--- /dev/null
+(* Copyright (C) 2000, 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/.
+ *)
+
+(* $Id$ *)
+
+open Printf
+
+exception UnificationFailure of string Lazy.t;;
+exception Uncertain of string Lazy.t;;
+exception AssertFailure of string Lazy.t;;
+
+let verbose = false;;
+let debug_print = fun _ -> ()
+
+let profiler_toa = HExtlib.profile "fo_unif_subst.type_of_aux'"
+let profiler_beta_expand = HExtlib.profile "fo_unif_subst.beta_expand"
+let profiler_deref = HExtlib.profile "fo_unif_subst.deref'"
+let profiler_are_convertible = HExtlib.profile "fo_unif_subst.are_convertible"
+
+let profile = HExtlib.profile "U/CicTypeChecker.type_of_aux'"
+
+let type_of_aux' metasenv subst context term ugraph =
+let foo () =
+ try
+ profile.HExtlib.profile
+ (CicTypeChecker.type_of_aux' ~subst metasenv context term) ugraph
+ with
+ CicTypeChecker.TypeCheckerFailure msg ->
+ let msg =
+ lazy
+ (sprintf
+ "Kernel Type checking error:
+%s\n%s\ncontext=\n%s\nmetasenv=\n%s\nsubstitution=\n%s\nException:\n%s.\nToo bad."
+ (CicMetaSubst.ppterm ~metasenv subst term)
+ (CicMetaSubst.ppterm ~metasenv [] term)
+ (CicMetaSubst.ppcontext ~metasenv subst context)
+ (CicMetaSubst.ppmetasenv subst metasenv)
+ (CicMetaSubst.ppsubst ~metasenv subst) (Lazy.force msg)) in
+ raise (AssertFailure msg)
+ | CicTypeChecker.AssertFailure msg ->
+ let msg = lazy
+ (sprintf
+ "Kernel Type checking assertion failure:
+%s\n%s\ncontext=\n%s\nmetasenv=\n%s\nsubstitution=\n%s\nException:\n%s.\nToo bad."
+ (CicMetaSubst.ppterm ~metasenv subst term)
+ (CicMetaSubst.ppterm ~metasenv [] term)
+ (CicMetaSubst.ppcontext ~metasenv subst context)
+ (CicMetaSubst.ppmetasenv subst metasenv)
+ (CicMetaSubst.ppsubst ~metasenv subst) (Lazy.force msg)) in
+ raise (AssertFailure msg)
+in profiler_toa.HExtlib.profile foo ()
+;;
+
+let exists_a_meta l =
+ List.exists
+ (function
+ | Cic.Meta _
+ | Cic.Appl (Cic.Meta _::_) -> true
+ | _ -> false) l
+
+let rec deref subst t =
+ let snd (_,a,_) = a in
+ match t with
+ Cic.Meta(n,l) ->
+ (try
+ deref subst
+ (CicSubstitution.subst_meta
+ l (snd (CicUtil.lookup_subst n subst)))
+ with
+ CicUtil.Subst_not_found _ -> t)
+ | Cic.Appl(Cic.Meta(n,l)::args) ->
+ (match deref subst (Cic.Meta(n,l)) with
+ | Cic.Lambda _ as t ->
+ deref subst (CicReduction.head_beta_reduce (Cic.Appl(t::args)))
+ | r -> Cic.Appl(r::args))
+ | Cic.Appl(((Cic.Lambda _) as t)::args) ->
+ deref subst (CicReduction.head_beta_reduce (Cic.Appl(t::args)))
+ | t -> t
+;;
+
+let deref subst t =
+ let foo () = deref subst t
+ in profiler_deref.HExtlib.profile foo ()
+
+exception WrongShape;;
+let eta_reduce after_beta_expansion after_beta_expansion_body
+ before_beta_expansion
+ =
+ try
+ match before_beta_expansion,after_beta_expansion_body with
+ Cic.Appl l, Cic.Appl l' ->
+ let rec all_but_last check_last =
+ function
+ [] -> assert false
+ | [Cic.Rel 1] -> []
+ | [_] -> if check_last then raise WrongShape else []
+ | he::tl -> he::(all_but_last check_last tl)
+ in
+ let all_but_last check_last l =
+ match all_but_last check_last l with
+ [] -> assert false
+ | [he] -> he
+ | l -> Cic.Appl l
+ in
+ let t = CicSubstitution.subst (Cic.Rel (-1)) (all_but_last true l') in
+ let all_but_last = all_but_last false l in
+ (* here we should test alpha-equivalence; however we know by
+ construction that here alpha_equivalence is equivalent to = *)
+ if t = all_but_last then
+ all_but_last
+ else
+ after_beta_expansion
+ | _,_ -> after_beta_expansion
+ with
+ WrongShape -> after_beta_expansion
+
+let rec beta_expand num test_equality_only metasenv subst context t arg ugraph =
+ let module S = CicSubstitution in
+ let module C = Cic in
+let foo () =
+ let rec aux metasenv subst n context t' ugraph =
+ try
+
+ let subst,metasenv,ugraph1 =
+ fo_unif_subst test_equality_only subst context metasenv
+ (CicSubstitution.lift n arg) t' ugraph
+
+ in
