path: root/vernac/obligations.ml

open Printf
open Globnames
open Libobject
open Entries
open Decl_kinds
open Declare

(**
   - 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 Constr
open Vars
open Names
open Evd
open Pp
open CErrors
open Util

module NamedDecl = Context.Named.Declaration

let get_fix_exn, stm_get_fix_exn = Hook.make ()

let succfix (depth, fixrels) =
  (succ depth, List.map succ fixrels)

let check_evars env evm =
  Evar.Map.iter
  (fun key evi ->
   let (loc,k) = evar_source key evm in
     match k with
     | Evar_kinds.QuestionMark _
     | Evar_kinds.ImplicitArg (_,_,false) -> ()
     | _ ->
       Pretype_errors.error_unsolvable_implicit ?loc env evm key None)
  (Evd.undefined_map evm)

type oblinfo =
  { ev_name: int * Id.t;
    ev_hyps: Context.Named.t;
    ev_status: bool * Evar_kinds.obligation_definition_status;
    ev_chop: int option;
    ev_src: Evar_kinds.t Loc.located;
    ev_typ: types;
    ev_tac: unit Proofview.tactic option;
    ev_deps: Int.Set.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 Int.Set.empty in
  let transparent = ref Id.Set.empty in
  let evar_info id = List.assoc_f Evar.equal id evs in
  let rec substrec (depth, fixrels) c = match Constr.kind c with
    | Evar (k, args) ->
	let { ev_name = (id, idstr) ;
	      ev_hyps = hyps ; ev_chop = chop } =
	  try evar_info k
	  with Not_found ->
	    anomaly ~label:"eterm" (Pp.str "existential variable " ++ int (Evar.repr k) ++ str " not found.")
	in
        seen := Int.Set.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 =
             let open Context.Named.Declaration in
	     match hyps, args with
		 (LocalAssum _ :: tlh), (c :: tla) ->
		   aux tlh tla ((substrec (depth, fixrels) c) :: acc)
	       | (LocalDef _ :: tlh), (_ :: tla) ->
		   aux tlh tla acc
	       | [], [] -> acc
	       | _, _ -> acc (*failwith "subst_evars: invalid argument"*)
	  in aux hyps args []
	in
	  if List.exists
            (fun x -> match Constr.kind x with
            | Rel n -> Int.List.mem n fixrels
            | _ -> false) args
          then
	    transparent := Id.Set.add idstr !transparent;
	  mkApp (idf idstr, Array.of_list args)
    | Fix _ ->
	Constr.map_with_binders succfix substrec (depth, 1 :: fixrels) c
    | _ -> Constr.map_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.equal id acc in
  let rec substrec depth c = match Constr.kind c with
    | Var v -> (try mkRel (depth + (var_index v)) with Not_found -> c)
    | _ -> Constr.map_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 open Context.Named.Declaration in
  let rec aux acc n = function
      decl :: tl ->
	let t', s, trans = subst_evar_constr evs n mkVar (NamedDecl.get_type decl) in
	let t'' = subst_vars acc 0 t' in
	let rest, s', trans' = aux (NamedDecl.get_id decl :: acc) (succ n) tl in
	let s' = Int.Set.union s s' in
	let trans' = Id.Set.union trans trans' in
	  (match decl with
            | LocalDef (id,c,_) ->
		let c', s'', trans'' = subst_evar_constr evs n mkVar c in
		let c' = subst_vars acc 0 c' in
		  mkNamedProd_or_LetIn (LocalDef (id, c', t'')) rest,
		Int.Set.union s'' s',
		Id.Set.union trans'' trans'
	    | LocalAssum (id,_) ->
		mkNamedProd_or_LetIn (LocalAssum (id, 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 (List.rev hyps)

let trunc_named_context n ctx =
  let len = List.length ctx in
    List.firstn (len - n) ctx

let rec chop_product n t =
  let pop t = Vars.lift (-1) t in
  if Int.equal n 0 then Some t
  else
    match Constr.kind t with
      | Prod (_, _, b) ->  if noccurn 1 b then chop_product (pred n) (pop b) else None
      | _ -> None

let evar_dependencies evm oev =
  let one_step deps =
    Evar.Set.fold (fun ev s ->
      let evi = Evd.find evm ev in
      let deps' = evars_of_filtered_evar_info evi in
      if Evar.Set.mem oev deps' then
        invalid_arg ("Ill-formed evar map: cycle detected for evar " ^ Pp.string_of_ppcmds @@ Evar.print oev)
      else Evar.Set.union deps' s)
      deps deps
  in
  let rec aux deps =
    let deps' = one_step deps in
      if Evar.Set.equal deps deps' then deps
      else aux deps'
  in aux (Evar.Set.singleton oev)

let move_after (id, ev, deps as obl) l = 
  let rec aux restdeps = function
    | (id', _, _) as obl' :: tl -> 
	let restdeps' = Evar.Set.remove id' restdeps in
	  if Evar.Set.is_empty restdeps' then
	    obl' :: obl :: tl
	  else obl' :: aux restdeps' tl
    | [] -> [obl]
  in aux (Evar.Set.remove id deps) l
    
let sort_dependencies evl =
  let rec aux l found list =
    match l with
    | (id, ev, deps) as obl :: tl ->
	let found' = Evar.Set.union found (Evar.Set.singleton id) in
	  if Evar.Set.subset deps found' then
	    aux tl found' (obl :: list)
	  else aux (move_after obl tl) found list
    | [] -> List.rev list
  in aux evl Evar.Set.empty []

