exception UnificationFailure of string Lazy.t;;
exception Uncertain of string Lazy.t;;
exception AssertFailure of string Lazy.t;;
+exception KeepReducing of string Lazy.t;;
+exception KeepReducingThis of
+ string Lazy.t * (NCicReduction.machine * bool) *
+ (NCicReduction.machine * bool) ;;
let (===) x y = Pervasives.compare x y = 0 ;;
-let uncert_exc metasenv subst context t1 t2 =
- Uncertain (lazy (
+let mk_msg metasenv subst context t1 t2 =
+ (lazy (
"Can't unify " ^ NCicPp.ppterm ~metasenv ~subst ~context t1 ^
" with " ^ NCicPp.ppterm ~metasenv ~subst ~context t2))
-;;
-
-let fail_exc metasenv subst context t1 t2 =
- UnificationFailure (lazy (
- "Can't unify " ^ NCicPp.ppterm ~metasenv ~subst ~context t1 ^
- " with " ^ NCicPp.ppterm ~metasenv ~subst ~context t2))
-;;
-
-let mk_appl hd tl =
- match hd with
- | NCic.Appl l -> NCic.Appl (l@tl)
- | _ -> NCic.Appl (hd :: tl)
-;;
-let flexible l =
- List.exists
- (function
- | NCic.Meta _
- | NCic.Appl (NCic.Meta _::_) -> true
- | _ -> false) l
+let mk_appl ~upto hd tl =
+ NCicReduction.head_beta_reduce ~upto
+ (match hd with
+ | NCic.Appl l -> NCic.Appl (l@tl)
+ | _ -> NCic.Appl (hd :: tl))
;;
exception WrongShape;;
-let eta_reduce =
- let delift_if_not_occur body orig =
+let eta_reduce subst t =
+ let delift_if_not_occur body =
try
- NCicSubstitution.psubst ~avoid_beta_redexes:true
- (fun () -> raise WrongShape) [()] body
- with WrongShape -> orig
+ Some (NCicSubstitution.psubst ~avoid_beta_redexes:true
+ (fun () -> raise WrongShape) [()] body)
+ with WrongShape -> None
+ in
+ let rec eat_lambdas ctx = function
+ | NCic.Lambda (name, src, tgt) ->
+ eat_lambdas ((name, src) :: ctx) tgt
+ | NCic.Meta (i,lc) as t->
+ (try
+ let _,_,t,_ = NCicUtils.lookup_subst i subst in
+ let t = NCicSubstitution.subst_meta lc t in
+ eat_lambdas ctx t
+ with NCicUtils.Subst_not_found _ -> ctx, t)
+ | t -> ctx, t
in
- function
- | NCic.Lambda(_, _, NCic.Appl [hd; NCic.Rel 1]) as orig ->
- delift_if_not_occur hd orig
- | NCic.Lambda(_, _, NCic.Appl (hd :: l)) as orig
- when HExtlib.list_last l = NCic.Rel 1 ->
- let body =
- let args, _ = HExtlib.split_nth (List.length l - 1) l in
- NCic.Appl (hd::args)
- in
- delift_if_not_occur body orig
- | t -> t
+ let context_body = eat_lambdas [] t in
+ let rec aux = function
+ | [],body -> body
+ | (name, src)::ctx, (NCic.Appl (hd::[NCic.Rel 1]) as bo) ->
+ (match delift_if_not_occur hd with
+ | None -> aux (ctx,NCic.Lambda(name,src, bo))
+ | Some bo -> aux (ctx,bo))
+ | (name, src)::ctx, (NCic.Appl args as bo)
+ when HExtlib.list_last args = NCic.Rel 1 ->
+ let args, _ = HExtlib.split_nth (List.length args - 1) args in
+ (match delift_if_not_occur (NCic.Appl args) with
+ | None -> aux (ctx,NCic.Lambda(name,src, bo))
+ | Some bo -> aux (ctx,bo))
+ | (name, src) :: ctx, t ->
+ aux (ctx,NCic.Lambda(name,src, t))
+ in
+ aux context_body
;;
-
+
module C = NCic;;
module Ref = NReference;;
+let debug = ref false;;
let indent = ref "";;
-let inside c = indent := !indent ^ String.make 1 c;;
-let outside () = indent := String.sub !indent 0 (String.length !indent -1);;
-
-(*
-let pp s =
+let times = ref [];;
+let pp s =
+ if !debug then
prerr_endline (Printf.sprintf "%-20s" !indent ^ " " ^ Lazy.force s)
-;;
-*)
-
-let pp _ = ();;
+;;
+let inside c =
+ if !debug then
+ begin
+ let time1 = Unix.gettimeofday () in
+ indent := !indent ^ String.make 1 c;
+ times := time1 :: !times;
+ prerr_endline ("{{{" ^ !indent ^ " ")
+ end
+;;
+let outside exc_opt =
+ if !debug then
+ begin
+ let time2 = Unix.gettimeofday () in
+ let time1 =
+ match !times with time1::tl -> times := tl; time1 | [] -> assert false in
+ prerr_endline ("}}} " ^ !indent ^ " " ^ string_of_float (time2 -. time1));
+ (match exc_opt with
+ | Some e -> prerr_endline ("exception raised: " ^ Printexc.to_string e)
+ | None -> ());
+ try
+ indent := String.sub !indent 0 (String.length !indent -1)
+ with
+ Invalid_argument _ -> indent := "??"; ()
+ end
+;;
-let fix_sorts swap metasenv subst context meta t =
- let rec aux () = function
- | NCic.Sort (NCic.Type u) as orig ->
- if swap then
- match NCicEnvironment.sup u with
- | None -> prerr_endline "no sup for" ;
- raise (fail_exc metasenv subst context meta t)
- | Some u1 -> if u = u1 then orig else NCic.Sort (NCic.Type u1)
- else
- NCic.Sort (NCic.Type (
- match NCicEnvironment.sup NCicEnvironment.type0 with
- | Some x -> x
- | _ -> assert false))
- | NCic.Meta _ as orig -> orig
- | t -> NCicUtils.map (fun _ _ -> ()) () aux t
- in
- aux () t
+let ppcontext ~metasenv ~subst c =
+ "\nctx:\n"^ NCicPp.ppcontext ~metasenv ~subst c
;;
+let ppmetasenv ~subst m = "\nmenv:\n" ^ NCicPp.ppmetasenv ~subst m;;
+
+let ppcontext ~metasenv:_metasenv ~subst:_subst _context = "";;
+let ppmetasenv ~subst:_subst _metasenv = "";;
+let ppterm ~metasenv ~subst ~context = NCicPp.ppterm ~metasenv ~subst ~context;;
+(* let ppterm ~metasenv:_ ~subst:_ ~context:_ _ = "";; *)
-let rec beta_expand num test_eq_only swap metasenv subst context t arg =
- let rec aux (n,context,test_eq_only as k) (metasenv, subst as acc) t' =
+let is_locked n subst =
try
- let metasenv, subst =
- if swap then
- unify test_eq_only metasenv subst context t' (NCicSubstitution.lift n arg)
- else
- unify test_eq_only metasenv subst context (NCicSubstitution.lift n arg) t'
- in
- (metasenv, subst), NCic.Rel (1 + n)
- with Uncertain _ | UnificationFailure _ ->
- match t' with
- | NCic.Rel m as orig ->
- (metasenv, subst), if m <= n then orig else NCic.Rel (m+1)
- (* 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 *)
- | NCic.Meta (i,(shift,lc)) ->
- (metasenv,subst), NCic.Meta (i,(shift+1,lc))
- | NCic.Prod (name, src, tgt) as orig ->
- let (metasenv, subst), src1 = aux (n,context,true) acc src in
- let k = n+1, (name, NCic.Decl src) :: context, test_eq_only in
- let ms, tgt1 = aux k (metasenv, subst) tgt in
- if src == src1 && tgt == tgt1 then ms, orig else
- ms, NCic.Prod (name, src1, tgt1)
- | t ->
- NCicUntrusted.map_term_fold_a
- (fun e (n,ctx,teq) -> n+1,e::ctx,teq) k aux acc t
+ match NCicUtils.lookup_subst n subst with
+ | tag, _,_,_ when NCicMetaSubst.is_out_scope_tag tag -> true
+ | _ -> false