+ subst,metasenv,C.Rel (1 + n),ugraph1
+ with
+ Uncertain _
+ | UnificationFailure _ ->
+ match t' with
+ | C.Rel m -> subst,metasenv,
+ (if m <= n then C.Rel m else C.Rel (m+1)),ugraph
+ | C.Var (uri,exp_named_subst) ->
+ let subst,metasenv,exp_named_subst',ugraph1 =
+ aux_exp_named_subst metasenv subst n context exp_named_subst ugraph
+ in
+ subst,metasenv,C.Var (uri,exp_named_subst'),ugraph1
+ | C.Meta (i,l) ->
+ (* andrea: in general, beta_expand can create badly typed
+ terms. This happens quite seldom in practice, UNLESS we
+ iterate on the local context. For this reason, we renounce
+ to iterate and just lift *)
+ let l =
+ List.map
+ (function
+ Some t -> Some (CicSubstitution.lift 1 t)
+ | None -> None) l in
+ subst, metasenv, C.Meta (i,l), ugraph
+ | C.Sort _
+ | C.Implicit _ as t -> subst,metasenv,t,ugraph
+ | C.Cast (te,ty) ->
+ let subst,metasenv,te',ugraph1 =
+ aux metasenv subst n context te ugraph in
+ let subst,metasenv,ty',ugraph2 =
+ aux metasenv subst n context ty ugraph1 in
+ (* TASSI: sure this is in serial? *)
+ subst,metasenv,(C.Cast (te', ty')),ugraph2
+ | C.Prod (nn,s,t) ->
+ let subst,metasenv,s',ugraph1 =
+ aux metasenv subst n context s ugraph in
+ let subst,metasenv,t',ugraph2 =
+ aux metasenv subst (n+1) ((Some (nn, C.Decl s))::context) t
+ ugraph1
+ in
+ (* TASSI: sure this is in serial? *)
+ subst,metasenv,(C.Prod (nn, s', t')),ugraph2
+ | C.Lambda (nn,s,t) ->
+ let subst,metasenv,s',ugraph1 =
+ aux metasenv subst n context s ugraph in
+ let subst,metasenv,t',ugraph2 =
+ aux metasenv subst (n+1) ((Some (nn, C.Decl s))::context) t ugraph1
+ in
+ (* TASSI: sure this is in serial? *)
+ subst,metasenv,(C.Lambda (nn, s', t')),ugraph2
+ | C.LetIn (nn,s,ty,t) ->
+ let subst,metasenv,s',ugraph1 =
+ aux metasenv subst n context s ugraph in
+ let subst,metasenv,ty',ugraph1 =
+ aux metasenv subst n context ty ugraph in
+ let subst,metasenv,t',ugraph2 =
+ aux metasenv subst (n+1) ((Some (nn, C.Def (s,ty)))::context) t
+ ugraph1
+ in
+ (* TASSI: sure this is in serial? *)
+ subst,metasenv,(C.LetIn (nn, s', ty', t')),ugraph2
+ | C.Appl l ->
+ let subst,metasenv,revl',ugraph1 =
+ List.fold_left
+ (fun (subst,metasenv,appl,ugraph) t ->
+ let subst,metasenv,t',ugraph1 =
+ aux metasenv subst n context t ugraph in
+ subst,metasenv,(t'::appl),ugraph1
+ ) (subst,metasenv,[],ugraph) l
+ in
+ subst,metasenv,(C.Appl (List.rev revl')),ugraph1
+ | C.Const (uri,exp_named_subst) ->
+ let subst,metasenv,exp_named_subst',ugraph1 =
+ aux_exp_named_subst metasenv subst n context exp_named_subst ugraph
+ in
+ subst,metasenv,(C.Const (uri,exp_named_subst')),ugraph1
+ | C.MutInd (uri,i,exp_named_subst) ->
+ let subst,metasenv,exp_named_subst',ugraph1 =
+ aux_exp_named_subst metasenv subst n context exp_named_subst ugraph
+ in
+ subst,metasenv,(C.MutInd (uri,i,exp_named_subst')),ugraph1
+ | C.MutConstruct (uri,i,j,exp_named_subst) ->
+ let subst,metasenv,exp_named_subst',ugraph1 =
+ aux_exp_named_subst metasenv subst n context exp_named_subst ugraph
+ in
+ subst,metasenv,(C.MutConstruct (uri,i,j,exp_named_subst')),ugraph1
+ | C.MutCase (sp,i,outt,t,pl) ->
+ let subst,metasenv,outt',ugraph1 =
+ aux metasenv subst n context outt ugraph in
+ let subst,metasenv,t',ugraph2 =
+ aux metasenv subst n context t ugraph1 in
+ let subst,metasenv,revpl',ugraph3 =
+ List.fold_left
+ (fun (subst,metasenv,pl,ugraph) t ->
+ let subst,metasenv,t',ugraph1 =
+ aux metasenv subst n context t ugraph in
+ subst,metasenv,(t'::pl),ugraph1
+ ) (subst,metasenv,[],ugraph2) pl
+ in
+ subst,metasenv,(C.MutCase (sp,i,outt', t', List.rev revpl')),ugraph3
+ (* TASSI: not sure this is serial *)
+ | C.Fix (i,fl) ->
+(*CSC: not implemented
+ let tylen = List.length fl in
+ let substitutedfl =
+ List.map
+ (fun (name,i,ty,bo) -> (name, i, aux n ty, aux (n+tylen) bo))
+ fl
+ in
+ C.Fix (i, substitutedfl)
+*)
+ subst,metasenv,(CicSubstitution.lift 1 t' ),ugraph
