(* $Id$ *)
-
-(*open Printf
-
-(* PROFILING *)
-(*
-let deref_counter = ref 0
-let apply_subst_context_counter = ref 0
-let apply_subst_metasenv_counter = ref 0
-let lift_counter = ref 0
-let subst_counter = ref 0
-let whd_counter = ref 0
-let are_convertible_counter = ref 0
-let metasenv_length = ref 0
-let context_length = ref 0
-let reset_counters () =
- apply_subst_counter := 0;
- apply_subst_context_counter := 0;
- apply_subst_metasenv_counter := 0;
- lift_counter := 0;
- subst_counter := 0;
- whd_counter := 0;
- are_convertible_counter := 0;
- metasenv_length := 0;
- context_length := 0
-let print_counters () =
- debug_print (lazy (Printf.sprintf
-"apply_subst: %d
-apply_subst_context: %d
-apply_subst_metasenv: %d
-lift: %d
-subst: %d
-whd: %d
-are_convertible: %d
-metasenv length: %d (avg = %.2f)
-context length: %d (avg = %.2f)
-"
- !apply_subst_counter !apply_subst_context_counter
- !apply_subst_metasenv_counter !lift_counter !subst_counter !whd_counter
- !are_convertible_counter !metasenv_length
- ((float !metasenv_length) /. (float !apply_subst_metasenv_counter))
- !context_length
- ((float !context_length) /. (float !apply_subst_context_counter))
- ))*)
-
-
-
exception MetaSubstFailure of string Lazy.t
exception Uncertain of string Lazy.t
-exception AssertFailure of string Lazy.t
-exception DeliftingARelWouldCaptureAFreeVariable;;
-
-let debug_print = fun _ -> ()
-
-type substitution = (int * (Cic.context * Cic.term)) list
-
-(*
-let rec deref subst =
- let third _,_,a = a in
- function
- Cic.Meta(n,l) as t ->
- (try
- deref subst
- (CicSubstitution.subst_meta
- l (third (CicUtil.lookup_subst n subst)))
- with
- CicUtil.Subst_not_found _ -> t)
- | t -> t
-;;
-*)
-
-let lookup_subst = CicUtil.lookup_subst
-;;
-
-(* clean_up_meta take a metasenv and a term and make every local context
-of each occurrence of a metavariable consistent with its canonical context,
-with respect to the hidden hipothesis *)
(*
-let clean_up_meta subst metasenv t =
- let module C = Cic in
- let rec aux t =
- match t with
- C.Rel _
- | C.Sort _ -> t
- | C.Implicit _ -> assert false
- | C.Meta (n,l) as t ->
- let cc =
- (try
- let (cc,_) = lookup_subst n subst in cc
- with CicUtil.Subst_not_found _ ->
- try
- let (_,cc,_) = CicUtil.lookup_meta n metasenv in cc
- with CicUtil.Meta_not_found _ -> assert false) in
- let l' =
- (try
- List.map2
- (fun t1 t2 ->
- match t1,t2 with
- None , _ -> None
- | _ , t -> t) cc l
- with
- Invalid_argument _ -> assert false) in
- C.Meta (n, l')
- | C.Cast (te,ty) -> C.Cast (aux te, aux ty)
- | C.Prod (name,so,dest) -> C.Prod (name, aux so, aux dest)
- | C.Lambda (name,so,dest) -> C.Lambda (name, aux so, aux dest)
- | C.LetIn (name,so,dest) -> C.LetIn (name, aux so, aux dest)
- | C.Appl l -> C.Appl (List.map aux l)
- | C.Var (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (uri,t) -> (uri, aux t)) exp_named_subst
- in
- C.Var (uri, exp_named_subst')
- | C.Const (uri, exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (uri,t) -> (uri, aux t)) exp_named_subst
- in
- C.Const (uri, exp_named_subst')
- | C.MutInd (uri,tyno,exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (uri,t) -> (uri, aux t)) exp_named_subst
- in
- C.MutInd (uri, tyno, exp_named_subst')
- | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (uri,t) -> (uri, aux t)) exp_named_subst
- in
- C.MutConstruct (uri, tyno, consno, exp_named_subst')
- | C.MutCase (uri,tyno,out,te,pl) ->
- C.MutCase (uri, tyno, aux out, aux te, List.map aux pl)
- | C.Fix (i,fl) ->
- let fl' =
- List.map
- (fun (name,j,ty,bo) -> (name, j, aux ty, aux bo)) fl
- in
- C.Fix (i, fl')
- | C.CoFix (i,fl) ->
- let fl' =
- List.map
- (fun (name,ty,bo) -> (name, aux ty, aux bo)) fl
- in
- C.CoFix (i, fl')
- in
- aux t *)