+ with NCicUtils.Subst_not_found _ -> false
+;;
+let rec mk_irl stop base =
+ if base > stop then []
+ else (NCic.Rel base) :: mk_irl stop (base+1)
+;;
+
+(* the argument must be a term in whd *)
+let rec could_reduce =
+ function
+ | C.Meta _ -> true
+ | C.Appl (C.Const (Ref.Ref (_,Ref.Fix (_,recno,_)))::args)
+ when List.length args > recno -> could_reduce (List.nth args recno)
+ | C.Match (_,_,arg,_) -> could_reduce arg
+ | C.Appl (he::_) -> could_reduce he
+ | C.Sort _ | C.Rel _ | C.Prod _ | C.Lambda _ | C.Const _ -> false
+ | C.Appl [] | C.LetIn _ | C.Implicit _ -> assert false
+;;
+
+let rec lambda_intros rdb metasenv subst context argsno ty =
+ pp (lazy ("LAMBDA INTROS: " ^ ppterm ~metasenv ~subst ~context ty));
+ match argsno with
+ 0 ->
+ let metasenv, _, bo, _ =
+ NCicMetaSubst.mk_meta metasenv context ~with_type:ty `IsTerm
+ in
+ metasenv, bo
+ | _ ->
+ (match NCicReduction.whd ~subst context ty with
+ C.Prod (n,so,ta) ->
+ let metasenv,bo =
+ lambda_intros rdb metasenv subst
+ ((n,C.Decl so)::context) (argsno - 1) ta
+ in
+ metasenv,C.Lambda (n,so,bo)
+ | _ -> assert false)
+;;
+
+let unopt exc = function None -> raise exc | Some x -> x ;;
+
+let fix metasenv subst is_sup test_eq_only exc t =
+ (*D*) inside 'f'; try let rc =
+ pp (lazy (NCicPp.ppterm ~metasenv ~subst ~context:[] t));
+ let rec aux test_eq_only metasenv = function
+ | NCic.Prod (n,so,ta) ->
+ let metasenv,so = aux true metasenv so in
+ let metasenv,ta = aux test_eq_only metasenv ta in
+ metasenv,NCic.Prod (n,so,ta)
+ | NCic.Sort (NCic.Type [(`CProp|`Type),_]) as orig when test_eq_only ->
+ metasenv,orig
+ | NCic.Sort (NCic.Type _) when test_eq_only -> raise exc
+ | NCic.Sort (NCic.Type u) when is_sup ->
+ metasenv, NCic.Sort (NCic.Type (unopt exc (NCicEnvironment.sup u)))
+ | NCic.Sort (NCic.Type u) ->
+ metasenv, NCic.Sort (NCic.Type
+ (unopt exc (NCicEnvironment.inf ~strict:false u)))
+ | NCic.Meta (n,_) as orig ->
+ (try
+ let _,_,_,_ = NCicUtils.lookup_subst n subst in metasenv,orig
+ with NCicUtils.Subst_not_found _ ->
+ let metasenv, _ = NCicMetaSubst.extend_meta metasenv n in
+ metasenv, orig)
+ | t ->
+ NCicUntrusted.map_term_fold_a (fun _ x -> x) test_eq_only aux metasenv t
in
- let argty = NCicTypeChecker.typeof ~metasenv ~subst context arg in
- let fresh_name = "Hbeta" ^ string_of_int num in
- let (metasenv,subst), t1 =
- aux (0, context, test_eq_only) (metasenv, subst) t in
- let t2 = eta_reduce (NCic.Lambda (fresh_name,argty,t1)) in
- try
- ignore(NCicTypeChecker.typeof ~metasenv ~subst context t2);
- metasenv, subst, t2
- with NCicTypeChecker.TypeCheckerFailure _ ->
- metasenv, subst, NCic.Lambda ("_", argty, NCicSubstitution.lift 1 arg)
+ aux test_eq_only metasenv t
+ (*D*) in outside None; rc with exn -> outside (Some exn); raise exn
+;;
+
+let metasenv_to_subst n (kind,context,ty) metasenv subst =
+ let infos,metasenv = List.partition (fun (n',_) -> n = n') metasenv in
+ let attrs,octx,oty = match infos with [_,infos] -> infos | _ -> assert false in
+ if octx=context && oty=ty then
+ (n,(NCicUntrusted.set_kind kind attrs, octx, oty))::metasenv,subst
+ else
+ let metasenv, _, bo, _ =
+ NCicMetaSubst.mk_meta metasenv context ~attrs ~with_type:ty kind in
+ let subst = (n,(NCicUntrusted.set_kind kind attrs,octx,bo,oty))::subst in
+ metasenv,subst
+;;
+
+let rec sortfy exc metasenv subst context t =
+ let t = NCicReduction.whd ~subst context t in
+ let metasenv,subst =
+ match t with
+ | NCic.Sort _ -> metasenv, subst
+ | NCic.Meta (n,_) ->
+ let attrs, context, ty = NCicUtils.lookup_meta n metasenv in
+ let kind = NCicUntrusted.kind_of_meta attrs in
+ if kind = `IsSort then
+ metasenv,subst
+ else
+ (match ty with
+ | NCic.Implicit (`Typeof _) ->
+ metasenv_to_subst n (`IsSort,[],ty) metasenv subst
+ | ty ->
+ let metasenv,subst,ty = sortfy exc metasenv subst context ty in
+ metasenv_to_subst n (`IsSort,[],ty) metasenv subst)
+ | NCic.Implicit _ -> assert false
+ | _ -> raise exc
+ in
+ metasenv,subst,t
-and beta_expand_many test_equality_only swap metasenv subst context t args =
-(* (*D*) inside 'B'; try let rc = *)
- pp (lazy (String.concat ", "
- (List.map (NCicPp.ppterm ~metasenv ~subst ~context)
- args) ^ " ∈ " ^ NCicPp.ppterm ~metasenv ~subst ~context t));
- let _, subst, metasenv, hd =
- List.fold_right
- (fun arg (num,subst,metasenv,t) ->
- let metasenv, subst, t =
- beta_expand num test_equality_only swap metasenv subst context t arg
+let tipify exc metasenv subst context t ty =
+ let is_type attrs =
+ match NCicUntrusted.kind_of_meta attrs with
+ `IsType | `IsSort -> true
+ | `IsTerm -> false
+ in
+ let rec optimize_meta metasenv subst =
+ function
+ NCic.Meta (n,lc) ->
+ (try
+ let attrs,_,_ = NCicUtils.lookup_meta n metasenv in
+ if is_type attrs then
+ metasenv,subst,true
+ else
+ let _,cc,ty = NCicUtils.lookup_meta n metasenv in
+ let metasenv,subst,ty = sortfy exc metasenv subst cc ty in
+ let metasenv =
+ NCicUntrusted.replace_in_metasenv n
+ (fun attrs,cc,_ -> NCicUntrusted.set_kind `IsType attrs, cc, ty)
+ metasenv
in
- num+1,subst,metasenv,t)
- args (1,subst,metasenv,t)
- in
- pp (lazy ("Head syntesized by b-exp: " ^
- NCicPp.ppterm ~metasenv ~subst ~context hd));
- metasenv, subst, hd
-(* (*D*) in outside (); rc with exn -> outside (); raise exn *)
+ metasenv,subst,false
+ with
+ NCicUtils.Meta_not_found _ ->
+ let attrs, _,bo,_ = NCicUtils.lookup_subst n subst in
+ if is_type attrs then
+ metasenv,subst,true
+ else
+ let _,cc,_,ty = NCicUtils.lookup_subst n subst in
+ let metasenv,subst,ty = sortfy exc metasenv subst cc ty in
+ let subst =
+ NCicUntrusted.replace_in_subst n
+ (fun attrs,cc,bo,_->NCicUntrusted.set_kind `IsType attrs,cc,bo,ty)
+ subst
+ in
+ optimize_meta metasenv subst (NCicSubstitution.subst_meta lc bo))
+ | _ -> metasenv,subst,false
+ in
+ let metasenv,subst,b = optimize_meta metasenv subst t in
+ if b then
+ metasenv,subst,t
+ else
+ let metasenv,subst,_ = sortfy exc metasenv subst context ty in
+ metasenv,subst,t
+;;
-and instantiate test_eq_only metasenv subst context n lc t swap =
+let rec instantiate rdb test_eq_only metasenv subst context n lc t swap =
(*D*) inside 'I'; try let rc =