+ | C.CoFix (i,fl) ->
+(*CSC: not implemented
+ let tylen = List.length fl in
+ let substitutedfl =
+ List.map
+ (fun (name,ty,bo) -> (name, aux n ty, aux (n+tylen) bo))
+ fl
+ in
+ C.CoFix (i, substitutedfl)
+
+*)
+ subst,metasenv,(CicSubstitution.lift 1 t'), ugraph
+
+ and aux_exp_named_subst metasenv subst n context ens ugraph =
+ List.fold_right
+ (fun (uri,t) (subst,metasenv,l,ugraph) ->
+ let subst,metasenv,t',ugraph1 = aux metasenv subst n context t ugraph in
+ subst,metasenv,((uri,t')::l),ugraph1) ens (subst,metasenv,[],ugraph)
+ in
+ let argty,ugraph1 = type_of_aux' metasenv subst context arg ugraph in
+ let fresh_name =
+ FreshNamesGenerator.mk_fresh_name ~subst
+ metasenv context (Cic.Name ("Hbeta" ^ string_of_int num)) ~typ:argty
+ in
+ let subst,metasenv,t',ugraph2 = aux metasenv subst 0 context t ugraph1 in
+ let t'' = eta_reduce (C.Lambda (fresh_name,argty,t')) t' t in
+ subst, metasenv, t'', ugraph2
+in profiler_beta_expand.HExtlib.profile foo ()
+
+
+and beta_expand_many test_equality_only metasenv subst context t args ugraph =
+ let _,subst,metasenv,hd,ugraph =
+ List.fold_right
+ (fun arg (num,subst,metasenv,t,ugraph) ->
+ let subst,metasenv,t,ugraph1 =
+ beta_expand num test_equality_only
+ metasenv subst context t arg ugraph
+ in
+ num+1,subst,metasenv,t,ugraph1
+ ) args (1,subst,metasenv,t,ugraph)
+ in
+ subst,metasenv,hd,ugraph
+
+
+(* NUOVA UNIFICAZIONE *)
+(* A substitution is a (int * Cic.term) list that associates a
+ metavariable i with its body.
+ A metaenv is a (int * Cic.term) list that associate a metavariable
+ i with is type.
+ fo_unif_new takes a metasenv, a context, two terms t1 and t2 and gives back
+ a new substitution which is _NOT_ unwinded. It must be unwinded before
+ applying it. *)
+
+and fo_unif_subst test_equality_only subst context metasenv t1 t2 ugraph =
+ let module C = Cic in
+ let module R = CicReduction in
+ let module S = CicSubstitution in
+ let t1 = deref subst t1 in
+ let t2 = deref subst t2 in
+ let (&&&) a b = (a && b) || ((not a) && (not b)) in
+(* let bef = Sys.time () in *)
+ let b,ugraph =
+ if not (CicUtil.is_meta_closed (CicMetaSubst.apply_subst subst t1) &&& CicUtil.is_meta_closed (CicMetaSubst.apply_subst subst t2)) then
+ false,ugraph
+ else
+let foo () =
+ R.are_convertible ~subst ~metasenv context t1 t2 ugraph
+in profiler_are_convertible.HExtlib.profile foo ()
+ in
+(* let aft = Sys.time () in
+if (aft -. bef > 2.0) then prerr_endline ("LEEEENTO: " ^ CicMetaSubst.ppterm_in_context subst ~metasenv t1 context ^ " <===> " ^ CicMetaSubst.ppterm_in_context subst ~metasenv t2 context); *)
+ if b then
+ subst, metasenv, ugraph
+ else
+ match (t1, t2) with
+ | (C.Meta (n,ln), C.Meta (m,lm)) when n=m ->
+ let _,subst,metasenv,ugraph1 =
+ (try
+ List.fold_left2
+ (fun (j,subst,metasenv,ugraph) t1 t2 ->
+ match t1,t2 with
+ None,_
+ | _,None -> j+1,subst,metasenv,ugraph
+ | Some t1', Some t2' ->
+ (* First possibility: restriction *)
+ (* Second possibility: unification *)
+ (* Third possibility: convertibility *)
+ let b, ugraph1 =
+ R.are_convertible
+ ~subst ~metasenv context t1' t2' ugraph
+ in
+ if b then
+ j+1,subst,metasenv, ugraph1
+ else
+ (try
+ let subst,metasenv,ugraph2 =
+ fo_unif_subst
+ test_equality_only
+ subst context metasenv t1' t2' ugraph
+ in
+ j+1,subst,metasenv,ugraph2
+ with
+ Uncertain _
+ | UnificationFailure _ ->
+debug_print (lazy ("restringo Meta n." ^ (string_of_int n) ^ "on variable n." ^ (string_of_int j)));
+ let metasenv, subst =
+ CicMetaSubst.restrict
+ subst [(n,j)] metasenv in
+ j+1,subst,metasenv,ugraph1)
+ ) (1,subst,metasenv,ugraph) ln lm
+ with
+ Exit ->
+ raise
+ (UnificationFailure (lazy "1"))
+ (*
+ (sprintf
+ "Error trying to unify %s with %s: the algorithm tried to check whether the two substitutions are convertible; if they are not, it tried to unify the two substitutions. No restriction was attempted."