-
(*** Functions to apply a substitution ***)
let apply_subst_gen ~appl_fun subst term =
(fun (i, _, _) -> not (List.mem_assoc i subst))
metasenv)
-(***** Pretty printing functions ******)
-
-let ppterm ~metasenv subst term =
- CicPp.ppterm ~metasenv (apply_subst subst term)
-
-let ppterm_in_name_context ~metasenv subst term name_context =
- CicPp.pp ~metasenv (apply_subst subst term) name_context
-
-let ppterm_in_context ~metasenv subst term context =
- let name_context =
- List.map (function None -> None | Some (n,_) -> Some n) context
- in
- ppterm_in_name_context ~metasenv subst term name_context
-
-let ppterm_in_context_ref = ref ppterm_in_context
-let set_ppterm_in_context f =
- ppterm_in_context_ref := f
-let use_low_level_ppterm_in_context = ref false
-
-let ppterm_in_context ~metasenv subst term context =
- if !use_low_level_ppterm_in_context then
- ppterm_in_context ~metasenv subst term context
- else
- !ppterm_in_context_ref ~metasenv subst term context
-
-let ppcontext' ~metasenv ?(sep = "\n") subst context =
- let separate s = if s = "" then "" else s ^ sep in
- List.fold_right
- (fun context_entry (i,name_context) ->
- match context_entry with
- Some (n,Cic.Decl t) ->
- sprintf "%s%s : %s" (separate i) (CicPp.ppname n)
- (ppterm_in_name_context ~metasenv subst t name_context),
- (Some n)::name_context
- | Some (n,Cic.Def (bo,ty)) ->
- sprintf "%s%s : %s := %s" (separate i) (CicPp.ppname n)
- (ppterm_in_name_context ~metasenv subst ty name_context)
- (ppterm_in_name_context ~metasenv subst bo name_context), (Some n)::name_context
- | None ->
- sprintf "%s_ :? _" (separate i), None::name_context
- ) context ("",[])
-
-let ppsubst_unfolded ~metasenv subst =
- String.concat "\n"
- (List.map
- (fun (idx, (c, t,ty)) ->
- let context,name_context = ppcontext' ~metasenv ~sep:"; " subst c in
- sprintf "%s |- ?%d : %s := %s" context idx
-(ppterm_in_name_context ~metasenv [] ty name_context)
- (ppterm_in_name_context ~metasenv subst t name_context))
- subst)
-(*
- Printf.sprintf "?%d := %s" idx (CicPp.ppterm term))
- subst) *)
-;;
-
-let ppsubst ~metasenv subst =
- String.concat "\n"
- (List.map
- (fun (idx, (c, t, ty)) ->
- let context,name_context = ppcontext' ~metasenv ~sep:"; " [] c in
- sprintf "%s |- ?%d : %s := %s" context idx (ppterm_in_name_context ~metasenv [] ty name_context)
- (ppterm_in_name_context ~metasenv [] t name_context))
- subst)
-;;
-
-let ppcontext ~metasenv ?sep subst context =
- fst (ppcontext' ~metasenv ?sep subst context)
-
-let ppmetasenv ?(sep = "\n") subst metasenv =
- String.concat sep
- (List.map
- (fun (i, c, t) ->
- let context,name_context = ppcontext' ~metasenv ~sep:"; " subst c in
- sprintf "%s |- ?%d: %s" context i
- (ppterm_in_name_context ~metasenv subst t name_context))
- (List.filter
- (fun (i, _, _) -> not (List.mem_assoc i subst))
- metasenv))
-
let tempi_type_of_aux_subst = ref 0.0;;
let tempi_subst = ref 0.0;;
let tempi_type_of_aux = ref 0.0;;
+*)
-(**** DELIFT ****)
-(* the delift function takes in input a metavariable index, an ordered list of
- * optional terms [t1,...,tn] and a term t, and substitutes every tk = Some
- * (rel(nk)) with rel(k). Typically, the list of optional terms is the explicit
- * substitution that is applied to a metavariable occurrence and the result of
- * the delift function is a term the implicit variable can be substituted with
- * to make the term [t] unifiable with the metavariable occurrence. In general,
- * the problem is undecidable if we consider equivalence in place of alpha
- * convertibility. Our implementation, though, is even weaker than alpha
- * convertibility, since it replace the term [tk] if and only if [tk] is a Rel
- * (missing all the other cases). Does this matter in practice?