- pp (lazy(string_of_int n ^ " :=?= "^
- NCicPp.ppterm ~metasenv ~subst ~context t));
- let unify test_eq_only m s c t1 t2 =
- if swap then unify test_eq_only m s c t2 t1
- else unify test_eq_only m s c t1 t2
+ pp (lazy(string_of_int n^" :=?= "^ppterm ~metasenv ~subst ~context t));
+ let exc =
+ UnificationFailure (mk_msg metasenv subst context (NCic.Meta (n,lc)) t) in
+ let move_to_subst i ((_,cc,t,_) as infos) metasenv subst =
+ let metasenv = List.remove_assoc i metasenv in
+ pp(lazy(string_of_int n ^ " :==> "^ ppterm ~metasenv ~subst ~context:cc t));
+ metasenv, (i,infos) :: subst
in
- let name, ctx, ty = NCicUtils.lookup_meta n metasenv in
- let metasenv, subst, t =
- match ty with
- | NCic.Implicit (`Typeof _) ->
- metasenv,subst, t
- (* fix_sorts swap metasenv subst context (NCic.Meta(n,lc)) t *)
- | _ ->
- pp (lazy (
- "typeof: " ^ NCicPp.ppterm ~metasenv ~subst ~context t ^ "\nctx:\n"^
- NCicPp.ppcontext ~metasenv ~subst context ^ "\nmenv:\n"^
- NCicPp.ppmetasenv ~subst metasenv));
- let t, ty_t =
- try t, NCicTypeChecker.typeof ~subst ~metasenv context t
- with
- | NCicTypeChecker.AssertFailure msg ->
- (pp (lazy "fine typeof (fallimento)");
- let ft =
- fix_sorts swap metasenv subst context (NCic.Meta (n,lc)) t
+ let delift_to_subst test_eq_only n lc (attrs,cc,ty) t context metasenv subst =
+ pp (lazy(string_of_int n ^ " := 111 = "^
+ ppterm ~metasenv ~subst ~context t));
+ let (metasenv, subst), t =
+ try
+ NCicMetaSubst.delift
+ ~unify:(fun m s c t1 t2 ->
+ let ind = !indent in
+ let res =
+ try Some (unify rdb test_eq_only m s c t1 t2 false)
+ with UnificationFailure _ | Uncertain _ -> None
in
- if ft == t then
- (prerr_endline ( ("ILLTYPED: " ^
- NCicPp.ppterm ~metasenv ~subst ~context t
- ^ "\nBECAUSE:" ^ Lazy.force msg ^ "\nCONTEXT:\n" ^
- NCicPp.ppcontext ~metasenv ~subst context ^ "\nMENV:\n" ^
- NCicPp.ppmetasenv ~subst metasenv
- ));
- assert false)
- else
- try
- pp (lazy ("typeof: " ^
- NCicPp.ppterm ~metasenv ~subst ~context ft));
- ft, NCicTypeChecker.typeof ~subst ~metasenv context ft
- with NCicTypeChecker.AssertFailure _ ->
- assert false)
- | NCicTypeChecker.TypeCheckerFailure msg ->
- pp msg; assert false
- in
- let lty = NCicSubstitution.subst_meta lc ty in
- pp (lazy("On the types: " ^
- NCicPp.ppterm ~metasenv ~subst ~context:ctx ty ^ " ~~~ " ^
- NCicPp.ppterm ~metasenv ~subst ~context lty ^ " === "
- ^ NCicPp.ppterm ~metasenv ~subst ~context ty_t));
- let metasenv,subst= unify test_eq_only metasenv subst context lty ty_t in
- metasenv, subst, t
- in
- pp (lazy(string_of_int n ^ " := 111 = "^
- NCicPp.ppterm ~metasenv ~subst ~context t));
- let (metasenv, subst), t =
- try NCicMetaSubst.delift metasenv subst context n lc t
- with NCicMetaSubst.Uncertain msg ->
- pp (lazy ("delift fails: " ^ Lazy.force msg));
- raise (Uncertain msg)
- | NCicMetaSubst.MetaSubstFailure msg ->
- pp (lazy ("delift fails: " ^ Lazy.force msg));
- raise (UnificationFailure msg)
- in
- pp (lazy(string_of_int n ^ " := 222 = "^
- NCicPp.ppterm ~metasenv ~subst ~context:ctx t
- ^ "\n" ^ NCicPp.ppmetasenv ~subst metasenv
-
- ));
- (* Unifying the types may have already instantiated n. *)
- try
- let _, _,oldt,_ = NCicUtils.lookup_subst n subst in
- let oldt = NCicSubstitution.subst_meta lc oldt in
- let t = NCicSubstitution.subst_meta lc t in
- (* conjecture: always fail --> occur check *)
- unify test_eq_only metasenv subst context oldt t
- with NCicUtils.Subst_not_found _ ->
- (* by cumulativity when unify(?,Type_i)
- * we could ? := Type_j with j <= i... *)
- let subst = (n, (name, ctx, t, ty)) :: subst in
- pp (lazy ("?"^string_of_int n^" := "^NCicPp.ppterm
- ~metasenv ~subst ~context (NCicSubstitution.subst_meta lc t)));
- let metasenv =
- List.filter (fun (m,_) -> not (n = m)) metasenv
+ indent := ind; res)
+ metasenv subst context n lc t
+ with NCicMetaSubst.Uncertain msg ->
+ pp (lazy ("delift is uncertain: " ^ Lazy.force msg));
+ raise (Uncertain msg)
+ | NCicMetaSubst.MetaSubstFailure msg ->
+ pp (lazy ("delift fails: " ^ Lazy.force msg));
+ raise (UnificationFailure msg)
in
- metasenv, subst
- (*D*) in outside(); rc with exn -> outside (); raise exn
-
-and unify test_eq_only metasenv subst context t1 t2 =
- (*D*) inside 'U'; try let rc =
- let fo_unif test_eq_only metasenv subst t1 t2 =
+ pp (lazy(string_of_int n ^ " := 222 = "^
+ ppterm ~metasenv ~subst ~context:cc t^ppmetasenv ~subst metasenv));
+ (* Unifying the types may have already instantiated n. *)
+ try
+ let _, _,oldt,_ = NCicUtils.lookup_subst n subst in
+ let oldt = NCicSubstitution.subst_meta lc oldt in
+ let t = NCicSubstitution.subst_meta lc t in
+ (* conjecture: always fail --> occur check *)
+ unify rdb test_eq_only metasenv subst context t oldt false
+ with NCicUtils.Subst_not_found _ ->
+ move_to_subst n (attrs,cc,t,ty) metasenv subst
+ in
+ let attrs,cc,ty = NCicUtils.lookup_meta n metasenv in
+ let kind = NCicUntrusted.kind_of_meta attrs in
+ let metasenv,t = fix metasenv subst swap test_eq_only exc t in
+ let ty_t = NCicTypeChecker.typeof ~metasenv ~subst context t in
+ let metasenv,subst,t =
+ match kind with
+ `IsSort -> sortfy exc metasenv subst context t
+ | `IsType -> tipify exc metasenv subst context t ty_t
+ | `IsTerm -> metasenv,subst,t in
+ match kind with
+ | `IsSort ->
+ (match ty,t with
+ NCic.Implicit (`Typeof _), NCic.Sort _ ->
+ move_to_subst n (attrs,cc,t,ty_t) metasenv subst
+ | NCic.Sort (NCic.Type u1), NCic.Sort s ->
+ let s =
+ match s,swap with
+ NCic.Type u2, false ->
+ NCic.Sort (NCic.Type
+ (unopt exc (NCicEnvironment.inf ~strict:false
+ (unopt exc (NCicEnvironment.inf ~strict:true u1) @ u2))))
+ | NCic.Type u2, true ->
+ if NCicEnvironment.universe_lt u2 u1 then
+ NCic.Sort (NCic.Type u2)
+ else (raise exc)
+ | NCic.Prop,_ -> NCic.Sort NCic.Prop
+ in
+ move_to_subst n (attrs,cc,s,ty) metasenv subst
+ | NCic.Implicit (`Typeof _), NCic.Meta _ ->
+ move_to_subst n (attrs,cc,t,ty_t) metasenv subst
+ | _, NCic.Meta _
+ | NCic.Meta _, NCic.Sort _ ->
+ pp (lazy ("On the types: " ^
+ ppterm ~metasenv ~subst ~context ty ^ "=<=" ^
+ ppterm ~metasenv ~subst ~context ty_t));
+ let metasenv, subst =