+ (CicMetaSubst.ppterm ~metasenv subst t1)
+ (CicMetaSubst.ppterm ~metasenv subst t2))) *)
+ | Invalid_argument _ ->
+ raise
+ (UnificationFailure (lazy "2")))
+ (*
+ (sprintf
+ "Error trying to unify %s with %s: the lengths of the two local contexts do not match."
+ (CicMetaSubst.ppterm ~metasenv subst t1)
+ (CicMetaSubst.ppterm ~metasenv subst t2)))) *)
+ in subst,metasenv,ugraph1
+ | (C.Meta (n,_), C.Meta (m,_)) when n>m ->
+ fo_unif_subst test_equality_only subst context metasenv t2 t1 ugraph
+ | (C.Meta (n,l), t)
+ | (t, C.Meta (n,l)) ->
+ let swap =
+ match t1,t2 with
+ C.Meta (n,_), C.Meta (m,_) when n < m -> false
+ | _, C.Meta _ -> false
+ | _,_ -> true
+ in
+ let lower = fun x y -> if swap then y else x in
+ let upper = fun x y -> if swap then x else y in
+ let fo_unif_subst_ordered
+ test_equality_only subst context metasenv m1 m2 ugraph =
+ fo_unif_subst test_equality_only subst context metasenv
+ (lower m1 m2) (upper m1 m2) ugraph
+ in
+ begin
+ let subst,metasenv,ugraph1 =
+ let (_,_,meta_type) = CicUtil.lookup_meta n metasenv in
+ (try
+ let tyt,ugraph1 =
+ type_of_aux' metasenv subst context t ugraph
+ in
+ fo_unif_subst
+ test_equality_only
+ subst context metasenv tyt (S.subst_meta l meta_type) ugraph1
+ with
+ UnificationFailure _ as e -> raise e
+ | Uncertain msg -> raise (UnificationFailure msg)
+ | AssertFailure _ ->
+ debug_print (lazy "siamo allo huge hack");
+ (* TODO huge hack!!!!
+ * we keep on unifying/refining in the hope that
+ * the problem will be eventually solved.
+ * In the meantime we're breaking a big invariant:
+ * the terms that we are unifying are no longer well
+ * typed in the current context (in the worst case
+ * we could even diverge) *)
+ (subst, metasenv,ugraph)) in
+ let t',metasenv,subst =
+ try
+ CicMetaSubst.delift n subst context metasenv l t
+ with
+ (CicMetaSubst.MetaSubstFailure msg)->
+ raise (UnificationFailure msg)
+ | (CicMetaSubst.Uncertain msg) -> raise (Uncertain msg)
+ in
+ let t'',ugraph2 =
+ match t' with
+ C.Sort (C.Type u) when not test_equality_only ->
+ let u' = CicUniv.fresh () in
+ let s = C.Sort (C.Type u') in
+ (try
+ let ugraph2 =
+ CicUniv.add_ge (upper u u') (lower u u') ugraph1
+ in
+ s,ugraph2
+ with
+ CicUniv.UniverseInconsistency msg ->
+ raise (UnificationFailure msg))
+ | _ -> t',ugraph1
+ in
+ (* Unifying the types may have already instantiated n. Let's check *)
+ try
+ let (_, oldt,_) = CicUtil.lookup_subst n subst in
+ let lifted_oldt = S.subst_meta l oldt in
+ fo_unif_subst_ordered
+ test_equality_only subst context metasenv t lifted_oldt ugraph2
+ with
+ CicUtil.Subst_not_found _ ->
+ let (_, context, ty) = CicUtil.lookup_meta n metasenv in
+ let subst = (n, (context, t'',ty)) :: subst in
+ let metasenv =
+ List.filter (fun (m,_,_) -> not (n = m)) metasenv in
+ subst, metasenv, ugraph2
+ end
+ | (C.Var (uri1,exp_named_subst1),C.Var (uri2,exp_named_subst2))
+ | (C.Const (uri1,exp_named_subst1),C.Const (uri2,exp_named_subst2)) ->
+ if UriManager.eq uri1 uri2 then
+ fo_unif_subst_exp_named_subst test_equality_only subst context metasenv
+ exp_named_subst1 exp_named_subst2 ugraph
+ else
+ raise (UnificationFailure (lazy
+ (sprintf
+ "Can't unify %s with %s due to different constants"
+ (CicMetaSubst.ppterm ~metasenv subst t1)
+ (CicMetaSubst.ppterm ~metasenv subst t2))))
+ | C.MutInd (uri1,i1,exp_named_subst1),C.MutInd (uri2,i2,exp_named_subst2) ->
+ if UriManager.eq uri1 uri2 && i1 = i2 then
+ fo_unif_subst_exp_named_subst
+ test_equality_only
+ subst context metasenv exp_named_subst1 exp_named_subst2 ugraph
+ else
+ raise (UnificationFailure
+ (lazy
+ (sprintf
+ "Can't unify %s with %s due to different inductive principles"
+ (CicMetaSubst.ppterm ~metasenv subst t1)
+ (CicMetaSubst.ppterm ~metasenv subst t2))))