- * The metavariable index is the index of the metavariable that must not occur
- * in the term (for occur check).
- *)
exception NotInTheList;;
-let position n =
- let rec aux k =
- function
- [] -> raise NotInTheList
- | (Some (Cic.Rel m))::_ when m=n -> k
- | _::tl -> aux (k+1) tl in
- aux 1
+let position n (shift, lc) =
+ match lc with
+ | NCic.Irl len when n <= shift || n > shift + len -> raise NotInTheList
+ | NCic.Itl len -> n - shift
+ | NCic.Ctx tl ->
+ let rec aux k = function
+ | [] -> raise NotInTheList
+ | (Cic.Rel m)::_ when m + shift = n -> k
+ | _::tl -> aux (k+1) tl
+ in
+ aux 1 tl
;;
-
+(*
exception Occur;;
let rec force_does_not_occur subst to_be_restricted t =
in
restrict subst (more_to_be_restricted @ more_to_be_restricted') metasenv
;;
+*)
-(*CSC: maybe we should rename delift in abstract, as I did in my dissertation *)(*Andrea: maybe not*)
-
-let delift n subst context metasenv l t =
-(* INVARIANT: we suppose that t is not another occurrence of Meta(n,_),
- otherwise the occur check does not make sense *)
+let newmeta =
+ let maxmeta = ref 0 in
+ fun () -> incr maxmeta; !maxmeta
+;;
-(*
- debug_print (lazy ("sto deliftando il termine " ^ (CicPp.ppterm t) ^ " rispetto
- al contesto locale " ^ (CicPp.ppterm (Cic.Meta(0,l)))));
+let restrict metasenv subst i to_be_restricted =
+ let force_does_not_occur_in_context to_be_restricted = function
+ | None -> [], None
+ | Some (name, Cic.Decl t) ->
+ let (more_to_be_restricted, t') =
+ force_does_not_occur subst to_be_restricted t
+ in
+ more_to_be_restricted, Some (name, Cic.Decl t')
+ | Some (name, Cic.Def (bo, ty)) ->
+ let (more_to_be_restricted, bo') =
+ force_does_not_occur subst to_be_restricted bo
+ in
+ let more_to_be_restricted, ty' =
+ let more_to_be_restricted', ty' =
+ force_does_not_occur subst to_be_restricted ty
+ in
+ more_to_be_restricted @ more_to_be_restricted',
+ ty'
+ in
+ more_to_be_restricted, Some (name, Cic.Def (bo', ty'))
+ in
+ let rec erase i to_be_restricted n = function
+ | [] -> [], to_be_restricted, []
+ | hd::tl ->
+ let more_to_be_restricted,restricted,tl' =
+ erase (i+1) to_be_restricted n tl
+ in
+ let restrict_me = List.mem i restricted in
+ if restrict_me then
+ more_to_be_restricted, restricted, None:: tl'
+ else
+ (try
+ let more_to_be_restricted', hd' =
+ let delifted_restricted =
+ let rec aux =
+ function
+ [] -> []
+ | j::tl when j > i -> (j - i)::aux tl
+ | _::tl -> aux tl
+ in
+ aux restricted
+ in
+ force_does_not_occur_in_context delifted_restricted hd
+ in
+ more_to_be_restricted @ more_to_be_restricted',
+ restricted, hd' :: tl'
+ with Occur ->
+ more_to_be_restricted, (i :: restricted), None :: tl')
+ in
+ let (more_to_be_restricted, metasenv) = (* restrict metasenv *)
+ List.fold_right
+ (fun (n, context, t) (more, metasenv) ->
+ let to_be_restricted =