+ unify rdb false metasenv subst context ty_t ty false in
+ delift_to_subst test_eq_only n lc (attrs,cc,ty) t
+ context metasenv subst
+ | _ -> assert false)
+ | `IsType
+ | `IsTerm ->
+ (match ty with
+ NCic.Implicit (`Typeof _) ->
+ let (metasenv, subst), ty_t =
+ try
+ NCicMetaSubst.delift
+ ~unify:(fun m s c t1 t2 ->
+ let ind = !indent in
+ let res = try Some (unify rdb test_eq_only m s c t1 t2 false )
+ with UnificationFailure _ | Uncertain _ -> None
+ in
+ indent := ind; res)
+ metasenv subst context n lc ty_t
+ with NCicMetaSubst.Uncertain msg ->
+ pp (lazy ("delift is uncertain: " ^ Lazy.force msg));
+ raise (Uncertain msg)
+ | NCicMetaSubst.MetaSubstFailure msg ->
+ pp (lazy ("delift fails: " ^ Lazy.force msg));
+ raise (UnificationFailure msg)
+ in
+ delift_to_subst test_eq_only n lc (attrs,cc,ty_t) t context metasenv
+ subst
+ | _ ->
+ let lty = NCicSubstitution.subst_meta lc ty in
+ pp (lazy ("On the types: " ^
+ ppterm ~metasenv ~subst ~context ty_t ^ "=<=" ^
+ ppterm ~metasenv ~subst ~context lty));
+ let metasenv, subst =
+ unify rdb false metasenv subst context ty_t lty false
+ in
+ delift_to_subst test_eq_only n lc (attrs,cc,ty) t context metasenv
+ subst)
+ (*D*) in outside None; rc with exn -> outside (Some exn); raise exn
+
+and unify rdb test_eq_only metasenv subst context t1 t2 swap =
+ (*D*) inside 'U'; try let rc =
+ let fo_unif test_eq_only metasenv subst (norm1,t1) (norm2,t2) =
(*D*) inside 'F'; try let rc =
- pp (lazy(" " ^ NCicPp.ppterm ~metasenv ~subst ~context t1 ^ " === " ^
- NCicPp.ppterm ~metasenv ~subst ~context t2));
+ pp (lazy(" " ^ ppterm ~metasenv ~subst ~context t1 ^
+ (if swap then " ==>?== "
+ else " ==<?==" ) ^
+ ppterm ~metasenv ~subst ~context t2 ^ ppmetasenv
+ ~subst metasenv));
+ pp (lazy(" " ^ ppterm ~metasenv ~subst:[] ~context t1 ^
+ (if swap then " ==>??== "
+ else " ==<??==" ) ^
+ ppterm ~metasenv ~subst:[] ~context t2 ^ ppmetasenv
+ ~subst metasenv));
if t1 === t2 then
metasenv, subst
+(* CSC: To speed up Oliboni's stuff. Why is it necessary, anyway?
+ else if
+ NCicUntrusted.metas_of_term subst context t1 = [] &&
+ NCicUntrusted.metas_of_term subst context t2 = []
+ then
+ if NCicReduction.are_convertible ~metasenv ~subst context t1 t2 then
+ metasenv,subst
+ else
+ raise (UnificationFailure (lazy "Closed terms not convertible"))
+*)
else
match (t1,t2) with
- | (C.Sort (C.Type a), C.Sort (C.Type b)) when not test_eq_only ->
+ | C.Appl [_], _ | _, C.Appl [_] | C.Appl [], _ | _, C.Appl []
+ | C.Appl (C.Appl _::_), _ | _, C.Appl (C.Appl _::_) ->
+ prerr_endline "Appl [Appl _;_] or Appl [] or Appl [_] invariant";
+ assert false
+ | (C.Sort (C.Type a), C.Sort (C.Type b)) when not test_eq_only ->
+ let a, b = if swap then b,a else a,b in
if NCicEnvironment.universe_leq a b then metasenv, subst
- else raise (fail_exc metasenv subst context t1 t2)
+ else raise (UnificationFailure (mk_msg metasenv subst context t1 t2))
| (C.Sort (C.Type a), C.Sort (C.Type b)) ->
if NCicEnvironment.universe_eq a b then metasenv, subst
- else raise (fail_exc metasenv subst context t1 t2)
- | (C.Sort C.Prop,C.Sort (C.Type _)) ->
+ else raise (UnificationFailure (mk_msg metasenv subst context t1 t2))
+ | (C.Sort C.Prop,C.Sort (C.Type _)) when not swap ->
+ if (not test_eq_only) then metasenv, subst
+ else raise (UnificationFailure (mk_msg metasenv subst context t1 t2))
+ | (C.Sort (C.Type _), C.Sort C.Prop) when swap ->
if (not test_eq_only) then metasenv, subst
- else raise (fail_exc metasenv subst context t1 t2)
+ else raise (UnificationFailure (mk_msg metasenv subst context t1 t2))
| (C.Lambda (name1,s1,t1), C.Lambda(_,s2,t2))
| (C.Prod (name1,s1,t1), C.Prod(_,s2,t2)) ->
- let metasenv, subst = unify true metasenv subst context s1 s2 in
- unify test_eq_only metasenv subst ((name1, C.Decl s1)::context) t1 t2
+ let metasenv, subst = unify rdb true metasenv subst context s1 s2 swap in
+ unify rdb test_eq_only metasenv subst ((name1, C.Decl s1)::context) t1 t2 swap
| (C.LetIn (name1,ty1,s1,t1), C.LetIn(_,ty2,s2,t2)) ->
- let metasenv,subst=unify test_eq_only metasenv subst context ty1 ty2 in
- let metasenv,subst=unify test_eq_only metasenv subst context s1 s2 in
+ let metasenv,subst=unify rdb test_eq_only metasenv subst context ty1 ty2 swap in
+ let metasenv,subst=unify rdb test_eq_only metasenv subst context s1 s2 swap in
let context = (name1, C.Def (s1,ty1))::context in
- unify test_eq_only metasenv subst context t1 t2
+ unify rdb test_eq_only metasenv subst context t1 t2 swap
| (C.Meta (n1,(s1,l1 as lc1)),C.Meta (n2,(s2,l2 as lc2))) when n1 = n2 ->
(try
(fun t1 t2 (metasenv, subst, to_restrict, i) ->
try
let metasenv, subst =
- unify test_eq_only metasenv subst context
+ unify rdb (*test_eq_only*) true metasenv subst context
(NCicSubstitution.lift s1 t1) (NCicSubstitution.lift s2 t2)
+ swap
in
metasenv, subst, to_restrict, i-1
with UnificationFailure _ | Uncertain _ ->
l1 l2 (metasenv, subst, [], List.length l1)
in
if to_restrict <> [] then
- let metasenv, subst, _ =
+ let metasenv, subst, _, _ =
NCicMetaSubst.restrict metasenv subst n1 to_restrict
in
metasenv, subst
let _,_,term,_ = NCicUtils.lookup_subst n1 subst in
let term1 = NCicSubstitution.subst_meta lc1 term in
let term2 = NCicSubstitution.subst_meta lc2 term in
- unify test_eq_only metasenv subst context term1 term2
+ unify rdb test_eq_only metasenv subst context term1 term2 swap
with NCicUtils.Subst_not_found _-> raise (UnificationFailure msg))
- | C.Meta (n,lc), t ->
- (try
- let _,_,term,_ = NCicUtils.lookup_subst n subst in
- let term = NCicSubstitution.subst_meta lc term in
- unify test_eq_only metasenv subst context term t
- with NCicUtils.Subst_not_found _->
- instantiate test_eq_only metasenv subst context n lc t false)
-
- | t, C.Meta (n,lc) ->
- (try
- let _,_,term,_ = NCicUtils.lookup_subst n subst in
- let term = NCicSubstitution.subst_meta lc term in
- unify test_eq_only metasenv subst context t term
- with NCicUtils.Subst_not_found _->
- instantiate test_eq_only metasenv subst context n lc t true)
-
- | NCic.Appl (NCic.Meta (i,l)::args), _ when List.mem_assoc i subst ->
- let _,_,term,_ = NCicUtils.lookup_subst i subst in
