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(* -*- compile-command: "make -C ../.. plugins/subtac/subtac_plugin.cma" -*- *)
(**
- 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 Sign
open Names
open Evd
open List
open Pp
open Util
open Subtac_utils
open Proof_type
let trace s =
if !Flags.debug then (msgnl s; msgerr s)
else ()
let succfix (depth, fixrels) =
(succ depth, List.map succ fixrels)
type oblinfo =
{ ev_name: int * identifier;
ev_hyps: named_context;
ev_status: obligation_definition_status;
ev_chop: int option;
ev_loc: Util.loc;
ev_typ: types;
ev_tac: tactic option;
ev_deps: Intset.t }
(** Substitute evar references in t using De Bruijn indices,
where n binders were passed through. *)
let subst_evar_constr evs n idf t =
let seen = ref Intset.empty in
let transparent = ref Idset.empty in
let evar_info id = List.assoc id evs in
let rec substrec (depth, fixrels) c = match kind_of_term c with
| Evar (k, args) ->
let { ev_name = (id, idstr) ;
ev_hyps = hyps ; ev_chop = chop } =
try evar_info k
with Not_found ->
anomaly ("eterm: existential variable " ^ string_of_int k ^ " not found")
in
seen := Intset.add id !seen;
(* Evar arguments are created in inverse order,
and we must not apply to defined ones (i.e. LetIn's)
*)
let args =
let n = match chop with None -> 0 | Some c -> c in
let (l, r) = list_chop n (List.rev (Array.to_list args)) in
List.rev r
in
let args =
let rec aux hyps args acc =
match hyps, args with
((_, None, _) :: tlh), (c :: tla) ->
aux tlh tla ((substrec (depth, fixrels) c) :: acc)
| ((_, Some _, _) :: tlh), (_ :: tla) ->
aux tlh tla acc
| [], [] -> acc
| _, _ -> acc (*failwith "subst_evars: invalid argument"*)
in aux hyps args []
in
if List.exists (fun x -> match kind_of_term x with Rel n -> List.mem n fixrels | _ -> false) args then
transparent := Idset.add idstr !transparent;
mkApp (idf idstr, Array.of_list args)
| Fix _ ->
map_constr_with_binders succfix substrec (depth, 1 :: fixrels) c
| _ -> map_constr_with_binders succfix substrec (depth, fixrels) c
in
let t' = substrec (0, []) t in
t', !seen, !transparent
(** 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 = Util.list_index id acc 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 hyps concl =
let rec aux acc n = function
(id, copt, t) :: tl ->
let t', s, trans = subst_evar_constr evs n mkVar t in
let t'' = subst_vars acc 0 t' in
let rest, s', trans' = aux (id :: acc) (succ n) tl in
let s' = Intset.union s s' in
let trans' = Idset.union trans trans' in
(match copt with
Some c ->
let c', s'', trans'' = subst_evar_constr evs n mkVar c in
let c' = subst_vars acc 0 c' in
mkNamedProd_or_LetIn (id, Some c', t'') rest,
Intset.union s'' s',
Idset.union trans'' trans'
| None ->
mkNamedProd_or_LetIn (id, None, t'') rest, s', trans')
| [] ->
let t', s, trans = subst_evar_constr evs n mkVar concl in
subst_vars acc 0 t', s, trans
in aux [] 0 (rev hyps)
open Tacticals
let trunc_named_context n ctx =
let len = List.length ctx in
list_firstn (len - n) ctx
let rec chop_product n t =
if n = 0 then Some t
else
match kind_of_term t with
| Prod (_, _, b) -> if noccurn 1 b then chop_product (pred n) (Termops.pop b) else None
| _ -> None
let evar_dependencies evm ev =
let one_step deps =
Intset.fold (fun ev s ->
let evi = Evd.find evm ev in
Intset.union (Evarutil.evars_of_evar_info evi) s)
deps deps
in
let rec aux deps =
let deps' = one_step deps in
if Intset.equal deps deps' then deps
else aux deps'
in aux (Intset.singleton ev)
let sort_dependencies evl =
List.stable_sort
(fun (id, ev, deps) (id', ev', deps') ->
if id = id' then 0
else if Intset.mem id deps' then -1
else if Intset.mem id' deps then 1
else Pervasives.compare id id')
evl
let map_evar_body f = function
| Evar_empty -> Evar_empty
| Evar_defined c -> Evar_defined (f c)
open Environ
let map_evar_info f evi =
{ evi with evar_hyps = val_of_named_context (map_named_context f (named_context_of_val evi.evar_hyps));
evar_concl = f evi.evar_concl;
evar_body = map_evar_body f evi.evar_body }
let eterm_obligations env name isevars evm fs ?status t ty =
(* 'Serialize' the evars *)
let nc = Environ.named_context env in
let nc_len = Sign.named_context_length nc in
let evl = List.rev (to_list evm) in
let evl = List.map (fun (id, ev) -> (id, ev, evar_dependencies evm id)) evl in
let sevl = sort_dependencies evl in
let evl = List.map (fun (id, ev, _) -> id, ev) sevl in
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 ->
let hyps = Evd.evar_filtered_context ev in
let hyps = trunc_named_context nc_len hyps in
let evtyp, deps, transp = etype_of_evar l hyps ev.evar_concl in
let evtyp, hyps, chop =
match chop_product fs evtyp with
| Some t -> t, trunc_named_context fs hyps, fs
| None -> evtyp, hyps, 0
in
let loc, k = evar_source id isevars in
let status = match k with QuestionMark o -> Some o | _ -> status in
let status, chop = match status with
| Some (Define true as stat) ->
if chop <> fs then Define false, None
else stat, Some chop
| Some s -> s, None
| None -> Define true, None
in
let tac = match ev.evar_extra with
| Some t ->
if Dyn.tag t = "tactic" then
Some (Tacinterp.interp
(Tacinterp.globTacticIn (Tacinterp.tactic_out t)))
else None
| None -> None
in
let info = { ev_name = (n, nstr);
ev_hyps = hyps; ev_status = status; ev_chop = chop;
ev_loc = loc; ev_typ = evtyp ; ev_deps = deps; ev_tac = tac }
in (id, info) :: l)
evn []
in
let t', _, transparent = (* Substitute evar refs in the term by variables *)
subst_evar_constr evts 0 mkVar t
in
let ty, _, _ = subst_evar_constr evts 0 mkVar ty in
let evars =
List.map (fun (ev, info) ->
let { ev_name = (_, name); ev_status = status;
ev_loc = loc; ev_typ = typ; ev_deps = deps; ev_tac = tac } = info
in
let status = match status with
| Define true when Idset.mem name transparent -> Define false
| _ -> status
in name, typ, loc, status, deps, tac) evts
in
let evnames = List.map (fun (ev, info) -> ev, snd info.ev_name) evts in
let evmap f c = pi1 (subst_evar_constr evts 0 f c) in
Array.of_list (List.rev evars), (evnames, evmap), t', ty
let mkMetas n = list_tabulate (fun _ -> Evarutil.mk_new_meta ()) n
|