open Environ

let eterm_obligations env name evm fs ?status t ty = 
  (* 'Serialize' the evars *)
  let nc = Environ.named_context env in
  let nc_len = Context.Named.length nc in
  let evm = Evarutil.nf_evar_map_undefined evm in
  let evl = Evarutil.non_instantiated evm in
  let evl = Evar.Map.bindings evl 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
			      (Id.to_string name ^ "_obligation_" ^ string_of_int (succ !i))),
		       ev)) evl
  in
  let evts =
    (* Remove existential variables in types and build the corresponding products *)
    List.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 evm in
	 let status = match k with
           | Evar_kinds.QuestionMark (o,_) -> o
           | _ -> match status with
                 | Some o -> o
                 | None -> Evar_kinds.Define (not (Program.get_proofs_transparency ()))
         in
         let force_status, status, chop = match status with
	   | Evar_kinds.Define true as stat ->
	      if not (Int.equal chop fs) then true, Evar_kinds.Define false, None
	      else false, stat, Some chop
	   | s -> false, s, None
	 in
	 let info = { ev_name = (n, nstr);
		      ev_hyps = hyps; ev_status = force_status, status; ev_chop = chop;
		      ev_src = loc, k; ev_typ = evtyp ; ev_deps = deps; ev_tac = None }
	 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 = force_status, status;
	    ev_src = src; ev_typ = typ; ev_deps = deps; ev_tac = tac } = info
      in
      let force_status, status = match status with
	| Evar_kinds.Define true when Id.Set.mem name transparent ->
	  true, Evar_kinds.Define false
	| _ -> force_status, status
      in name, typ, src, (force_status, 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 tactics_module = ["Program";"Tactics"]
let safe_init_constant md name () =
  Coqlib.check_required_library ("Coq"::md);
  Universes.constr_of_global (Coqlib.coq_reference "Obligations" md name)
let hide_obligation = safe_init_constant tactics_module "obligation"

let pperror cmd = CErrors.user_err ~hdr:"Program" cmd
let error s = pperror (str s)

let reduce c =
  EConstr.Unsafe.to_constr (Reductionops.clos_norm_flags CClosure.betaiota (Global.env ()) Evd.empty (EConstr.of_constr c))

exception NoObligations of Id.t option

let explain_no_obligations = function
    Some ident -> str "No obligations for program " ++ Id.print ident
  | None -> str "No obligations remaining"

type obligation_info =
    (Names.Id.t * types * Evar_kinds.t Loc.located *
       (bool * Evar_kinds.obligation_definition_status)
       * Int.Set.t * unit Proofview.tactic option) array

type 'a obligation_body = 
  | DefinedObl of 'a
  | TermObl of constr

type obligation =
  { obl_name : Id.t;
    obl_type : types;
    obl_location : Evar_kinds.t Loc.located;
    obl_body : pconstant obligation_body option;
    obl_status : bool * Evar_kinds.obligation_definition_status;
    obl_deps : Int.Set.t;
    obl_tac : unit Proofview.tactic option;
  }

type obligations = (obligation array * int)

type fixpoint_kind =
  | IsFixpoint of (Misctypes.lident option * Constrexpr.recursion_order_expr) list
  | IsCoFixpoint

type notations = (Misctypes.lstring * Constrexpr.constr_expr * Notation_term.scope_name option) list

type program_info_aux = {
  prg_name: Id.t;
  prg_body: constr;
  prg_type: constr;
  prg_ctx:  UState.t;
  prg_univdecl: Univdecls.universe_decl;
  prg_obligations: obligations;
  prg_deps : Id.t list;
  prg_fixkind : fixpoint_kind option ;
  prg_implicits : (Constrexpr.explicitation * (bool * bool * bool)) list;
  prg_notations : notations ;
  prg_kind : definition_kind;
  prg_reduce : constr -> constr;
  prg_hook : (UState.t -> unit) Lemmas.declaration_hook;
  prg_opaque : bool;
  prg_sign: named_context_val;
}

type program_info = program_info_aux CEphemeron.key

let get_info x =
  try CEphemeron.get x
  with CEphemeron.InvalidKey ->
    CErrors.anomaly Pp.(str "Program obligation can't be accessed by a worker.")

let assumption_message = Declare.assumption_message

let default_tactic = ref (Proofview.tclUNIT ())

(* true = hide obligations *)
let hide_obligations = ref false

let set_hide_obligations = (:=) hide_obligations
let get_hide_obligations () = !hide_obligations

open Goptions
let _ =
  declare_bool_option
    { optdepr  = false;
      optname  = "Hidding of Program obligations";
      optkey   = ["Hide";"Obligations"];
      optread  = get_hide_obligations;
      optwrite = set_hide_obligations; }

let shrink_obligations = ref true

let set_shrink_obligations = (:=) shrink_obligations
let get_shrink_obligations () = !shrink_obligations

let _ =
  declare_bool_option
    { optdepr  = true; (* remove in 8.8 *)
      optname  = "Shrinking of Program obligations";
      optkey   = ["Shrink";"Obligations"];
      optread  = get_shrink_obligations;
      optwrite = set_shrink_obligations; }

let evar_of_obligation o = make_evar (Global.named_context_val ()) o.obl_type

let get_obligation_body expand obl =
  match obl.obl_body with
  | None -> None
  | Some c ->
     if expand && snd obl.obl_status == Evar_kinds.Expand then
       match c with
       | DefinedObl pc -> Some (constant_value_in (Global.env ()) pc)
       | TermObl c -> Some c
     else (match c with
	   | DefinedObl pc -> Some (mkConstU pc)
	   | TermObl c -> Some c)

let obl_substitution expand obls deps =
  Int.Set.fold
    (fun x acc ->
       let xobl = obls.(x) in
       match get_obligation_body expand xobl with
       | None -> acc
       | Some oblb -> (xobl.obl_name, (xobl.obl_type, oblb)) :: acc)
    deps []

let subst_deps expand obls deps t =
  let osubst = obl_substitution expand obls deps in
    (Vars.replace_vars (List.map (fun (n, (_, b)) -> n, b) osubst) t)

let rec prod_app t n =
  match Constr.kind (EConstr.Unsafe.to_constr (Termops.strip_outer_cast Evd.empty (EConstr.of_constr t))) (** FIXME *) with
    | Prod (_,_,b) -> subst1 n b
    | LetIn (_, b, t, b') -> prod_app (subst1 b b') n
    | _ ->
	user_err ~hdr:"prod_app"
	  (str"Needed a product, but didn't find one" ++ fnl ())


