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(**
- Get types of existentials ;
- Flatten dependency tree (prefix order) ;
- Replace existentials by De Bruijn indices in term, applied to the right arguments ;
- Apply term prefixed by quantification on "existentials".
*)
open Term
open Names
open Evd
open List
open Pp
open Util
let reverse_array arr =
Array.of_list (List.rev (Array.to_list arr))
let trace s =
if !Options.debug then (msgnl s; msgerr s)
else ()
(** Utilities to find indices in lists *)
let list_index x l =
let rec aux i = function
k :: tl -> if k = x then i else aux (succ i) tl
| [] -> raise Not_found
in aux 0 l
let list_assoc_index x l =
let rec aux i = function
(k, _, v) :: tl -> if k = x then i else aux (succ i) tl
| [] -> raise Not_found
in aux 0 l
(** Substitute evar references in t using De Bruijn indices,
where n binders were passed through. *)
let subst_evar_constr evs n t =
let seen = ref Intset.empty in
let evar_info id =
let rec aux i = function
(k, x) :: tl ->
if k = id then x else aux (succ i) tl
| [] -> raise Not_found
in aux 0 evs
in
let rec substrec depth c = match kind_of_term c with
| Evar (k, args) ->
let (id, idstr), hyps, _, _ =
try evar_info k
with Not_found ->
anomaly ("eterm: existential variable " ^ string_of_int k ^ " not found")
in
seen := Intset.add id !seen;
(try trace (str "Evar " ++ int k ++ str " found, applied to " ++ int (Array.length args) ++ str "arguments," ++
int (List.length hyps) ++ str " hypotheses"); with _ -> () );
(* Evar arguments are created in inverse order,
and we must not apply to defined ones (i.e. LetIn's)
*)
let args =
let rec aux hyps args acc =
match hyps, args with
((_, None, _) :: tlh), (c :: tla) ->
aux tlh tla ((map_constr_with_binders succ substrec depth c) :: acc)
| ((_, Some _, _) :: tlh), (_ :: tla) ->
aux tlh tla acc
| [], [] -> acc
| _, _ -> acc (*failwith "subst_evars: invalid argument"*)
in aux hyps (Array.to_list args) []
in
mkApp (mkVar idstr, Array.of_list args)
| _ -> map_constr_with_binders succ substrec depth c
in
let t' = substrec 0 t in
t', !seen
(** Substitute variable references in t using De Bruijn indices,
where n binders were passed through. *)
let subst_vars acc n t =
let var_index id =
let idx = list_index id acc in
idx + 1
in
let rec substrec depth c = match kind_of_term c with
| Var v -> (try mkRel (depth + (var_index v)) with Not_found -> c)
| _ -> map_constr_with_binders succ substrec depth c
in
substrec 0 t
(** Rewrite type of an evar ([ H1 : t1, ... Hn : tn |- concl ])
to a product : forall H1 : t1, ..., forall Hn : tn, concl.
Changes evars and hypothesis references to variable references.
*)
let etype_of_evar evs ev hyps =
let rec aux acc n = function
(id, copt, t) :: tl ->
let t', s = subst_evar_constr evs n t in
let t'' = subst_vars acc 0 t' in
let copt', s =
match copt with
Some c ->
let c', s' = subst_evar_constr evs n c in
Some c', Intset.union s s'
| None -> None, s
in
let copt' = option_map (subst_vars acc 0) copt' in
let rest, s' = aux (id :: acc) (succ n) tl in
mkNamedProd_or_LetIn (id, copt', t'') rest, Intset.union s' s
| [] ->
let t', s = subst_evar_constr evs n ev.evar_concl in
subst_vars acc 0 t', s
in aux [] 0 (rev hyps)
open Tacticals
let rec take n l =
if n = 0 then [] else List.hd l :: take (pred n) (List.tl l)
let trunc_named_context n ctx =
let len = List.length ctx in
take (len - n) ctx
let eterm_obligations name nclen evm t tycon =
(* 'Serialize' the evars, we assume that the types of the existentials
refer to previous existentials in the list only *)
let evl = List.rev (to_list evm) in
trace (str "Eterm, transformed to list");
let evn =
let i = ref (-1) in
List.rev_map (fun (id, ev) -> incr i;
(id, (!i, id_of_string (string_of_id name ^ "_obligation_" ^ string_of_int (succ !i))), ev)) evl
in
let evts =
(* Remove existential variables in types and build the corresponding products *)
fold_right
(fun (id, (n, nstr), ev) l ->
trace (str "Eterm: " ++ str "treating evar: " ++ int id);
let hyps = Environ.named_context_of_val ev.evar_hyps in
let hyps = trunc_named_context nclen hyps in
trace (str "Named context is: " ++ Printer.pr_named_context (Global.env ()) hyps);
let evtyp, deps = etype_of_evar l ev hyps in
trace (str "Evar " ++ str (string_of_int n) ++ str "'s type is: " ++ Termops.print_constr_env (Global.env ()) evtyp);
let y' = (id, ((n, nstr), hyps, evtyp, deps)) in
y' :: l)
evn []
in
let t', _ = (* Substitute evar refs in the term by variables *)
subst_evar_constr evts 0 t
in
let evars =
List.map (fun (_, ((_, name), _, typ, deps)) -> name, typ, deps) evts
in
(try
trace (str "Term given to eterm" ++ spc () ++
Termops.print_constr_env (Global.env ()) t);
trace (str "Term constructed in eterm" ++ spc () ++
Termops.print_constr_env (Global.env ()) t');
ignore(iter
(fun (name, typ, deps) ->
trace (str "Evar :" ++ spc () ++ str (string_of_id name) ++
Termops.print_constr_env (Global.env ()) typ))
evars);
with _ -> ());
Array.of_list (List.rev evars), t'
let mkMetas n =
let rec aux i acc =
if i > 0 then aux (pred i) (Evarutil.mk_new_meta () :: acc)
else acc
in aux n []
(* let eterm evm t (tycon : types option) = *)
(* let t, tycon, evs = eterm_term evm t tycon in *)
(* match tycon with *)
(* Some typ -> Tactics.apply_term (mkCast (t, DEFAULTcast, typ)) [] *)
(* | None -> Tactics.apply_term t (mkMetas (List.length evs)) *)
(* open Tacmach *)
let etermtac (evm, t) = assert(false) (*eterm evm t None *)
|