- let term = NCicSubstitution.subst_meta l term in
- unify test_eq_only metasenv subst context (mk_appl term args) t2
-
- | _, NCic.Appl (NCic.Meta (i,l)::args) when List.mem_assoc i subst ->
- let _,_,term,_ = NCicUtils.lookup_subst i subst in
- let term = NCicSubstitution.subst_meta l term in
- unify test_eq_only metasenv subst context t1 (mk_appl term args)
-
| NCic.Appl (NCic.Meta (i,_)::_ as l1),
NCic.Appl (NCic.Meta (j,_)::_ as l2) when i=j ->
(try
List.fold_left2
(fun (metasenv, subst) t1 t2 ->
- unify test_eq_only metasenv subst context t1 t2)
+ unify rdb (*test_eq_only*) true metasenv subst context t1
+ t2 swap)
(metasenv,subst) l1 l2
with Invalid_argument _ ->
- raise (fail_exc metasenv subst context t1 t2))
-
- | NCic.Appl (NCic.Meta (i,l)::args), _ when not (flexible args) ->
- (* we verify that none of the args is a Meta,
- since beta expanding w.r.t a metavariable makes no sense *)
- let metasenv, subst, beta_expanded =
- beta_expand_many
- test_eq_only false
- metasenv subst context t2 args
+ raise (UnificationFailure (mk_msg metasenv subst context t1 t2)))
+
+ | _, NCic.Meta (n, _) when is_locked n subst && not swap->
+ (let (metasenv, subst), i =
+ match NCicReduction.whd ~subst context t1 with
+ | NCic.Appl (NCic.Meta (i,l) as meta :: args) ->
+ let metasenv, lambda_Mj =
+ lambda_intros rdb metasenv subst context (List.length args)
+ (NCicTypeChecker.typeof ~metasenv ~subst context meta)
+ in
+ unify rdb test_eq_only metasenv subst context
+ (C.Meta (i,l)) lambda_Mj false,
+ i
+ | NCic.Meta (i,_) -> (metasenv, subst), i
+ | _ ->
+ raise (UnificationFailure (lazy "Locked term vs non
+ flexible term; probably not saturated enough yet!"))
+ in
+ let t1 = NCicReduction.whd ~subst context t1 in
+ let j, lj =
+ match t1 with NCic.Meta (j,l) -> j, l | _ -> assert false
in
- unify test_eq_only metasenv subst context
- (C.Meta (i,l)) beta_expanded
-
- | _, NCic.Appl (NCic.Meta (i,l)::args) when not(flexible args) ->
- let metasenv, subst, beta_expanded =
- beta_expand_many
- test_eq_only true
- metasenv subst context t1 args
+ let metasenv, subst =
+ instantiate rdb test_eq_only metasenv subst context j lj t2 true
in
- unify test_eq_only metasenv subst context
- beta_expanded (C.Meta (i,l))
+ (* We need to remove the out_scope_tags to avoid propagation of
+ them that triggers again the ad-hoc case *)
+ let subst =
+ List.map (fun (i,(tag,ctx,bo,ty)) ->
+ let tag =
+ List.filter
+ (function `InScope | `OutScope _ -> false | _ -> true) tag
+ in
+ i,(tag,ctx,bo,ty)
+ ) subst
+ in
+ (try
+ let name, ctx, term, ty = NCicUtils.lookup_subst i subst in
+ let term = eta_reduce subst term in
+ let subst = List.filter (fun (j,_) -> j <> i) subst in
+ metasenv, ((i, (name, ctx, term, ty)) :: subst)
+ with Not_found -> assert false))
+ | NCic.Meta (n, _), _ when is_locked n subst && swap ->
+ unify rdb test_eq_only metasenv subst context t2 t1 false
+
+ | t, C.Meta (n,lc) when List.mem_assoc n subst ->
+ let _,_,term,_ = NCicUtils.lookup_subst n subst in
+ let term = NCicSubstitution.subst_meta lc term in
+ unify rdb test_eq_only metasenv subst context t term swap
+ | C.Meta (n,_), _ when List.mem_assoc n subst ->
+ unify rdb test_eq_only metasenv subst context t2 t1 (not swap)
+
+ | _, NCic.Appl (NCic.Meta (i,l)::args) when List.mem_assoc i subst ->
+ let _,_,term,_ = NCicUtils.lookup_subst i subst in
+ let term = NCicSubstitution.subst_meta l term in
+ unify rdb test_eq_only metasenv subst context t1
+ (mk_appl ~upto:(List.length args) term args) swap
+ | NCic.Appl (NCic.Meta (i,_)::_), _ when List.mem_assoc i subst ->
+ unify rdb test_eq_only metasenv subst context t2 t1 (not swap)
+
+ | C.Meta (n,_), C.Meta (m,lc') when
+ let _,cc1,_ = NCicUtils.lookup_meta n metasenv in
+ let _,cc2,_ = NCicUtils.lookup_meta m metasenv in
+ (n < m && cc1 = cc2) ||
+ let len1 = List.length cc1 in
+ let len2 = List.length cc2 in
+ len2 < len1 && cc2 = fst (HExtlib.split_nth len2 cc1) ->
+ instantiate rdb test_eq_only metasenv subst context m lc'
+ (NCicReduction.head_beta_reduce ~subst t1) (not swap)
+ | C.Meta (n,lc), C.Meta (m,lc') when
+ let _,_,tyn = NCicUtils.lookup_meta n metasenv in
+ let _,_,tym = NCicUtils.lookup_meta m metasenv in
+ let tyn = NCicSubstitution.subst_meta lc tyn in
+ let tym = NCicSubstitution.subst_meta lc tym in
+ match tyn,tym with
+ NCic.Sort NCic.Type u1, NCic.Sort NCic.Type u2 ->
+ NCicEnvironment.universe_lt u1 u2
+ | _,_ -> false ->
+ instantiate rdb test_eq_only metasenv subst context m lc'
+ (NCicReduction.head_beta_reduce ~subst t1) (not swap)
+ | C.Meta (n,lc), t ->
+ instantiate rdb test_eq_only metasenv subst context n lc
+ (NCicReduction.head_beta_reduce ~subst t) swap
+ | t, C.Meta (n,lc) ->
+ instantiate rdb test_eq_only metasenv subst context n lc
+ (NCicReduction.head_beta_reduce ~subst t) (not swap)
+
+ (* higher order unification case *)
+ | NCic.Appl (NCic.Meta (i,l) as meta :: args), _ ->
+ (* this easy_case handles "(? ?) =?= (f a)", same number of
+ * args, preferring the instantiation "f" over "\_.f a" for the
+ * metavariable in head position. Since the arguments of the meta
+ * are flexible, delift would ignore them generating a constant
+ * function even in the easy case above *)
+ let easy_case =
+ match t2 with
+ | NCic.Appl (f :: f_args)
+ when
+ List.exists (NCicMetaSubst.is_flexible context ~subst) args ->
+ let mlen = List.length args in
+ let flen = List.length f_args in
+ let min_len = min mlen flen in
+ let mhe,margs = HExtlib.split_nth (mlen - min_len) args in
+ let fhe,fargs = HExtlib.split_nth (flen - min_len) f_args in
+ (try
+ Some (List.fold_left2
+ (fun (m, s) t1 t2 ->
+ unify rdb test_eq_only m s context t1 t2 swap
+ ) (metasenv,subst)
+ ((NCicUntrusted.mk_appl meta mhe)::margs)
+ ((NCicUntrusted.mk_appl f fhe)::fargs))
+ with UnificationFailure _ | Uncertain _ | KeepReducing _ ->
+ None)
+ | _ -> None
+ in
+ (match easy_case with
+ | Some ms -> ms
+ | None ->
+ (* This case handles "(?_f ..ti..) =?= t2", abstracting every
+ * non flexible ti (delift skips local context items that are
+ * flexible) from t2 in two steps:
+ * 1) ?_f := \..xi.. .?
