+ let newmeta =
+ List.fold_left
+ (fun maxm arg ->
+ match arg with
+ | C.Meta (i, _) -> (max maxm i)
+ | _ -> assert false)
+ newmeta args
+ in
+ let p =
+ if List.length args = 0 then
+ C.Rel index
+ else
+ C.Appl ((C.Rel index)::args)
+ in (
+ match head with
+ | C.Appl [C.MutInd (uri, _, _); ty; t1; t2] when uri = eq_uri ->
+ Printf.printf "OK: %s\n" (CicPp.ppterm term);
+ Some (p, (ty, t1, t2), newmetas, args), (newmeta+1)
+ | _ -> None, newmeta
+ )
+ | C.Appl [C.MutInd (uri, _, _); ty; t1; t2] when uri = eq_uri ->
+ Some (C.Rel index,
+ (ty, S.lift index t1, S.lift index t2), [], []), (newmeta+1)
+ | _ -> None, newmeta
+ in (
+ match do_find context term with
+ | Some p, newmeta ->
+ let tl, newmeta' = (aux (index+1) newmeta tl) in
+ p::tl, max newmeta newmeta'
+ | None, _ ->
+ aux (index+1) newmeta tl
+ )
+ | _::tl ->
+ aux (index+1) newmeta tl
+ in
+ aux 1 newmeta context
+;;
+
+
+let fix_metas newmeta ((proof, (ty, left, right), menv, args) as equality) =
+ let newargs, _ =
+ List.fold_right
+ (fun t (newargs, index) ->
+ match t with
+ | Cic.Meta (i, l) -> ((Cic.Meta (index, l))::newargs, index+1)
+ | _ -> assert false)
+ args ([], newmeta)
+ in
+ let repl where =
+ ProofEngineReduction.replace ~equality:(=) ~what:args ~with_what:newargs
+ ~where
+ in
+ let menv', _ =
+ List.fold_right
+ (fun (i, context, term) (menv, index) ->
+ ((index, context, term)::menv, index+1))
+ menv ([], newmeta)
+ in
+ (newmeta + (List.length newargs) + 1,
+ (repl proof, (repl ty, repl left, repl right), menv', newargs))
+;;
+
+
+exception TermIsNotAnEquality;;
+
+let equality_of_term ?(eq_uri=HelmLibraryObjects.Logic.eq_URI) proof = function
+ | Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2] when uri = eq_uri ->
+ (proof, (ty, t1, t2), [], [])
+ | _ ->
+ raise TermIsNotAnEquality
+;;
+
+
+type environment = Cic.metasenv * Cic.context * CicUniv.universe_graph;;
+
+
+let superposition_left (metasenv, context, ugraph) target source =
+ let module C = Cic in
+ let module S = CicSubstitution in
+ let module M = CicMetaSubst in
+ let module HL = HelmLibraryObjects in
+ let module CR = CicReduction in
+ (* we assume that target is ground (does not contain metavariables): this
+ * should always be the case (I hope, at least) *)
+ let proof, (eq_ty, left, right), _, _ = target in
+ let eqproof, (ty, t1, t2), newmetas, args = source in
+
+ (* ALB: TODO check that ty and eq_ty are indeed equal... *)
+ assert (eq_ty = ty);
+
+ let where, is_left =
+ match nonrec_kbo left right with
+ | Lt -> right, false
+ | Gt -> left, true
+ | _ -> (
+ Printf.printf "????????? %s = %s" (CicPp.ppterm left)
+ (CicPp.ppterm right);
+ print_newline ();
+ assert false (* again, for ground terms this shouldn't happen... *)
+ )
+ in
+ let metasenv' = newmetas @ metasenv in
+ let res1 =
+ List.filter
+ (fun (t, s, m, ug) ->
+ nonrec_kbo (M.apply_subst s t1) (M.apply_subst s t2) = Gt)
+ (beta_expand t1 ty where context metasenv' ugraph)
+ and res2 =
+ List.filter
+ (fun (t, s, m, ug) ->
+ nonrec_kbo (M.apply_subst s t2) (M.apply_subst s t1) = Gt)
+ (beta_expand t2 ty where context metasenv' ugraph)
+ in
+(* let what, other = *)
+(* if is_left then left, right *)
+(* else right, left *)
+(* in *)
+ let build_new what other eq_URI (t, s, m, ug) =
