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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_evars evs n t =
let evar_info id =
let rec aux i = function
(k, h, v) :: tl ->
trace (str "Searching for " ++ int id ++ str " found: " ++ int k);
if k = id then (i, h, v) else aux (succ i) tl
| [] -> raise Not_found
in
let (idx, hyps, v) = aux 0 evs in
n + idx + 1, hyps
in
let rec substrec depth c = match kind_of_term c with
| Evar (k, args) ->
(let index, hyps =
try evar_info k
with Not_found ->
anomaly ("eterm: existential variable " ^ string_of_int k ^ " not found")
in
(try trace (str "Evar " ++ int k ++ str " found, applied to " ++ int (Array.length args) ++ str "arguments," ++
int (List.length hyps) ++ str " hypotheses"); with _ -> () );
let ex = mkRel (index + depth) in
(* 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
| _, _ -> failwith "subst_evars: invalid argument"
in aux hyps (Array.to_list args) []
in
mkApp (ex, Array.of_list args))
| _ -> map_constr_with_binders succ substrec depth c
in
substrec 0 t
(** 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 De Bruijn indices.
*)
let etype_of_evar evs ev hyps =
let rec aux acc n = function
(id, copt, t) :: tl ->
let t' = subst_evars evs n t in
let t'' = subst_vars acc 0 t' in
mkNamedProd_or_LetIn (id, copt, t'') (aux (id :: acc) (succ n) tl)
| [] ->
let t' = subst_evars evs n ev.evar_concl in
subst_vars acc 0 t'
in aux [] 0 (rev hyps)
open Tacticals
let eterm_term 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 evts =
(* Remove existential variables in types and build the corresponding products *)
fold_right
(fun (id, ev) l ->
trace (str "Eterm: " ++ str "treating evar: " ++ int id);
let hyps = Environ.named_context_of_val ev.evar_hyps in
let y' = (id, hyps, etype_of_evar l ev hyps) in
y' :: l)
evl []
in
let t' = (* Substitute evar refs in the term by De Bruijn indices *)
subst_evars evts 0 t
in
let evar_names =
List.map (fun (id, _, c) -> (id_of_string ("Evar" ^ string_of_int id)), c) evts
in
let evar_bl =
List.map (fun (id, c) -> Name id, None, c) evar_names
in
let anon_evar_bl = List.map (fun (_, x, y) -> (Anonymous, x, y)) evar_bl in
(* Generalize over the existential variables *)
let t'' = Termops.it_mkLambda_or_LetIn t' evar_bl
and tycon = option_map
(fun typ -> Termops.it_mkProd_wo_LetIn typ anon_evar_bl) tycon
in
let _declare_evar (id, c) =
let id = id_of_string ("Evar" ^ string_of_int id) in
ignore(Declare.declare_variable id (Names.empty_dirpath, Declare.SectionLocalAssum c,
Decl_kinds.IsAssumption Decl_kinds.Definitional))
in
let _declare_assert acc (id, c) =
let id = id_of_string ("Evar" ^ string_of_int id) in
tclTHEN acc (Tactics.assert_tac false (Name id) c)
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(option_map
(fun typ ->
trace (str "Type :" ++ spc () ++
Termops.print_constr_env (Global.env ()) typ))
tycon);
with _ -> ());
t'', tycon, evar_names
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) = eterm evm t None
|