+ * 2) ?_f ..ti.. =?= t2 --unif_machines-->
+ ?_f[..ti..] =?= t2 --instantiate-->
+ delift [..ti..] t2 *)
+ let metasenv, lambda_Mj =
+ lambda_intros rdb metasenv subst context (List.length args)
+ (NCicTypeChecker.typeof ~metasenv ~subst context meta)
+ in
+ let metasenv, subst =
+ unify rdb test_eq_only metasenv subst context
+ (C.Meta (i,l)) lambda_Mj swap
+ in
+ let metasenv, subst =
+ unify rdb test_eq_only metasenv subst context t1 t2 swap
+ in
+ (try
+ let name, ctx, term, ty = NCicUtils.lookup_subst i subst in
+ let term = eta_reduce subst term in
+ let subst = List.filter (fun (j,_) -> j <> i) subst in
+ metasenv, ((i, (name, ctx, term, ty)) :: subst)
+ with Not_found -> assert false))
+
+ | _, NCic.Appl (NCic.Meta (_,_) :: _) ->
+ unify rdb test_eq_only metasenv subst context t2 t1 (not swap)
(* processing this case here we avoid a useless small delta step *)
| (C.Appl ((C.Const r1) as _hd1::tl1), C.Appl (C.Const r2::tl2))
when Ref.eq r1 r2 ->
let relevance = NCicEnvironment.get_relevance r1 in
- let relevance = match r1 with
- | Ref.Ref (_,Ref.Con (_,_,lno)) ->
- let _,relevance = HExtlib.split_nth lno relevance in
- HExtlib.mk_list false lno @ relevance
- | _ -> relevance
- in
let metasenv, subst, _ =
try
List.fold_left2
let b, relevance =
match relevance with b::tl -> b,tl | _ -> true, [] in
let metasenv, subst =
- try unify test_eq_only metasenv subst context t1 t2
+ try unify rdb test_eq_only metasenv subst context t1 t2
+ swap
with UnificationFailure _ | Uncertain _ when not b ->
metasenv, subst
in
metasenv, subst, relevance)
(metasenv, subst, relevance) tl1 tl2
- with Invalid_argument _ ->
- raise (uncert_exc metasenv subst context t1 t2)
+ with
+ Invalid_argument _ ->
+ raise (Uncertain (mk_msg metasenv subst context t1 t2))
+ | KeepReducing _ | KeepReducingThis _ -> assert false
in
metasenv, subst
| (C.Match (Ref.Ref (_,Ref.Ind (_,tyno,_)) as ref1,outtype1,term1,pl1),
- C.Match (ref2,outtype2,term2,pl2)) ->
- let _,_,itl,_,_ = NCicEnvironment.get_checked_indtys ref1 in
- let _,_,ty,_ = List.nth itl tyno in
- let rec remove_prods ~subst context ty =
+ C.Match (ref2,outtype2,term2,pl2)) when Ref.eq ref1 ref2 ->
+ let _,_,itl,_,_ = NCicEnvironment.get_checked_indtys ref1 in
+ let _,_,ty,_ = List.nth itl tyno in
+ let rec remove_prods ~subst context ty =
let ty = NCicReduction.whd ~subst context ty in
match ty with
| C.Sort _ -> ty
- | C.Prod (name,so,ta) ->
+ | C.Prod (name,so,ta) ->
remove_prods ~subst ((name,(C.Decl so))::context) ta
| _ -> assert false
in
| C.Sort C.Prop -> true
| _ -> false
in
- let rec remove_prods ~subst context ty =
- let ty = NCicReduction.whd ~subst context ty in
- match ty with
- | C.Sort _ -> ty
- | C.Prod (name,so,ta) ->
- remove_prods ~subst ((name,(C.Decl so))::context) ta
- | _ -> assert false
- in
- if not (Ref.eq ref1 ref2) then
- raise (uncert_exc metasenv subst context t1 t2)
- else
+ (* if not (Ref.eq ref1 ref2) then
+ raise (Uncertain (mk_msg metasenv subst context t1 t2))
+ else*)
let metasenv, subst =
- unify test_eq_only metasenv subst context outtype1 outtype2 in
+ unify rdb test_eq_only metasenv subst context outtype1 outtype2 swap in
let metasenv, subst =
- try unify test_eq_only metasenv subst context term1 term2
+ try unify rdb test_eq_only metasenv subst context term1 term2 swap
with UnificationFailure _ | Uncertain _ when is_prop ->
metasenv, subst
in
(try
List.fold_left2
- (fun (metasenv,subst) ->
- unify test_eq_only metasenv subst context)
+ (fun (metasenv,subst) t1 t2 ->
+ unify rdb test_eq_only metasenv subst context t1 t2 swap)
(metasenv, subst) pl1 pl2
- with Invalid_argument _ ->
- raise (uncert_exc metasenv subst context t1 t2))
+ with Invalid_argument _ -> assert false)
| (C.Implicit _, _) | (_, C.Implicit _) -> assert false
- | _ -> raise (uncert_exc metasenv subst context t1 t2)
- (*D*) in outside(); rc with exn -> outside (); raise exn
+ | _ when norm1 && norm2 ->
+ if (could_reduce t1 || could_reduce t2) then
+ raise (Uncertain (mk_msg metasenv subst context t1 t2))
+ else
+ raise (UnificationFailure (mk_msg metasenv subst context t1 t2))
+ | _ -> raise (KeepReducing (mk_msg metasenv subst context t1 t2))
+ (*D*) in outside None; rc with exn -> outside (Some exn); raise exn
+ in
+ let fo_unif test_eq_only metasenv subst (norm1,t1 as nt1) (norm2,t2 as nt2)=
+ try fo_unif test_eq_only metasenv subst nt1 nt2
+ with
+ UnificationFailure _ | Uncertain _ when not norm1 || not norm2 ->
+ raise (KeepReducing (mk_msg metasenv subst context t1 t2))
+ in
+ let try_hints metasenv subst (_,t1 as mt1) (_,t2 as mt2) (* exc*) =
+ if NCicUntrusted.metas_of_term subst context t1 = [] &&
+ NCicUntrusted.metas_of_term subst context t2 = []
+ then None
+ else begin
+ (*D*) inside 'H'; try let rc =
+ pp(lazy ("\nProblema:\n" ^
+ ppterm ~metasenv ~subst ~context t1 ^ " =?= " ^
+ ppterm ~metasenv ~subst ~context t2));
+ let candidates =
+ NCicUnifHint.look_for_hint rdb metasenv subst context t1 t2
+ in
+ let rec cand_iter = function
+ | [] -> None (* raise exc *)
+ | (metasenv,(c1,c2),premises)::tl ->
+ pp (lazy ("\nProvo il candidato:\n" ^
+ String.concat "\n"
+ (List.map
+ (fun (a,b) ->
+ ppterm ~metasenv ~subst ~context a ^ " =?= " ^
+ ppterm ~metasenv ~subst ~context b) premises) ^
+ "\n-------------------------------------------\n"^
+ ppterm ~metasenv ~subst ~context c1 ^ " = " ^
+ ppterm ~metasenv ~subst ~context c2));
+ try
+ (*D*) inside 'K'; try let rc =
+ let metasenv,subst =
+ fo_unif test_eq_only metasenv subst mt1 (false,c1) in
+ let metasenv,subst =
+ fo_unif test_eq_only metasenv subst (false,c2) mt2 in
+ let metasenv,subst =
+ List.fold_left
+ (fun (metasenv, subst) (x,y) ->
+ unify rdb test_eq_only metasenv subst context x y false)
+ (metasenv, subst) (List.rev premises)
+ in
+ pp(lazy("FUNZIONA!"));
+ Some (metasenv, subst)
+ (*D*) in outside None; rc with exn -> outside (Some exn); raise exn
+ with
+ KeepReducing _ | UnificationFailure _ | Uncertain _ -> cand_iter tl
+ | KeepReducingThis _ -> assert false
+ in
+ cand_iter candidates
+ (*D*) in outside None; rc with exn -> outside (Some exn); raise exn
+ end
+ in
+ let put_in_whd m1 m2 =
+ NCicReduction.reduce_machine ~delta:max_int ~subst context m1,