+ | C.MutConstruct (uri1,i1,j1,exp_named_subst1),
+ C.MutConstruct (uri2,i2,j2,exp_named_subst2) ->
+ if UriManager.eq uri1 uri2 && i1 = i2 && j1 = j2 then
+ fo_unif_subst_exp_named_subst
+ test_equality_only
+ subst context metasenv exp_named_subst1 exp_named_subst2 ugraph
+ else
+ raise (UnificationFailure
+ (lazy
+ (sprintf
+ "Can't unify %s with %s due to different inductive constructors"
+ (CicMetaSubst.ppterm ~metasenv subst t1)
+ (CicMetaSubst.ppterm ~metasenv subst t2))))
+ | (C.Implicit _, _) | (_, C.Implicit _) -> assert false
+ | (C.Cast (te,ty), t2) -> fo_unif_subst test_equality_only
+ subst context metasenv te t2 ugraph
+ | (t1, C.Cast (te,ty)) -> fo_unif_subst test_equality_only
+ subst context metasenv t1 te ugraph
+ | (C.Prod (n1,s1,t1), C.Prod (_,s2,t2)) ->
+ let subst',metasenv',ugraph1 =
+ fo_unif_subst true subst context metasenv s1 s2 ugraph
+ in
+ fo_unif_subst test_equality_only
+ subst' ((Some (n1,(C.Decl s1)))::context) metasenv' t1 t2 ugraph1
+ | (C.Lambda (n1,s1,t1), C.Lambda (_,s2,t2)) ->
+ let subst',metasenv',ugraph1 =
+ fo_unif_subst test_equality_only subst context metasenv s1 s2 ugraph
+ in
+ fo_unif_subst test_equality_only
+ subst' ((Some (n1,(C.Decl s1)))::context) metasenv' t1 t2 ugraph1
+ | (C.LetIn (_,s1,ty1,t1), t2)
+ | (t2, C.LetIn (_,s1,ty1,t1)) ->
+ fo_unif_subst
+ test_equality_only subst context metasenv t2 (S.subst s1 t1) ugraph
+ | (C.Appl l1, C.Appl l2) ->
+ (* andrea: this case should be probably rewritten in the
+ spirit of deref *)
+ (match l1,l2 with
+ | C.Meta (i,_)::args1, C.Meta (j,_)::args2 when i = j ->
+ (try
+ List.fold_left2
+ (fun (subst,metasenv,ugraph) t1 t2 ->
+ fo_unif_subst
+ test_equality_only subst context metasenv t1 t2 ugraph)
+ (subst,metasenv,ugraph) l1 l2
+ with (Invalid_argument msg) ->
+ raise (UnificationFailure (lazy msg)))
+ | C.Meta (i,l)::args, _ when not(exists_a_meta args) ->
+ (* we verify that none of the args is a Meta,
+ since beta expanding with respoect to a metavariable
+ makes no sense *)
+ (*
+ (try
+ let (_,t,_) = CicUtil.lookup_subst i subst in
+ let lifted = S.subst_meta l t in
+ let reduced = CicReduction.head_beta_reduce (Cic.Appl (lifted::args)) in
+ fo_unif_subst
+ test_equality_only
+ subst context metasenv reduced t2 ugraph
+ with CicUtil.Subst_not_found _ -> *)
+ let subst,metasenv,beta_expanded,ugraph1 =
+ beta_expand_many
+ test_equality_only metasenv subst context t2 args ugraph
+ in
+ fo_unif_subst test_equality_only subst context metasenv
+ (C.Meta (i,l)) beta_expanded ugraph1
+ | _, C.Meta (i,l)::args when not(exists_a_meta args) ->
+ (* (try
+ let (_,t,_) = CicUtil.lookup_subst i subst in
+ let lifted = S.subst_meta l t in
+ let reduced = CicReduction.head_beta_reduce (Cic.Appl (lifted::args)) in
+ fo_unif_subst
+ test_equality_only
+ subst context metasenv t1 reduced ugraph
+ with CicUtil.Subst_not_found _ -> *)
+ let subst,metasenv,beta_expanded,ugraph1 =
+ beta_expand_many
+ test_equality_only
+ metasenv subst context t1 args ugraph
+ in
+ fo_unif_subst test_equality_only subst context metasenv
+ (C.Meta (i,l)) beta_expanded ugraph1
+ | _,_ ->
+ let lr1 = List.rev l1 in
+ let lr2 = List.rev l2 in
+ let rec
+ fo_unif_l test_equality_only subst metasenv (l1,l2) ugraph =
+ match (l1,l2) with
+ [],_
+ | _,[] -> assert false
+ | ([h1],[h2]) ->
+ fo_unif_subst
+ test_equality_only subst context metasenv h1 h2 ugraph
+ | ([h],l)
+ | (l,[h]) ->
+ fo_unif_subst test_equality_only subst context metasenv
+ h (C.Appl (List.rev l)) ugraph
+ | ((h1::l1),(h2::l2)) ->
+ let subst', metasenv',ugraph1 =
+ fo_unif_subst
+ test_equality_only
+ subst context metasenv h1 h2 ugraph
+ in
+ fo_unif_l
+ test_equality_only subst' metasenv' (l1,l2) ugraph1
+ in
+ (try
+ fo_unif_l
+ test_equality_only subst metasenv (lr1, lr2) ugraph
+ with
+ | UnificationFailure s