(* prod_appvect T [| a1 ; ... ; an |] -> (T a1 ... an) *)
let prod_applist t nL = List.fold_left prod_app t nL

let replace_appvars subst =
  let rec aux c = 
    let f, l = decompose_app c in
      if isVar f then
	try
	  let c' = List.map (Constr.map aux) l in
	  let (t, b) = Id.List.assoc (destVar f) subst in
	    mkApp (delayed_force hide_obligation, 
		   [| prod_applist t c'; applistc b c' |])
	with Not_found -> Constr.map aux c
      else Constr.map aux c
  in Constr.map aux
       
let subst_prog expand obls ints prg =
  let subst = obl_substitution expand obls ints in
    if get_hide_obligations () then
      (replace_appvars subst prg.prg_body,
       replace_appvars subst ((* Termops.refresh_universes *) prg.prg_type))
    else 
      let subst' = List.map (fun (n, (_, b)) -> n, b) subst in
	(Vars.replace_vars subst' prg.prg_body,
	 Vars.replace_vars subst' ((* Termops.refresh_universes *) prg.prg_type))

let subst_deps_obl obls obl =
  let t' = subst_deps true obls obl.obl_deps obl.obl_type in
    { obl with obl_type = t' }

module ProgMap = Id.Map

let map_replace k v m = ProgMap.add k (CEphemeron.create v) (ProgMap.remove k m)

let map_keys m = ProgMap.fold (fun k _ l -> k :: l) m []

let from_prg, program_tcc_summary_tag =
  Summary.ref_tag ProgMap.empty ~name:"program-tcc-table"

let close sec =
  if not (ProgMap.is_empty !from_prg) then
    let keys = map_keys !from_prg in
      user_err ~hdr:"Program" 
	(str "Unsolved obligations when closing " ++ str sec ++ str":" ++ spc () ++
	   prlist_with_sep spc (fun x -> Id.print x) keys ++
	   (str (if Int.equal (List.length keys) 1 then " has " else " have ") ++
	      str "unsolved obligations"))

let input : program_info ProgMap.t -> obj =
  declare_object
    { (default_object "Program state") with
      cache_function = (fun (na, pi) -> from_prg := pi);
      load_function = (fun _ (_, pi) -> from_prg := pi);
      discharge_function = (fun _ -> close "section"; None);
      classify_function = (fun _ -> close "module"; Dispose) }
    
open Evd

let progmap_remove prg =
  Lib.add_anonymous_leaf (input (ProgMap.remove prg.prg_name !from_prg))
  
let progmap_add n prg =
  Lib.add_anonymous_leaf (input (ProgMap.add n prg !from_prg))

let progmap_replace prg' = 
  Lib.add_anonymous_leaf (input (map_replace prg'.prg_name prg' !from_prg))

let rec intset_to = function
    -1 -> Int.Set.empty
  | n -> Int.Set.add n (intset_to (pred n))

let subst_body expand prg =
  let obls, _ = prg.prg_obligations in
  let ints = intset_to (pred (Array.length obls)) in
    subst_prog expand obls ints prg

let declare_definition prg =
  let body, typ = subst_body true prg in
  let nf = Universes.nf_evars_and_universes_opt_subst (fun x -> None)
    (Evd.evar_universe_context_subst prg.prg_ctx) in
  let opaque = prg.prg_opaque in
  let fix_exn = Hook.get get_fix_exn () in
  let typ = nf typ in
  let body = nf body in
  let env = Global.env () in
  let uvars = Univ.LSet.union
      (Univops.universes_of_constr env typ)
      (Univops.universes_of_constr env body) in
  let uctx = UState.restrict prg.prg_ctx uvars in
  let univs = UState.check_univ_decl ~poly:(pi2 prg.prg_kind) uctx prg.prg_univdecl in
  let ce = definition_entry ~fix_exn ~opaque ~types:typ ~univs body in
  let () = progmap_remove prg in
  let ubinders = UState.universe_binders uctx in
  DeclareDef.declare_definition prg.prg_name
    prg.prg_kind ce ubinders prg.prg_implicits
    (Lemmas.mk_hook (fun l r -> Lemmas.call_hook fix_exn prg.prg_hook l r uctx; r))

let rec lam_index n t acc =
  match Constr.kind t with
    | Lambda (Name n', _, _) when Id.equal n n' ->
      acc
    | Lambda (_, _, b) ->
	lam_index n b (succ acc)
    | _ -> raise Not_found

let compute_possible_guardness_evidences (n,_) fixbody fixtype =
  match n with
  | Some { CAst.loc; v = n } -> [lam_index n fixbody 0]
  | None ->
      (* If recursive argument was not given by user, we try all args.
	 An earlier approach was to look only for inductive arguments,
	 but doing it properly involves delta-reduction, and it finally
         doesn't seem to worth the effort (except for huge mutual
	 fixpoints ?) *)
      let m = Termops.nb_prod Evd.empty (EConstr.of_constr fixtype) (** FIXME *) in
      let ctx = fst (decompose_prod_n_assum m fixtype) in
	List.map_i (fun i _ -> i) 0 ctx

let mk_proof c = ((c, Univ.ContextSet.empty), Safe_typing.empty_private_constants)