+ List.map snd (List.filter (fun (m, _) -> m = n) to_be_restricted)
+ in
+ let (more_to_be_restricted, restricted, context') =
+ (* just an optimization *)
+ if to_be_restricted = [] then
+ [],[],context
+ else
+ erase 1 to_be_restricted n context
+ in
+ try
+ let more_to_be_restricted', t' =
+ force_does_not_occur subst restricted t
+ in
+ let metasenv' = (n, context', t') :: metasenv in
+ (more @ more_to_be_restricted @ more_to_be_restricted',
+ metasenv')
+ with Occur ->
+ raise (MetaSubstFailure (lazy (sprintf
+ "Cannot restrict the context of the metavariable ?%d over the hypotheses %s since metavariable's type depends on at least one of them"
+ n (names_of_context_indexes context to_be_restricted)))))
+ metasenv ([], [])
+ in
+ let (more_to_be_restricted', subst) = (* restrict subst *)
+ List.fold_right
+ (* TODO: cambiare dopo l'aggiunta del ty *)
+ (fun (n, (context, term,ty)) (more, subst') ->
+ let to_be_restricted =
+ List.map snd (List.filter (fun (m, _) -> m = n) to_be_restricted)
+ in
+ (try
+ let (more_to_be_restricted, restricted, context') =
+ (* just an optimization *)
+ if to_be_restricted = [] then
+ [], [], context
+ else
+ erase 1 to_be_restricted n context
+ in
+ let more_to_be_restricted', term' =
+ force_does_not_occur subst restricted term
+ in
+ let more_to_be_restricted'', ty' =
+ force_does_not_occur subst restricted ty in
+ let subst' = (n, (context', term',ty')) :: subst' in
+ let more =
+ more @ more_to_be_restricted
+ @ more_to_be_restricted'@more_to_be_restricted'' in
+ (more, subst')
+ with Occur ->
+ let error_msg = lazy (sprintf
+ "Cannot restrict the context of the metavariable ?%d over the hypotheses %s since ?%d is already instantiated with %s and at least one of the hypotheses occurs in the substituted term"
+ n (names_of_context_indexes context to_be_restricted) n
+ (ppterm ~metasenv subst term))
+ in
+ (* DEBUG
+ debug_print (lazy error_msg);
+ debug_print (lazy ("metasenv = \n" ^ (ppmetasenv metasenv subst)));
+ debug_print (lazy ("subst = \n" ^ (ppsubst subst)));
+ debug_print (lazy ("context = \n" ^ (ppcontext subst context))); *)
+ raise (MetaSubstFailure error_msg)))
+ subst ([], [])
+ in
+ restrict subst (more_to_be_restricted @ more_to_be_restricted') metasenv
+;;
*)
+;;
- let module S = CicSubstitution in
- let l =
- let (_, canonical_context, _) =
- try
- CicUtil.lookup_meta n metasenv
- with CicUtil.Meta_not_found _ ->
- raise (MetaSubstFailure (lazy
- ("delifting error: the metavariable " ^ string_of_int n ^ " is not " ^
- "declared in the metasenv")))
- in
- List.map2 (fun ct lt ->
- match (ct, lt) with
- | None, _ -> None
- | Some _, _ -> lt)
- canonical_context l
+(* INVARIANT: we suppose that t is not another occurrence of Meta(n,_),
+ otherwise the occur check does not make sense in case of unification
+ of ?n with ?n *)
+let delift metasenv subst context n l t =