+ | Uncertain s as exn ->
+ (match l1, l2 with
+ | (((Cic.Const (uri1, ens1)) as c1) :: tl1),
+ (((Cic.Const (uri2, ens2)) as c2) :: tl2) when
+ CoercDb.is_a_coercion' c1 &&
+ CoercDb.is_a_coercion' c2 &&
+ not (UriManager.eq uri1 uri2) ->
+(*DEBUGGING ONLY:
+prerr_endline ("<<<< " ^ CicMetaSubst.ppterm_in_context ~metasenv subst (C.Appl l1) context ^ " <==> " ^ CicMetaSubst.ppterm_in_context ~metasenv subst (C.Appl l2) context);
+let res =
+*)
+ let rec look_for_first_coercion c tl =
+ match
+ CicMetaSubst.apply_subst subst (HExtlib.list_last tl)
+ with
+ Cic.Appl ((Cic.Const (uri1,ens1) as c')::tl')
+ when CoercDb.is_a_coercion' c' ->
+ look_for_first_coercion c' tl'
+ | last_tl -> c,last_tl
+ in
+ let c1,last_tl1 = look_for_first_coercion c1 tl1 in
+ let c2,last_tl2 = look_for_first_coercion c2 tl2 in
+ let car1 =
+ CoercDb.coerc_carr_of_term (CoercGraph.source_of c1) in
+ let car2 =
+ CoercDb.coerc_carr_of_term (CoercGraph.source_of c2) in
+ if CoercDb.eq_carr car1 car2 then
+ (match last_tl1,last_tl2 with
+ C.Meta (i1,_),C.Meta(i2,_) when i1=i2 -> raise exn
+ | C.Meta _, _
+ | _, C.Meta _ ->
+ let subst,metasenv,ugraph =
+ fo_unif_subst test_equality_only subst context
+ metasenv last_tl1 last_tl2 ugraph
+ in
+ fo_unif_subst test_equality_only subst context
+ metasenv (C.Appl l1) (C.Appl l2) ugraph
+ | _ -> raise exn)
+ else
+ let meets =
+ CoercGraph.meets metasenv subst context car1 car2
+ in
+ (match meets with
+ | [] -> raise exn
+ | (carr,metasenv,to1,to2)::xxx ->
+ (match xxx with
+ [] -> ()
+ | (m2,_,c2,c2')::_ ->
+ let m1,_,c1,c1' = carr,metasenv,to1,to2 in
+ let unopt =
+ function Some (_,t) -> CicPp.ppterm t
+ | None -> "id"
+ in
+ HLog.warn
+ ("There are two minimal joins of "^
+ CoercDb.name_of_carr car1^" and "^
+ CoercDb.name_of_carr car2^": " ^
+ CoercDb.name_of_carr m1 ^ " via "^unopt c1^" + "^
+ unopt c1'^" and " ^ CoercDb.name_of_carr m2^" via "^
+ unopt c2^" + "^unopt c2'));
+ let last_tl1',(subst,metasenv,ugraph) =
+ match last_tl1,to1 with
+ | Cic.Meta (i1,l1),Some (last,coerced) ->
+ last,
+ fo_unif_subst test_equality_only subst context
+ metasenv coerced last_tl1 ugraph
+ | _ -> last_tl1,(subst,metasenv,ugraph)
+ in
+ let last_tl2',(subst,metasenv,ugraph) =
+ match last_tl2,to2 with
+ | Cic.Meta (i2,l2),Some (last,coerced) ->
+ last,
+ fo_unif_subst test_equality_only subst context
+ metasenv coerced last_tl2 ugraph
+ | _ -> last_tl2,(subst,metasenv,ugraph)
+ in
+ (*DEBUGGING ONLY:
+prerr_endline ("OK " ^ CicMetaSubst.ppterm_in_context ~metasenv subst last_tl1' context ^ " <==> " ^ CicMetaSubst.ppterm_in_context ~metasenv subst last_tl2' context);
+*)
+ let subst,metasenv,ugraph =
+ fo_unif_subst test_equality_only subst context
+ metasenv last_tl1' last_tl2' ugraph
+ in
+ fo_unif_subst test_equality_only subst context
+ metasenv (C.Appl l1) (C.Appl l2) ugraph)
+(*DEBUGGING ONLY:
+in
+let subst,metasenv,ugraph = res in
+prerr_endline (">>>> " ^ CicMetaSubst.ppterm_in_context ~metasenv subst (C.Appl l1) context ^ " <==> " ^ CicMetaSubst.ppterm_in_context ~metasenv subst (C.Appl l2) context);
+res
+*)
+ (*CSC: This is necessary because of the "elim H" tactic
+ where the type of H is only reducible to an
+ inductive type. This could be extended from inductive
+ types to any rigid term. However, the code is
+ duplicated in two places: inside applications and
+ outside them. Probably it would be better to
+ work with lambda-bar terms instead. *)
+ | (Cic.MutInd _::_, Cic.MutInd _::_) -> raise exn
+ | (_, Cic.MutInd _::_) ->
+ let t1' = R.whd ~subst context t1 in
+ (match t1' with
+ C.Appl (C.MutInd _::_) ->
+ fo_unif_subst test_equality_only
+ subst context metasenv t1' t2 ugraph
+ | _ -> raise (UnificationFailure (lazy "88")))
+ | (Cic.MutInd _::_,_) ->
+ let t2' = R.whd ~subst context t2 in