let declare_mutual_definition l =
  let len = List.length l in
  let first = List.hd l in
  let fixdefs, fixtypes, fiximps =
    List.split3
      (List.map (fun x -> 
	let subs, typ = (subst_body true x) in
	let term = snd (Reductionops.splay_lam_n (Global.env ()) Evd.empty len (EConstr.of_constr subs)) in
	let typ = snd (Reductionops.splay_prod_n (Global.env ()) Evd.empty len (EConstr.of_constr typ)) in
	let term = EConstr.Unsafe.to_constr term in
	let typ = EConstr.Unsafe.to_constr typ in
	  x.prg_reduce term, x.prg_reduce typ, x.prg_implicits) l)
  in
(*   let fixdefs = List.map reduce_fix fixdefs in *)
  let fixkind = Option.get first.prg_fixkind in
  let arrrec, recvec = Array.of_list fixtypes, Array.of_list fixdefs in
  let fixdecls = (Array.of_list (List.map (fun x -> Name x.prg_name) l), arrrec, recvec) in
  let (local,poly,kind) = first.prg_kind in
  let fixnames = first.prg_deps in
  let opaque = first.prg_opaque in
  let kind = if fixkind != IsCoFixpoint then Fixpoint else CoFixpoint in
  let indexes, fixdecls =
    match fixkind with
      | IsFixpoint wfl ->
	  let possible_indexes =
	    List.map3 compute_possible_guardness_evidences
              wfl fixdefs fixtypes in
	  let indexes = 
              Pretyping.search_guard (Global.env())
              possible_indexes fixdecls in
          Some indexes, 
          List.map_i (fun i _ ->
            mk_proof (mkFix ((indexes,i),fixdecls))) 0 l
      | IsCoFixpoint ->
          None,
          List.map_i (fun i _ ->
            mk_proof (mkCoFix (i,fixdecls))) 0 l
  in
  (* Declare the recursive definitions *)
  let univs = UState.const_univ_entry ~poly first.prg_ctx in
  let fix_exn = Hook.get get_fix_exn () in
  let kns = List.map4 (DeclareDef.declare_fix ~opaque (local, poly, kind) Universes.empty_binders univs)
    fixnames fixdecls fixtypes fiximps in
    (* Declare notations *)
    List.iter (Metasyntax.add_notation_interpretation (Global.env())) first.prg_notations;
    Declare.recursive_message (fixkind != IsCoFixpoint) indexes fixnames;
    let gr = List.hd kns in
    let kn = match gr with ConstRef kn -> kn | _ -> assert false in
    Lemmas.call_hook fix_exn first.prg_hook local gr first.prg_ctx;
    List.iter progmap_remove l; kn

let decompose_lam_prod c ty =
  let open Context.Rel.Declaration in
  let rec aux ctx c ty =
    match Constr.kind c, Constr.kind ty with
    | LetIn (x, b, t, c), LetIn (x', b', t', ty)
	 when Constr.equal b b' && Constr.equal t t' ->
       let ctx' = Context.Rel.add (LocalDef (x,b',t')) ctx in
       aux ctx' c ty
    | _, LetIn (x', b', t', ty) ->
       let ctx' = Context.Rel.add (LocalDef (x',b',t')) ctx in
       aux ctx' (lift 1 c) ty
    | LetIn (x, b, t, c), _ ->
       let ctx' = Context.Rel.add (LocalDef (x,b,t)) ctx in
       aux ctx' c (lift 1 ty)
    | Lambda (x, b, t), Prod (x', b', t')
       (* By invariant, must be convertible *) ->
       let ctx' = Context.Rel.add (LocalAssum (x,b')) ctx in
       aux ctx' t t'
    | Cast (c, _, _), _ -> aux ctx c ty
    | _, _ -> ctx, c, ty
  in aux Context.Rel.empty c ty

let shrink_body c ty =
  let ctx, b, ty =
    match ty with
    | None ->
       let ctx, b = decompose_lam_assum c in
       ctx, b, None
    | Some ty ->
       let ctx, b, ty = decompose_lam_prod c ty in
       ctx, b, Some ty
  in
  let b', ty', n, args =
    List.fold_left (fun (b, ty, i, args) decl ->
        if noccurn 1 b && Option.cata (noccurn 1) true ty then
	  subst1 mkProp b, Option.map (subst1 mkProp) ty, succ i, args
	else
          let open Context.Rel.Declaration in
	  let args = if is_local_assum decl then mkRel i :: args else args in
          mkLambda_or_LetIn decl b, Option.map (mkProd_or_LetIn decl) ty,
	  succ i, args)
     (b, ty, 1, []) ctx
  in ctx, b', ty', Array.of_list args

let unfold_entry cst = Hints.HintsUnfoldEntry [EvalConstRef cst]

let add_hint local prg cst =
  Hints.add_hints local [Id.to_string prg.prg_name] (unfold_entry cst)

let it_mkLambda_or_LetIn_or_clean t ctx =
  let open Context.Rel.Declaration in
  let fold t decl =
    if is_local_assum decl then mkLambda_or_LetIn decl t
    else
      if noccurn 1 t then subst1 mkProp t
      else mkLambda_or_LetIn decl t
  in
  Context.Rel.fold_inside fold ctx ~init:t