+ NCicReduction.reduce_machine ~delta:max_int ~subst context m2
+ in
+ let fo_unif_w_hints test_eq_only metasenv subst (_,t1 as m1) (_,t2 as m2) =
+ try fo_unif test_eq_only metasenv subst m1 m2
+ with
+ | UnificationFailure _ as exn -> raise exn
+ | KeepReducing _ | Uncertain _ as exn ->
+ let (t1,norm1 as tm1),(t2,norm2 as tm2) =
+ put_in_whd (0,[],t1,[]) (0,[],t2,[])
+ in
+ match
+ try_hints metasenv subst
+ (norm1,NCicReduction.unwind t1) (norm2,NCicReduction.unwind t2)
+ with
+ | Some x -> x
+ | None ->
+ match exn with
+ | KeepReducing msg -> raise (KeepReducingThis (msg,tm1,tm2))
+ | Uncertain _ as exn -> raise exn
+ | _ -> assert false
+ in
+ let fo_unif_heads_and_cont_or_unwind_and_hints
+ test_eq_only metasenv subst m1 m2 cont hm1 hm2
+ =
+ let ms, continuation =
+ (* calling the continuation inside the outermost try is an option
+ and makes unification stronger, but looks not frequent to me
+ that heads unify but not the arguments and that an hints can fix
+ that *)
+ try fo_unif test_eq_only metasenv subst m1 m2, cont
+ with
+ | UnificationFailure _
+ | KeepReducing _ | Uncertain _ as exn ->
+ let (t1,norm1),(t2,norm2) = hm1, hm2 in
+ match
+ try_hints metasenv subst
+ (norm1,NCicReduction.unwind t1) (norm2,NCicReduction.unwind t2)
+ with
+ | Some x -> x, fun x -> x
+ | None ->
+ match exn with
+ | KeepReducing msg -> raise (KeepReducingThis (msg,hm1,hm2))
+ | UnificationFailure _ | Uncertain _ as exn -> raise exn
+ | _ -> assert false
+ in
+ continuation ms
in
let height_of = function
| NCic.Const (Ref.Ref (_,Ref.Def h))
| NCic.Appl(NCic.Const(Ref.Ref(_,Ref.Fix (_,_,h)))::_) -> h
| _ -> 0
in
- let put_in_whd m1 m2 =
- NCicReduction.reduce_machine ~delta:max_int ~subst context m1,
- NCicReduction.reduce_machine ~delta:max_int ~subst context m2
- in
- let small_delta_step
+ let small_delta_step ~subst
((_,_,t1,_ as m1, norm1) as x1) ((_,_,t2,_ as m2, norm2) as x2)
=
assert (not (norm1 && norm2));
if norm1 then
- x1,NCicReduction.reduce_machine ~delta:(height_of t2 -1) ~subst context m2
+ x1,NCicReduction.reduce_machine ~delta:0 ~subst context m2
else if norm2 then
- NCicReduction.reduce_machine ~delta:(height_of t1 -1) ~subst context m1,x2
+ NCicReduction.reduce_machine ~delta:0 ~subst context m1,x2
else
let h1 = height_of t1 in
let h2 = height_of t2 in
function
| ((k1,e1,t1,s1),norm1 as m1),((k2,e2,t2,s2),norm2 as m2) ->
(*D*) inside 'M'; try let rc =
-(*
- pp (lazy((if are_normal then "*" else " ") ^ " " ^
- NCicPp.ppterm ~metasenv ~subst ~context (NCicReduction.unwind m1) ^
+ pp (lazy("UM: " ^
+ ppterm ~metasenv ~subst ~context
+ (NCicReduction.unwind (k1,e1,t1,s1)) ^
" === " ^
- NCicPp.ppterm ~metasenv ~subst ~context (NCicReduction.unwind m2)));
-*)
+ ppterm ~metasenv ~subst ~context
+ (NCicReduction.unwind (k2,e2,t2,s2))));
+ pp (lazy (string_of_bool norm1 ^ " ?? " ^ string_of_bool norm2));
let relevance = [] (* TO BE UNDERSTOOD
match t1 with
| C.Const r -> NCicEnvironment.get_relevance r
| _ -> [] *) in
- let unif_from_stack t1 t2 b metasenv subst =
+ let unif_from_stack (metasenv, subst) (t1, t2, b) =
try
- let t1 = NCicReduction.from_stack t1 in
- let t2 = NCicReduction.from_stack t2 in
+ let t1 = NCicReduction.from_stack ~delta:max_int t1 in
+ let t2 = NCicReduction.from_stack ~delta:max_int t2 in
unif_machines metasenv subst (put_in_whd t1 t2)
with UnificationFailure _ | Uncertain _ when not b ->
metasenv, subst
in
- let rec check_stack l1 l2 r (metasenv, subst) =
+ let rec check_stack l1 l2 r todo =
match l1,l2,r with
- | x1::tl1, x2::tl2, r::tr ->
- check_stack tl1 tl2 tr
- (unif_from_stack x1 x2 r metasenv subst)
- | x1::tl1, x2::tl2, [] ->
- check_stack tl1 tl2 []
- (unif_from_stack x1 x2 true metasenv subst)
+ | x1::tl1, x2::tl2, r::tr-> check_stack tl1 tl2 tr ((x1,x2,r)::todo)
+ | x1::tl1, x2::tl2, []-> check_stack tl1 tl2 [] ((x1,x2,true)::todo)
| l1, l2, _ ->
- fo_unif test_eq_only metasenv subst
- (NCicReduction.unwind (k1,e1,t1,List.rev l1))
- (NCicReduction.unwind (k2,e2,t2,List.rev l2))
+ NCicReduction.unwind (k1,e1,t1,List.rev l1),
+ NCicReduction.unwind (k2,e2,t2,List.rev l2),
+ todo
in
- try check_stack (List.rev s1) (List.rev s2) relevance (metasenv,subst)
- with UnificationFailure _ | Uncertain _ when not (norm1 && norm2) ->
- unif_machines metasenv subst (small_delta_step m1 m2)
- (*D*) in outside(); rc with exn -> outside (); raise exn
+ let check_stack l1 l2 r =
+ match t1, t2 with
+ | NCic.Meta _, _ | _, NCic.Meta _ ->
+ (NCicReduction.unwind (k1,e1,t1,s1)),
+ (NCicReduction.unwind (k2,e2,t2,s2)),[]
+ | _ -> check_stack l1 l2 r []
+ in
+ let hh1,hh2,todo = check_stack (List.rev s1) (List.rev s2) relevance in
+ try
+ fo_unif_heads_and_cont_or_unwind_and_hints
+ test_eq_only metasenv subst (norm1,hh1) (norm2,hh2)
+ (fun ms -> List.fold_left unif_from_stack ms todo)
+ m1 m2
+ with
+ | KeepReducing _ -> assert false
+ | KeepReducingThis _ ->
+ assert (not (norm1 && norm2));
+ unif_machines metasenv subst (small_delta_step ~subst m1 m2)
+ | UnificationFailure _ | Uncertain _ when (not (norm1 && norm2))
+ -> unif_machines metasenv subst (small_delta_step ~subst m1 m2)
+ | UnificationFailure msg
+ when could_reduce (NCicReduction.unwind (fst m1))
+ || could_reduce (NCicReduction.unwind (fst m2))
+ -> raise (Uncertain msg)
+ (*D*) in outside None; rc with exn -> outside (Some exn); raise exn
in
- try fo_unif test_eq_only metasenv subst t1 t2
- with UnificationFailure msg | Uncertain msg as exn ->
- try
- unif_machines metasenv subst
- (put_in_whd (0,[],t1,[]) (0,[],t2,[]))
- with
- | UnificationFailure _ -> raise (UnificationFailure msg)
- | Uncertain _ -> raise exn
- (*D*) in outside(); rc with exn -> outside (); raise exn
-;;
-
-let unify =
- indent := "";
- unify false;;
-
-
-
-(*
-
-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 ()
+ try fo_unif_w_hints test_eq_only metasenv subst (false,t1) (false,t2)
+ with
+ | KeepReducingThis (msg,tm1,tm2) ->
+ (try
+ unif_machines metasenv subst (tm1,tm2)
+ with
+ | UnificationFailure _ -> raise (UnificationFailure msg)
+ | Uncertain _ -> raise (Uncertain msg)
+ | KeepReducing _ -> assert false)
+ | KeepReducing _ -> assert false