+ (match t2' with
+ C.Appl (C.MutInd _::_) ->
+ fo_unif_subst test_equality_only
+ subst context metasenv t1 t2' ugraph
+ | _ -> raise
+ (UnificationFailure
+ (lazy ("not a mutind :"^CicMetaSubst.ppterm ~metasenv subst t2 ))))
+ | _ -> raise exn)))
+ | (C.MutCase (_,_,outt1,t1',pl1), C.MutCase (_,_,outt2,t2',pl2))->
+ let subst', metasenv',ugraph1 =
+ fo_unif_subst test_equality_only subst context metasenv outt1 outt2
+ ugraph in
+ let subst'',metasenv'',ugraph2 =
+ fo_unif_subst test_equality_only subst' context metasenv' t1' t2'
+ ugraph1 in
+ (try
+ List.fold_left2
+ (fun (subst,metasenv,ugraph) t1 t2 ->
+ fo_unif_subst
+ test_equality_only subst context metasenv t1 t2 ugraph
+ ) (subst'',metasenv'',ugraph2) pl1 pl2
+ with
+ Invalid_argument _ ->
+ raise (UnificationFailure (lazy "6.1")))
+ (* (sprintf
+ "Error trying to unify %s with %s: the number of branches is not the same."
+ (CicMetaSubst.ppterm ~metasenv subst t1)
+ (CicMetaSubst.ppterm ~metasenv subst t2)))) *)
+ | (C.Rel _, _) | (_, C.Rel _) ->
+ if t1 = t2 then
+ subst, metasenv,ugraph
+ else
+ raise (UnificationFailure (lazy
+ (sprintf
+ "Can't unify %s with %s because they are not convertible"
+ (CicMetaSubst.ppterm ~metasenv subst t1)
+ (CicMetaSubst.ppterm ~metasenv subst t2))))
+ | (C.Appl (C.Meta(i,l)::args),t2) when not(exists_a_meta args) ->
+ let subst,metasenv,beta_expanded,ugraph1 =
+ beta_expand_many
+ test_equality_only metasenv subst context t2 args ugraph
+ in
+ fo_unif_subst test_equality_only subst context metasenv
+ (C.Meta (i,l)) beta_expanded ugraph1
+ | (t1,C.Appl (C.Meta(i,l)::args)) when not(exists_a_meta args) ->
+ let subst,metasenv,beta_expanded,ugraph1 =
+ beta_expand_many
+ test_equality_only metasenv subst context t1 args ugraph
+ in
+ fo_unif_subst test_equality_only subst context metasenv
+ beta_expanded (C.Meta (i,l)) ugraph1
+(* Works iff there are no arguments applied to it; similar to the
+ case below
+ | (_, C.MutInd _) ->
+ let t1' = R.whd ~subst context t1 in
+ (match t1' with
+ C.MutInd _ ->
+ fo_unif_subst test_equality_only
+ subst context metasenv t1' t2 ugraph
+ | _ -> raise (UnificationFailure (lazy "8")))
+*)
+(* The following idea could be exploited again; right now we have no
+ longer any example requiring it
+ | (C.Prod _, t2) ->
+ let t2' = R.whd ~subst context t2 in
+ (match t2' with
+ C.Prod _ ->
+ fo_unif_subst test_equality_only
+ subst context metasenv t1 t2' ugraph
+ | _ -> raise (UnificationFailure (lazy "8")))
+ | (t1, C.Prod _) ->
+ let t1' = R.whd ~subst context t1 in
+ (match t1' with
+ C.Prod _ ->
+ fo_unif_subst test_equality_only
+ subst context metasenv t1' t2 ugraph
+ | _ -> (* raise (UnificationFailure "9")) *)
+ raise
+ (UnificationFailure (lazy (sprintf
+ "Can't unify %s with %s because they are not convertible"
+ (CicMetaSubst.ppterm ~metasenv subst t1)
+ (CicMetaSubst.ppterm ~metasenv subst t2)))))
+*)
+ | (_,_) ->
+ (* delta-beta reduction should almost never be a problem for
+ unification since:
+ 1. long computations require iota reduction
+ 2. it is extremely rare that a close term t1 (that could be unified
+ to t2) beta-delta reduces to t1' while t2 does not beta-delta
+ reduces in the same way. This happens only if one meta of t2
+ occurs in head position during beta reduction. In this unluky
+ case too much reduction will be performed on t1 and unification
+ will surely fail. *)
+ let t1' = CicReduction.head_beta_reduce ~delta:true t1 in
+ let t2' = CicReduction.head_beta_reduce ~delta:true t2 in
+ if t1 = t1' && t2 = t2' then
+ raise (UnificationFailure
+ (lazy
+ (sprintf
+ "Can't unify %s with %s because they are not convertible"
+ (CicMetaSubst.ppterm ~metasenv subst t1)
+ (CicMetaSubst.ppterm ~metasenv subst t2))))
+ else
+ try
+ fo_unif_subst test_equality_only subst context metasenv t1' t2' ugraph