let declare_obligation prg obl body ty uctx =
  let body = prg.prg_reduce body in
  let ty = Option.map prg.prg_reduce ty in
  match obl.obl_status with
  | _, Evar_kinds.Expand -> false, { obl with obl_body = Some (TermObl body) }
  | force, Evar_kinds.Define opaque ->
      let opaque = not force && opaque in
      let poly = pi2 prg.prg_kind in
      let ctx, body, ty, args =
	if get_shrink_obligations () && not poly then
	  shrink_body body ty else [], body, ty, [||]
      in
      let body = ((body,Univ.ContextSet.empty),Safe_typing.empty_private_constants) in
      let ce =
        { const_entry_body = Future.from_val ~fix_exn:(fun x -> x) body;
          const_entry_secctx = None;
	  const_entry_type = ty;
          const_entry_universes = uctx;
	  const_entry_opaque = opaque;
          const_entry_inline_code = false;
          const_entry_feedback = None;
      } in
      (** ppedrot: seems legit to have obligations as local *)
      let constant = Declare.declare_constant obl.obl_name ~local:true
	(DefinitionEntry ce,IsProof Property)
      in
      if not opaque then add_hint (Locality.make_section_locality None) prg constant;
      definition_message obl.obl_name;
      let body = match uctx with
        | Polymorphic_const_entry uctx ->
          Some (DefinedObl (constant, Univ.UContext.instance uctx))
        | Monomorphic_const_entry _ ->
          Some (TermObl (it_mkLambda_or_LetIn_or_clean (mkApp (mkConst constant, args)) ctx))
      in
      true, { obl with obl_body = body }

let init_prog_info ?(opaque = false) sign n udecl b t ctx deps fixkind
		   notations obls impls kind reduce hook =
  let obls', b =
    match b with
    | None ->
	assert(Int.equal (Array.length obls) 0);
	let n = Nameops.add_suffix n "_obligation" in
	  [| { obl_name = n; obl_body = None;
	       obl_location = Loc.tag Evar_kinds.InternalHole; obl_type = t;
	       obl_status = false, Evar_kinds.Expand; obl_deps = Int.Set.empty;
	       obl_tac = None } |],
	mkVar n
    | Some b ->
	Array.mapi
	  (fun i (n, t, l, o, d, tac) ->
            { obl_name = n ; obl_body = None; 
	      obl_location = l; obl_type = t; obl_status = o;
	      obl_deps = d; obl_tac = tac })
	  obls, b
  in
  let ctx = UState.make_flexible_nonalgebraic ctx in
    { prg_name = n ; prg_body = b; prg_type = reduce t; 
      prg_ctx = ctx; prg_univdecl = udecl;
      prg_obligations = (obls', Array.length obls');
      prg_deps = deps; prg_fixkind = fixkind ; prg_notations = notations ;
      prg_implicits = impls; prg_kind = kind; prg_reduce = reduce; 
      prg_hook = hook; prg_opaque = opaque;
      prg_sign = sign }

let map_cardinal m =
  let i = ref 0 in
  ProgMap.iter (fun _ v ->
		if snd (CEphemeron.get v).prg_obligations > 0 then incr i) m;
  !i

exception Found of program_info

let map_first m =
  try
    ProgMap.iter (fun _ v ->
		  if snd (CEphemeron.get v).prg_obligations > 0 then
		    raise (Found v)) m;
    assert(false)
  with Found x -> x

let get_prog name =
  let prg_infos = !from_prg in
    match name with
	Some n ->
	  (try get_info (ProgMap.find n prg_infos)
	   with Not_found -> raise (NoObligations (Some n)))
      | None ->
	  (let n = map_cardinal prg_infos in
	     match n with
		 0 -> raise (NoObligations None)
	       | 1 -> get_info (map_first prg_infos)
	       | _ ->
                let progs = Id.Set.elements (ProgMap.domain prg_infos) in
                let prog = List.hd progs in
                let progs = prlist_with_sep pr_comma Id.print progs in
                user_err 
                  (str "More than one program with unsolved obligations: " ++ progs
                  ++ str "; use the \"of\" clause to specify, as in \"Obligation 1 of " ++ Id.print prog ++ str "\""))

let get_any_prog () =
  let prg_infos = !from_prg in
  let n = map_cardinal prg_infos in
  if n > 0 then get_info (map_first prg_infos)
  else raise (NoObligations None)

let get_prog_err n =
  try get_prog n with NoObligations id -> pperror (explain_no_obligations id)

let get_any_prog_err () =
  try get_any_prog () with NoObligations id -> pperror (explain_no_obligations id)

let obligations_solved prg = Int.equal (snd prg.prg_obligations) 0

let all_programs () =
  ProgMap.fold (fun k p l -> p :: l) !from_prg []

type progress =
    | Remain of int
    | Dependent
    | Defined of global_reference

let obligations_message rem =
  if rem > 0 then
    if Int.equal rem 1 then
      Flags.if_verbose Feedback.msg_info (int rem ++ str " obligation remaining")
    else
      Flags.if_verbose Feedback.msg_info (int rem ++ str " obligations remaining")
  else
    Flags.if_verbose Feedback.msg_info (str "No more obligations remaining")

let update_obls prg obls rem =
  let prg' = { prg with prg_obligations = (obls, rem) } in
    progmap_replace prg';
    obligations_message rem;
    if rem > 0 then Remain rem
    else (
      match prg'.prg_deps with
      | [] ->
	  let kn = declare_definition prg' in
	    progmap_remove prg';
	    Defined kn
      | l ->
	  let progs = List.map (fun x -> get_info (ProgMap.find x !from_prg)) prg'.prg_deps in
	    if List.for_all (fun x -> obligations_solved x) progs then
	      let kn = declare_mutual_definition progs in
		Defined (ConstRef kn)
	    else Dependent)

let is_defined obls x = not (Option.is_empty obls.(x).obl_body)

let deps_remaining obls deps =
  Int.Set.fold
    (fun x acc ->
      if is_defined obls x then acc
      else x :: acc)
    deps []

let dependencies obls n =
  let res = ref Int.Set.empty in
    Array.iteri
      (fun i obl ->
	if not (Int.equal i n) && Int.Set.mem n obl.obl_deps then
	  res := Int.Set.add i !res)
      obls;
    !res

let goal_kind poly = Decl_kinds.Local, poly, Decl_kinds.DefinitionBody Decl_kinds.Definition

let goal_proof_kind poly = Decl_kinds.Local, poly, Decl_kinds.Proof Decl_kinds.Lemma

let kind_of_obligation poly o =
  match o with
  | Evar_kinds.Define false | Evar_kinds.Expand -> goal_kind poly
  | _ -> goal_proof_kind poly

let not_transp_msg =
  str "Obligation should be transparent but was declared opaque." ++ spc () ++
    str"Use 'Defined' instead."