+ let newgoal, newgoalproof =
+ match t with
+ | C.Lambda (nn, ty, bo) ->
+ let bo' = S.subst (M.apply_subst s other) bo in
+ let bo'' =
+ C.Appl (
+ [C.MutInd (HL.Logic.eq_URI, 0, []);
+ S.lift 1 eq_ty] @
+ if is_left then [bo'; S.lift 1 right] else [S.lift 1 left; bo'])
+ in
+ let t' = C.Lambda (nn, ty, bo'') in
+ S.subst (M.apply_subst s other) bo,
+ M.apply_subst s
+ (C.Appl [C.Const (eq_URI, []); ty; what; t';
+ proof; other; eqproof])
+ | _ -> assert false
+ in
+ let equation =
+ if is_left then (eq_ty, newgoal, right)
+ else (eq_ty, left, newgoal)
+ in
+ (eqproof, equation, [], [])
+ in
+ let new1 = List.map (build_new t1 t2 HL.Logic.eq_ind_URI) res1
+ and new2 = List.map (build_new t2 t1 HL.Logic.eq_ind_r_URI) res2 in
+ new1 @ new2
+;;
+
+
+let superposition_right newmeta (metasenv, context, ugraph) target source =
+ let module C = Cic in
+ let module S = CicSubstitution in
+ let module M = CicMetaSubst in
+ let module HL = HelmLibraryObjects in
+ let module CR = CicReduction in
+ let eqproof, (eq_ty, left, right), newmetas, args = target in
+ let eqp', (ty', t1, t2), newm', args' = source in
+ let maxmeta = ref newmeta in
+
+ (* TODO check if ty and ty' are equal... *)
+ assert (eq_ty = ty');
+
+(* let ok term subst other other_eq_side ugraph = *)
+(* match term with *)
+(* | C.Lambda (nn, ty, bo) -> *)
+(* let bo' = S.subst (M.apply_subst subst other) bo in *)
+(* let res, _ = CR.are_convertible context bo' other_eq_side ugraph in *)
+(* not res *)
+(* | _ -> assert false *)
+(* in *)
+ let condition left right what other (t, s, m, ug) =
+ let subst = M.apply_subst s in
+ let cmp1 = nonrec_kbo (subst what) (subst other) in
+ let cmp2 = nonrec_kbo (subst left) (subst right) in
+(* cmp1 = Gt && cmp2 = Gt *)
+ cmp1 <> Lt && cmp1 <> Le && cmp2 <> Lt && cmp2 <> Le
+(* && (ok t s other right ug) *)
+ in
+ let metasenv' = metasenv @ newmetas @ newm' in
+ let beta_expand = beta_expand ~metas_ok:false in
+ let res1 =
+ List.filter
+ (condition left right t1 t2)
+ (beta_expand t1 eq_ty left context metasenv' ugraph)
+ and res2 =
+ List.filter
+ (condition left right t2 t1)
+ (beta_expand t2 eq_ty left context metasenv' ugraph)
+ and res3 =
+ List.filter
+ (condition right left t1 t2)
+ (beta_expand t1 eq_ty right context metasenv' ugraph)
+ and res4 =
+ List.filter
+ (condition right left t2 t1)
+ (beta_expand t2 eq_ty right context metasenv' ugraph)
+ in
+ let newmetas = newmetas @ newm' in
+ let newargs = args @ args' in
+ let build_new what other is_left eq_URI (t, s, m, ug) =
+(* let what, other = *)
+(* if is_left then left, right *)
+(* else right, left *)
+(* in *)
+ let newterm, neweqproof =
+ match t with
+ | C.Lambda (nn, ty, bo) ->
+ let bo' = M.apply_subst s (S.subst other bo) in
+ let bo'' =
+ C.Appl (
+ [C.MutInd (HL.Logic.eq_URI, 0, []); S.lift 1 eq_ty] @
+ if is_left then [bo'; S.lift 1 right] else [S.lift 1 left; bo'])
+ in
+ let t' = C.Lambda (nn, ty, bo'') in
+ bo',
+ M.apply_subst s
+ (C.Appl [C.Const (eq_URI, []); ty; what; t'; eqproof; other; eqp'])
+ | _ -> assert false
+ in
+ let newmeta, newequality =
+ let left, right =
+ if is_left then (newterm, M.apply_subst s right)
+ else (M.apply_subst s left, newterm) in
+ fix_metas !maxmeta
+ (neweqproof, (eq_ty, left, right), newmetas, newargs)