+ with
+ UnificationFailure _
+ | Uncertain _ ->
+ raise (UnificationFailure
+ (lazy
+ (sprintf
+ "Can't unify %s with %s because they are not convertible"
+ (CicMetaSubst.ppterm ~metasenv subst t1)
+ (CicMetaSubst.ppterm ~metasenv subst t2))))
+
+and fo_unif_subst_exp_named_subst test_equality_only subst context metasenv
+ exp_named_subst1 exp_named_subst2 ugraph
+=
+ try
+ List.fold_left2
+ (fun (subst,metasenv,ugraph) (uri1,t1) (uri2,t2) ->
+ assert (uri1=uri2) ;
+ fo_unif_subst test_equality_only subst context metasenv t1 t2 ugraph
+ ) (subst,metasenv,ugraph) exp_named_subst1 exp_named_subst2
+ with
+ Invalid_argument _ ->
+ let print_ens ens =
+ String.concat " ; "
+ (List.map
+ (fun (uri,t) ->
+ UriManager.string_of_uri uri ^ " := " ^ (CicMetaSubst.ppterm ~metasenv subst t)
+ ) ens)
+ in
+ raise (UnificationFailure (lazy (sprintf
+ "Error trying to unify the two explicit named substitutions (local contexts) %s and %s: their lengths is different." (print_ens exp_named_subst1) (print_ens exp_named_subst2))))
+
+(* A substitution is a (int * Cic.term) list that associates a *)
+(* metavariable i with its body. *)
+(* metasenv is of type Cic.metasenv *)
+(* fo_unif takes a metasenv, a context, two terms t1 and t2 and gives back *)
+(* a new substitution which is already unwinded and ready to be applied and *)
+(* a new metasenv in which some hypothesis in the contexts of the *)
+(* metavariables may have been restricted. *)
+let fo_unif metasenv context t1 t2 ugraph =
+ fo_unif_subst false [] context metasenv t1 t2 ugraph ;;
+
+let enrich_msg msg subst context metasenv t1 t2 ugraph =
+ lazy (
+ if verbose then
+ sprintf "[Verbose] Unification error unifying %s of type %s with %s of type %s in context\n%s\nand metasenv\n%s\nand substitution\n%s\nbecause %s"
+ (CicMetaSubst.ppterm ~metasenv subst t1)
+ (try
+ let ty_t1,_ = type_of_aux' metasenv subst context t1 ugraph in
+ CicPp.ppterm ty_t1
+ with
+ | UnificationFailure s
+ | Uncertain s
+ | AssertFailure s -> sprintf "MALFORMED(t1): \n<BEGIN>%s\n<END>" (Lazy.force s))
+ (CicMetaSubst.ppterm ~metasenv subst t2)
+ (try
+ let ty_t2,_ = type_of_aux' metasenv subst context t2 ugraph in
+ CicPp.ppterm ty_t2
+ with
+ | UnificationFailure s
+ | Uncertain s
+ | AssertFailure s -> sprintf "MALFORMED(t2): \n<BEGIN>%s\n<END>" (Lazy.force s))
+ (CicMetaSubst.ppcontext ~metasenv subst context)
+ (CicMetaSubst.ppmetasenv subst metasenv)
+ (CicMetaSubst.ppsubst ~metasenv subst) (Lazy.force msg)
+ else
+ sprintf "Unification error unifying %s of type %s with %s of type %s in context\n%s\nand metasenv\n%s\nbecause %s"
+ (CicMetaSubst.ppterm_in_context ~metasenv subst t1 context)
+ (try
+ let ty_t1,_ = type_of_aux' metasenv subst context t1 ugraph in
+ CicMetaSubst.ppterm_in_context ~metasenv subst ty_t1 context
+ with
+ | UnificationFailure s
+ | Uncertain s
+ | AssertFailure s -> sprintf "MALFORMED(t1): \n<BEGIN>%s\n<END>" (Lazy.force s))
+ (CicMetaSubst.ppterm_in_context ~metasenv subst t2 context)
+ (try
+ let ty_t2,_ = type_of_aux' metasenv subst context t2 ugraph in
+ CicMetaSubst.ppterm_in_context ~metasenv subst ty_t2 context
+ with
+ | UnificationFailure s
+ | Uncertain s
+ | AssertFailure s -> sprintf "MALFORMED(t2): \n<BEGIN>%s\n<END>" (Lazy.force s))
+ (CicMetaSubst.ppcontext ~metasenv subst context)
+ (CicMetaSubst.ppmetasenv subst metasenv)
+ (Lazy.force msg)
+ )
+
+let fo_unif_subst subst context metasenv t1 t2 ugraph =
+ try
+ fo_unif_subst false subst context metasenv t1 t2 ugraph
+ with
+ | AssertFailure msg ->
+ raise (AssertFailure (enrich_msg msg subst context metasenv t1 t2 ugraph))
+ | UnificationFailure msg ->
+ raise (UnificationFailure (enrich_msg msg subst context metasenv t1 t2 ugraph))
+;;
projects / helm.git / blobdiff