let err_not_transp () = pperror not_transp_msg

let rec string_of_list sep f = function
    [] -> ""
  | x :: [] -> f x
  | x :: ((y :: _) as tl) -> f x ^ sep ^ string_of_list sep f tl

(* Solve an obligation using tactics, return the corresponding proof term *)

let solve_by_tac name evi t poly ctx =
  let id = name in
  let concl = EConstr.of_constr evi.evar_concl in
  (* spiwack: the status is dropped. *)
  let (entry,_,ctx') = Pfedit.build_constant_by_tactic 
    id ~goal_kind:(goal_kind poly) ctx evi.evar_hyps concl (Tacticals.New.tclCOMPLETE t) in
  let env = Global.env () in
  let entry = Safe_typing.inline_private_constants_in_definition_entry env entry in
  let body, () = Future.force entry.const_entry_body in
  let ctx' = Evd.merge_context_set ~sideff:true Evd.univ_rigid (Evd.from_ctx ctx') (snd body) in
  Inductiveops.control_only_guard (Global.env ()) (fst body);
  (fst body), entry.const_entry_type, Evd.evar_universe_context ctx'

let obligation_terminator name num guard hook auto pf =
  let open Proof_global in
  let term = Lemmas.universe_proof_terminator guard hook in
  match pf with
  | Admitted _ -> apply_terminator term pf
  | Proved (opq, id, proof) ->
    let (_, (entry, uctx, _)) = Pfedit.cook_this_proof proof in
    let env = Global.env () in
    let entry = Safe_typing.inline_private_constants_in_definition_entry env entry in
    let ty = entry.Entries.const_entry_type in
    let (body, cstr), () = Future.force entry.Entries.const_entry_body in
    let sigma = Evd.from_ctx uctx in
    let sigma = Evd.merge_context_set ~sideff:true Evd.univ_rigid sigma cstr in
    Inductiveops.control_only_guard (Global.env ()) body;
    (** Declare the obligation ourselves and drop the hook *)
    let prg = get_info (ProgMap.find name !from_prg) in
    (** Ensure universes are substituted properly in body and type *)
    let body = EConstr.to_constr sigma (EConstr.of_constr body) in
    let ty = Option.map (fun x -> EConstr.to_constr sigma (EConstr.of_constr x)) ty in
    let ctx = Evd.evar_universe_context sigma in
    let obls, rem = prg.prg_obligations in
    let obl = obls.(num) in
    let status =
      match obl.obl_status, opq with
      | (_, Evar_kinds.Expand), Vernacexpr.Opaque -> err_not_transp ()
      | (true, _), Vernacexpr.Opaque -> err_not_transp ()
      | (false, _), Vernacexpr.Opaque -> Evar_kinds.Define true
      | (_, Evar_kinds.Define true), Vernacexpr.Transparent ->
        Evar_kinds.Define false
      | (_, status), Vernacexpr.Transparent -> status
    in
    let obl = { obl with obl_status = false, status } in
    let ctx =
      if pi2 prg.prg_kind then ctx
      else UState.union prg.prg_ctx ctx
    in
    let uctx = UState.const_univ_entry ~poly:(pi2 prg.prg_kind) ctx in
    let (_, obl) = declare_obligation prg obl body ty uctx in
    let obls = Array.copy obls in
    let _ = obls.(num) <- obl in
    let prg_ctx =
      if pi2 (prg.prg_kind) then (* Polymorphic *)
        (** We merge the new universes and constraints of the
            polymorphic obligation with the existing ones *)
        UState.union prg.prg_ctx ctx
      else
        (** The first obligation declares the univs of the constant,
            each subsequent obligation declares its own additional
            universes and constraints if any *)
        UState.make (Global.universes ())
    in
    let prg = { prg with prg_ctx } in
    try
      ignore (update_obls prg obls (pred rem));
      if pred rem > 0 then
        begin
          let deps = dependencies obls num in
          if not (Int.Set.is_empty deps) then
            ignore (auto (Some name) None deps)
        end
    with e when CErrors.noncritical e ->
      let e = CErrors.push e in
      pperror (CErrors.iprint (ExplainErr.process_vernac_interp_error e))

let obligation_hook prg obl num auto ctx' _ gr =
  let obls, rem = prg.prg_obligations in
  let cst = match gr with ConstRef cst -> cst | _ -> assert false in
  let transparent = evaluable_constant cst (Global.env ()) in
  let () = match obl.obl_status with
      (true, Evar_kinds.Expand) 
    | (true, Evar_kinds.Define true) ->
       if not transparent then err_not_transp ()
    | _ -> ()
in
  let ctx' = match ctx' with None -> prg.prg_ctx | Some ctx' -> ctx' in
  let inst, ctx' =
    if not (pi2 prg.prg_kind) (* Not polymorphic *) then
      (* The universe context was declared globally, we continue
         from the new global environment. *)
      let evd = Evd.from_env (Global.env ()) in
      let ctx' = Evd.merge_universe_subst evd (Evd.universe_subst (Evd.from_ctx ctx')) in
      Univ.Instance.empty, Evd.evar_universe_context ctx'
    else
      (* We get the right order somehow, but surely it could be enforced in a clearer way. *)
      let uctx = UState.context ctx' in
      Univ.UContext.instance uctx, ctx'
  in
  let obl = { obl with obl_body = Some (DefinedObl (cst, inst)) } in
  let () = if transparent then add_hint true prg cst in
  let obls = Array.copy obls in
  let _ = obls.(num) <- obl in
  let prg = { prg with prg_ctx = ctx' } in
  let () =
    try ignore (update_obls prg obls (pred rem))
    with e when CErrors.noncritical e ->
      let e = CErrors.push e in
      pperror (CErrors.iprint (ExplainErr.process_vernac_interp_error e))
  in
  if pred rem > 0 then begin
    let deps = dependencies obls num in
    if not (Int.Set.is_empty deps) then
      ignore (auto (Some prg.prg_name) None deps)
  end