-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
+ (*D*) in outside None; rc with KeepReducing _ -> assert false | exn -> outside (Some exn); raise exn
-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 =
+and delift_type_wrt_terms rdb metasenv subst context t args =
+ let lc = List.rev args @ mk_irl (List.length context) (List.length args+1) in
+ let (metasenv, subst), t =
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
+ NCicMetaSubst.delift
+ ~unify:(fun m s c t1 t2 ->
+ let ind = !indent in
+ let res =
+ try Some (unify rdb false m s c t1 t2 false)
+ with UnificationFailure _ | Uncertain _ -> None
in
- num+1,subst,metasenv,t,ugraph1
- ) args (1,subst,metasenv,t,ugraph)
+ indent := ind; res)
+ metasenv subst context 0 (0,NCic.Ctx lc) t
+ with
+ NCicMetaSubst.MetaSubstFailure _
+ | NCicMetaSubst.Uncertain _ -> (metasenv, subst), t
in
- subst,metasenv,hd,ugraph
-
-and warn_if_not_unique xxx to1 to2 carr car1 car2 =
- match xxx with
- | [] -> ()
- | (m2,_,c2,c2')::_ ->
- let m1,c1,c1' = carr,to1,to2 in
- let unopt =
- function Some (_,t) -> CicPp.ppterm t
- | None -> "id"
- in
- HLog.warn
- ("There are two minimal joins of "^ CoercDb.string_of_carr car1^" and "^
- CoercDb.string_of_carr car2^": " ^
- CoercDb.string_of_carr m1^" via "^unopt c1^" + "^
- unopt c1'^" and "^ CoercDb.string_of_carr m2^" via "^
- unopt c2^" + "^unopt c2')
-
-(* 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.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
- (* {{{ pullback *)
- | (((Cic.Const (uri1, ens1)) as cc1) :: tl1),
- (((Cic.Const (uri2, ens2)) as cc2) :: tl2) when
- CoercDb.is_a_coercion cc1 <> None &&
- CoercDb.is_a_coercion cc2 <> None &&
- 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 inner_coerced t =
- let t = CicMetaSubst.apply_subst subst t in
- let rec aux c x t =
- match t with
- | Cic.Appl l ->
- (match CoercGraph.coerced_arg l with
- | None -> c, x
- | Some (t,_) -> aux (List.hd l) t t)
- | _ -> c, x
- in
- aux (Cic.Implicit None) (Cic.Implicit None) t
- in
- let c1,last_tl1 = inner_coerced (Cic.Appl l1) in
- let c2,last_tl2 = inner_coerced (Cic.Appl l2) in
- let car1, car2 =
- match
- CoercDb.is_a_coercion c1, CoercDb.is_a_coercion c2
- with
- | Some (s1,_,_,_,_), Some (s2,_,_,_,_) -> s1, s2
- | _ -> assert false
- in
- let head1_c, head2_c =
- match
- CoercDb.is_a_coercion cc1, CoercDb.is_a_coercion cc2
- with
- | Some (_,t1,_,_,_), Some (_,t2,_,_,_) -> t1, t2
- | _ -> assert false
- in
- let unfold uri ens args =
- let o, _ =
- CicEnvironment.get_obj CicUniv.oblivion_ugraph uri
- in
- assert (ens = []);
- match o with
- | Cic.Constant (_,Some bo,_,_,_) ->
- CicReduction.head_beta_reduce ~delta:false
- (Cic.Appl (bo::args))
- | _ -> assert false
- in
- let conclude subst metasenv ugraph last_tl1' last_tl2' =
- let subst',metasenv,ugraph =
-(*DEBUGGING ONLY:
-prerr_endline
- ("OK " ^ CicMetaSubst.ppterm_in_context ~metasenv subst last_tl1' context ^
- " <==> " ^ CicMetaSubst.ppterm_in_context ~metasenv subst last_tl2' context);
-*)
- fo_unif_subst test_equality_only subst context
- metasenv last_tl1' last_tl2' ugraph
- in
- if subst = subst' then raise exn
- else
-(*DEBUGGING ONLY:
-let subst,metasenv,ugrph as res =
-*)
- fo_unif_subst test_equality_only subst' context
- metasenv (C.Appl l1) (C.Appl l2) ugraph
-(*DEBUGGING ONLY:
-in
-(prerr_endline
- (">>>> "^CicMetaSubst.ppterm_in_context ~metasenv subst (C.Appl l1) context ^
- " <==> "^CicMetaSubst.ppterm_in_context ~metasenv subst (C.Appl l2) context);
-res)
-*)
- 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 (Cic.Appl l1) (Cic.Appl l2) ugraph
- | _ when CoercDb.eq_carr head1_c head2_c ->
- (* composite VS composition + metas avoiding
- * coercions not only in coerced position *)
- if c1 <> cc1 && c2 <> cc2 then
- conclude subst metasenv ugraph
- last_tl1 last_tl2
- else
- let l1, l2 =
- if c1 = cc1 then
- unfold uri1 ens1 tl1, Cic.Appl (cc2::tl2)
- else
- Cic.Appl (cc1::tl1), unfold uri2 ens2 tl2
- in
- fo_unif_subst test_equality_only subst context
- metasenv l1 l2 ugraph
- | _ -> raise exn
- else
- let grow1 =
- match last_tl1 with Cic.Meta _ -> true | _ -> false in
- let grow2 =
- match last_tl2 with Cic.Meta _ -> true | _ -> false in
- if not (grow1 || grow2) then
- (* no flexible terminals -> no pullback, but
- * we still unify them, in some cases it helps *)
- conclude subst metasenv ugraph last_tl1 last_tl2
- else
- let meets =
- CoercGraph.meets
- metasenv subst context (grow1,car1) (grow2,car2)
- in
- (match meets with
- | [] -> raise exn
- | (carr,metasenv,to1,to2)::xxx ->
- warn_if_not_unique xxx to1 to2 carr car1 car2;
- let last_tl1',(subst,metasenv,ugraph) =
- match grow1,to1 with
- | true,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 grow2,to2 with
- | true,Some (last,coerced) ->
- last,
- fo_unif_subst test_equality_only subst context
- metasenv coerced last_tl2 ugraph
- | _ -> last_tl2,(subst,metasenv,ugraph)
- in
- conclude subst metasenv ugraph last_tl1' last_tl2')
- (* }}} pullback *)
- (* {{{ 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 ))))
- (* }}} elim H *)
- | _ -> 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")))
-*)
- | (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.Prod _, _) ->
- (match CicReduction.whd ~subst context t2 with
- | C.Prod _ as t2 ->
- fo_unif_subst test_equality_only subst context metasenv t1 t2 ugraph
- | _ -> raise (UnificationFailure (lazy (CicMetaSubst.ppterm ~metasenv subst t2^"Not a product"))))
- | (_, C.Prod _) ->
- (match CicReduction.whd ~subst context t1 with
- | C.Prod _ as t1 ->
- fo_unif_subst test_equality_only subst context metasenv t1 t2 ugraph
- | _ -> raise (UnificationFailure (lazy (CicMetaSubst.ppterm ~metasenv subst t1^"Not a product"))))
- | (_,_) ->
- (* 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))))
+ metasenv, subst, t
+;;
-(* 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 unify rdb ?(test_eq_only=false) ?(swap=false) metasenv subst context t1 t2=
+ indent := "";
+ unify rdb test_eq_only metasenv subst context t1 t2 swap;;
-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))
+let fix_sorts m s =
+ fix m s true false (UnificationFailure (lazy "no sup"))
;;
-*)