+ let to_be_restricted = ref [] in
+ let rec aux k = function
+ | NCic.Rel n as t when n <= k -> t
+ | NCic.Rel n ->
+ (try
+ match List.nth context (n-k-1) with
+ | _,NCic.Def (bo,_) ->
+ (try C.Rel ((position (n-k) l) + k)
+ with NotInTheList ->
+ (* CSC: This bit of reduction hurts performances since it is
+ * possible to have an exponential explosion of the size of the
+ * proof. required for nat/nth_prime.ma *)
+ aux k (NCicSubstitution.lift n bo))
+ | _,NCic.Decl _ -> NCic.Rel ((position (n-k) l) + k)
+ with Failure _ -> assert false) (*Unbound variable found in delift*)
+ | NCic.Meta (i,l1) as orig ->
+ (try
+ let _,_,t,_ = NCicUtil.lookup_subst i subst in
+ aux k (NCicSubstitution.subst_meta l1 t)
+ with NCicUtil.Subst_not_found _ ->
+ (* see the top level invariant *)
+ if (i = n) then
+ raise (MetaSubstFailure (lazy (Printf.sprintf (
+ "Cannot unify the metavariable ?%d with a term that has "^^
+ "as subterm %s in which the same metavariable "^^
+ "occurs (occur check)") i
+ (NCicPp.ppterm ~context ~metasenv ~subst t))))
+ else
+ let shift1,lc1 = l1 in
+ let shift,lc = l in
+ match lc, lc1 with
+ | NCic.Irl len, NCic.Irl len1
+ when shift1 < shift || len1 + shift1 > len + shift ->
+ (* new meta with shortened l1
+ (1 -> shift - shift1 /\ shift + len + 1 -> shift1+len1)
+ subst += (i,new meta)
+ restrict checks (deleted entry cannot occur in the type...)
+ return that meta *)
+ assert false
+ | NCic.Irl len, NCic.Irl len1 when shift = 0 -> orig
+ | NCic.Irl len, NCic.Irl len1 ->
+ NCic.Meta (i, (shift1 - shift, lc1))
+ | _ ->
+ let lc1 = NCicUtils.expand_local_context lc1 in
+ let rec deliftl j = function
+ | [] -> []
+ | t::tl ->
+ let tl = deliftl (j+1) tl in
+ try (aux (k+shift1) t)::tl
+ with
+ | NotInTheList | MetaSubstFailure _ ->
+ to_be_restricted := (i,j)::!to_be_restricted;
+ tl
+ in
+ let l1 = deliftl 1 l1 in
+ C.Meta(i,l1)) (* or another ?k and possibly compress l1 *)
+ | t -> NCicUtils.map (fun _ k -> k+1) k aux t
in
+ let t = aux 0 t in
+ let metasenv, subst = restrict subst !to_be_restricted metasenv in
+ metasenv, subst, t
+;;
+
+
let to_be_restricted = ref [] in
let rec deliftaux k =
let module C = Cic in
i (ppterm ~metasenv subst t))))
else
begin
- (* I do not consider the term associated to ?i in subst since *)
- (* in this way I can restrict if something goes wrong. *)
let rec deliftl j =
function
[] -> []
delift_rels_from subst metasenv 1 n t
-(**** END OF DELIFT ****)
-
-
-(** {2 Format-like pretty printers} *)
-
-let fpp_gen ppf s =
- Format.pp_print_string ppf s;
- Format.pp_print_newline ppf ();
- Format.pp_print_flush ppf ()
-
-let fppsubst ppf subst = fpp_gen ppf (ppsubst ~metasenv:[] subst)
-let fppterm ppf term = fpp_gen ppf (CicPp.ppterm term)
-let fppmetasenv ppf metasenv = fpp_gen ppf (ppmetasenv [] metasenv)
-*)
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