let rec solve_obligation prg num tac =
  let user_num = succ num in
  let obls, rem = prg.prg_obligations in
  let obl = obls.(num) in
  let remaining = deps_remaining obls obl.obl_deps in
  let () =
    if not (Option.is_empty obl.obl_body) then
      pperror (str "Obligation" ++ spc () ++ int user_num ++ str "already" ++ spc() ++ str "solved.");
    if not (List.is_empty remaining) then
      pperror (str "Obligation " ++ int user_num ++ str " depends on obligation(s) "
        ++ str (string_of_list ", " (fun x -> string_of_int (succ x)) remaining));
  in
  let obl = subst_deps_obl obls obl in
  let kind = kind_of_obligation (pi2 prg.prg_kind) (snd obl.obl_status) in
  let evd = Evd.from_ctx prg.prg_ctx in
  let evd = Evd.update_sigma_env evd (Global.env ()) in
  let auto n tac oblset = auto_solve_obligations n ~oblset tac in
  let terminator guard hook =
    Proof_global.make_terminator
      (obligation_terminator prg.prg_name num guard hook auto) in
  let hook ctx = Lemmas.mk_hook (obligation_hook prg obl num auto ctx) in
  let () = Lemmas.start_proof_univs ~sign:prg.prg_sign obl.obl_name kind evd (EConstr.of_constr obl.obl_type) ~terminator hook in
  let _ = Pfedit.by !default_tactic in
  Option.iter (fun tac -> Proof_global.set_endline_tactic tac) tac

and obligation (user_num, name, typ) tac =
  let num = pred user_num in
  let prg = get_prog_err name in
  let obls, rem = prg.prg_obligations in
    if num < Array.length obls then
      let obl = obls.(num) in
	match obl.obl_body with
	    None -> solve_obligation prg num tac
	  | Some r -> error "Obligation already solved"
    else error (sprintf "Unknown obligation number %i" (succ num))


and solve_obligation_by_tac prg obls i tac =
  let obl = obls.(i) in
    match obl.obl_body with
    | Some _ -> None
    | None ->
	try
	  if List.is_empty (deps_remaining obls obl.obl_deps) then
	    let obl = subst_deps_obl obls obl in
	    let tac =
	      match tac with
	      | Some t -> t
	      | None ->
		  match obl.obl_tac with
		  | Some t -> t
		  | None -> !default_tactic
	    in
	    let evd = Evd.from_ctx prg.prg_ctx in
	    let evd = Evd.update_sigma_env evd (Global.env ()) in
	    let t, ty, ctx =
              solve_by_tac obl.obl_name (evar_of_obligation obl) tac
                (pi2 prg.prg_kind) (Evd.evar_universe_context evd)
            in
            let uctx = if pi2 prg.prg_kind
              then Polymorphic_const_entry (UState.context ctx)
              else Monomorphic_const_entry (UState.context_set ctx)
            in
            let prg = {prg with prg_ctx = ctx} in
            let def, obl' = declare_obligation prg obl t ty uctx in
              obls.(i) <- obl';
	      if def && not (pi2 prg.prg_kind) then (
	        (* Declare the term constraints with the first obligation only *)
	        let evd = Evd.from_env (Global.env ()) in
	        let evd = Evd.merge_universe_subst evd (Evd.universe_subst (Evd.from_ctx ctx)) in
		let ctx' = Evd.evar_universe_context evd in
		  Some {prg with prg_ctx = ctx'})
	      else Some prg
	  else None
	with e when CErrors.noncritical e ->
          let (e, _) = CErrors.push e in
          match e with
	  | Refiner.FailError (_, s) ->
	      user_err ?loc:(fst obl.obl_location) ~hdr:"solve_obligation" (Lazy.force s)
          | e -> None (* FIXME really ? *)

and solve_prg_obligations prg ?oblset tac =
  let obls, rem = prg.prg_obligations in
  let rem = ref rem in
  let obls' = Array.copy obls in
  let set = ref Int.Set.empty in
  let p = match oblset with
    | None -> (fun _ -> true)
    | Some s -> set := s;
      (fun i -> Int.Set.mem i !set)
  in
  let prgref = ref prg in
  let _ =
    Array.iteri (fun i x ->
      if p i then
        match solve_obligation_by_tac !prgref obls' i tac with
	| None -> ()
 	| Some prg' ->
	   prgref := prg';
	   let deps = dependencies obls i in
 	   (set := Int.Set.union !set deps;
 	    decr rem))
      obls'
  in
    update_obls !prgref obls' !rem

and solve_obligations n tac =
  let prg = get_prog_err n in
    solve_prg_obligations prg tac

and solve_all_obligations tac =
  ProgMap.iter (fun k v -> ignore(solve_prg_obligations (get_info v) tac)) !from_prg

and try_solve_obligation n prg tac =
  let prg = get_prog prg in
  let obls, rem = prg.prg_obligations in
  let obls' = Array.copy obls in
    match solve_obligation_by_tac prg obls' n tac with
    | Some prg' -> ignore(update_obls prg' obls' (pred rem))
    | None -> ()

and try_solve_obligations n tac =
  try ignore (solve_obligations n tac) with NoObligations _ -> ()

and auto_solve_obligations n ?oblset tac : progress =
  Flags.if_verbose Feedback.msg_info (str "Solving obligations automatically...");
  try solve_prg_obligations (get_prog_err n) ?oblset tac with NoObligations _ -> Dependent