+ in
+ maxmeta := newmeta;
+ newequality
+ in
+ let new1 = List.map (build_new t1 t2 true HL.Logic.eq_ind_URI) res1
+ and new2 = List.map (build_new t2 t1 true HL.Logic.eq_ind_r_URI) res2
+ and new3 = List.map (build_new t1 t2 false HL.Logic.eq_ind_URI) res3
+ and new4 = List.map (build_new t2 t1 false HL.Logic.eq_ind_r_URI) res4 in
+ let ok = function
+ | _, (_, left, right), _, _ ->
+ not (fst (CR.are_convertible context left right ugraph))
+ in
+ !maxmeta, (List.filter ok (new1 @ new2 @ new3 @ new4))
+;;
+
+
+let demodulation newmeta (metasenv, context, ugraph) target source =
+ let module C = Cic in
+ let module S = CicSubstitution in
+ let module M = CicMetaSubst in
+ let module HL = HelmLibraryObjects in
+ let module CR = CicReduction in
+
+ let proof, (eq_ty, left, right), metas, args = target
+ and proof', (ty, t1, t2), metas', args' = source in
+ if eq_ty <> ty then
+ newmeta, target
+ else
+ let get_params step =
+ match step with
+ | 3 -> true, t1, t2, HL.Logic.eq_ind_URI
+ | 2 -> false, t1, t2, HL.Logic.eq_ind_URI
+ | 1 -> true, t2, t1, HL.Logic.eq_ind_r_URI
+ | 0 -> false, t2, t1, HL.Logic.eq_ind_r_URI
+ | _ -> assert false
+ in
+ let rec demodulate newmeta step metasenv target =
+ let proof, (eq_ty, left, right), metas, args = target in
+ let is_left, what, other, eq_URI = get_params step in
+(* Printf.printf *)
+(* "demodulate\ntarget: %s = %s\nwhat: %s\nother: %s\nis_left: %s\n" *)
+(* (CicPp.ppterm left) (CicPp.ppterm right) (CicPp.ppterm what) *)
+(* (CicPp.ppterm other) (string_of_bool is_left); *)
+(* Printf.printf "step: %d\n" step; *)
+(* print_newline (); *)
+ let ok (t, s, m, ug) =
+ nonrec_kbo (M.apply_subst s what) (M.apply_subst s other) = Gt
+ in
+ let res =
+ List.filter ok
+ (beta_expand ~metas_ok:false ~match_only:true
+ what ty left context (metasenv @ metas) ugraph)
+ in
+ match res with
+ | [] ->
+ if step = 0 then newmeta, target
+ else demodulate newmeta (step-1) metasenv target
+ | (t, s, m, ug)::_ ->
+ let newterm, newproof =
+ match t with
+ | C.Lambda (nn, ty, bo) ->
+ let bo' = M.apply_subst s (S.subst other bo) in
+ let bo'' =
+ C.Appl (
+ [C.MutInd (HL.Logic.eq_URI, 0, []);
+ S.lift 1 eq_ty] @
+ if is_left then [bo'; S.lift 1 right]
+ else [S.lift 1 left; bo'])
+ in
+ let t' = C.Lambda (nn, ty, bo'') in
+ M.apply_subst s (S.subst other bo),
+ M.apply_subst s
+ (C.Appl [C.Const (eq_URI, []); ty; what; t';
+ proof; other; proof'])
+ | _ -> assert false
+ in
+ let newmeta, newtarget =
+ let left, right =
+ if is_left then (newterm, M.apply_subst s right)
+ else (M.apply_subst s left, newterm) in
+ let newmetasenv = metasenv @ metas in
+ let newargs = args @ args' in
+ fix_metas newmeta
+ (newproof, (eq_ty, left, right), newmetasenv, newargs)
+ in
+ let _, (_, left, right), _, _ = newtarget
+ and _, (_, oldleft, oldright), _, _ = target in
+(* Printf.printf *)
+(* "demodulate, newtarget: %s = %s\ntarget was: %s = %s\n" *)
+(* (CicPp.ppterm left) (CicPp.ppterm right) *)
+(* (CicPp.ppterm oldleft) (CicPp.ppterm oldright); *)
+(* print_newline (); *)
+ demodulate newmeta step metasenv newtarget
+ in
+ demodulate newmeta 3 (metasenv @ metas') target
+;;
+
+
+(*
+let demodulation newmeta env target source =
+ newmeta, target
+;;
+*)
+
+