open Pp
let show_obligations_of_prg ?(msg=true) prg =
  let n = prg.prg_name in
  let obls, rem = prg.prg_obligations in
  let showed = ref 5 in
    if msg then Feedback.msg_info (int rem ++ str " obligation(s) remaining: ");
    Array.iteri (fun i x ->
		   match x.obl_body with
		   | None ->
		       if !showed > 0 then (
		         decr showed;
			 let x = subst_deps_obl obls x in
			 Feedback.msg_info (str "Obligation" ++ spc() ++ int (succ i) ++ spc () ++
				   str "of" ++ spc() ++ Id.print n ++ str ":" ++ spc () ++
				   hov 1 (Printer.pr_constr_env (Global.env ()) Evd.empty x.obl_type ++
					    str "." ++ fnl ())))
		   | Some _ -> ())
      obls

let show_obligations ?(msg=true) n =
  let progs = match n with
    | None -> all_programs ()
    | Some n ->
	try [ProgMap.find n !from_prg]
	with Not_found -> raise (NoObligations (Some n))
  in List.iter (fun x -> show_obligations_of_prg ~msg (get_info x)) progs

let show_term n =
  let prg = get_prog_err n in
  let n = prg.prg_name in
    (Id.print n ++ spc () ++ str":" ++ spc () ++
	     Printer.pr_constr_env (Global.env ()) Evd.empty prg.prg_type ++ spc () ++ str ":=" ++ fnl ()
	    ++ Printer.pr_constr_env (Global.env ()) Evd.empty prg.prg_body)

let add_definition n ?term t ctx ?(univdecl=Univdecls.default_univ_decl)
                   ?(implicits=[]) ?(kind=Global,false,Definition) ?tactic
    ?(reduce=reduce) ?(hook=Lemmas.mk_hook (fun _ _ _ -> ())) ?(opaque = false) obls =
  let sign = Decls.initialize_named_context_for_proof () in
  let info = Id.print n ++ str " has type-checked" in
  let prg = init_prog_info sign ~opaque n univdecl term t ctx [] None [] obls implicits kind reduce hook in
  let obls,_ = prg.prg_obligations in
  if Int.equal (Array.length obls) 0 then (
    Flags.if_verbose Feedback.msg_info (info ++ str ".");
    let cst = declare_definition prg in
      Defined cst)
  else (
    let len = Array.length obls in
    let _ = Flags.if_verbose Feedback.msg_info (info ++ str ", generating " ++ int len ++ str (String.plural len " obligation")) in
      progmap_add n (CEphemeron.create prg);
      let res = auto_solve_obligations (Some n) tactic in
	match res with
	| Remain rem -> Flags.if_verbose (fun () -> show_obligations ~msg:false (Some n)) (); res
	| _ -> res)

let add_mutual_definitions l ctx ?(univdecl=Univdecls.default_univ_decl) ?tactic
                           ?(kind=Global,false,Definition) ?(reduce=reduce)
    ?(hook=Lemmas.mk_hook (fun _ _ _ -> ())) ?(opaque = false) notations fixkind =
  let sign = Decls.initialize_named_context_for_proof () in
  let deps = List.map (fun (n, b, t, imps, obls) -> n) l in
    List.iter
    (fun  (n, b, t, imps, obls) ->
     let prg = init_prog_info sign ~opaque n univdecl (Some b) t ctx deps (Some fixkind)
       notations obls imps kind reduce hook 
     in progmap_add n (CEphemeron.create prg)) l;
    let _defined =
      List.fold_left (fun finished x ->
	if finished then finished
	else
	  let res = auto_solve_obligations (Some x) tactic in
	    match res with
	    | Defined _ -> 
		(* If one definition is turned into a constant, 
		   the whole block is defined. *) true
	    | _ -> false)
	false deps
    in ()

let admit_prog prg =
  let obls, rem = prg.prg_obligations in
  let obls = Array.copy obls in
    Array.iteri 
      (fun i x ->
        match x.obl_body with
        | None ->
            let x = subst_deps_obl obls x in
            let ctx = Monomorphic_const_entry (UState.context_set prg.prg_ctx) in
            let kn = Declare.declare_constant x.obl_name ~local:true
              (ParameterEntry (None,(x.obl_type,ctx),None), IsAssumption Conjectural)
            in
              assumption_message x.obl_name;
              obls.(i) <- { x with obl_body = Some (DefinedObl (kn, Univ.Instance.empty)) }
        | Some _ -> ())
      obls;
    ignore(update_obls prg obls 0)

let rec admit_all_obligations () =
  let prg = try Some (get_any_prog ()) with NoObligations _ -> None in
  match prg with
  | None -> ()
  | Some prg ->
    admit_prog prg;
    admit_all_obligations ()

let admit_obligations n =
  match n with
  | None -> admit_all_obligations ()
  | Some _ ->
    let prg = get_prog_err n in
    admit_prog prg

let next_obligation n tac =
  let prg = match n with
  | None -> get_any_prog_err ()
  | Some _ -> get_prog_err n
  in
  let obls, rem = prg.prg_obligations in
  let is_open _ x = Option.is_empty x.obl_body && List.is_empty (deps_remaining obls x.obl_deps) in
  let i = match Array.findi is_open obls with
  | Some i -> i
  | None -> anomaly (Pp.str "Could not find a solvable obligation.")
  in
  solve_obligation prg i tac

let init_program () =
  Coqlib.check_required_library Coqlib.datatypes_module_name;
  Coqlib.check_required_library ["Coq";"Init";"Specif"];
  Coqlib.check_required_library ["Coq";"Program";"Tactics"]

let set_program_mode c =
  if c then
    if !Flags.program_mode then ()
    else begin
      init_program ();
      Flags.program_mode := true;
    end