1 files changed, 534 insertions, 0 deletions

diff --git a/plugins/subtac/subtac_command.ml b/plugins/subtac/subtac_command.ml
new file mode 100644
index 00000000..f2747225
--- /dev/null
+++ b/plugins/subtac/subtac_command.ml
@@ -0,0 +1,534 @@
+open Closure
+open RedFlags
+open Declarations
+open Entries
+open Libobject
+open Pattern
+open Matching
+open Pp
+open Rawterm
+open Sign
+open Tacred
+open Util
+open Names
+open Nameops
+open Libnames
+open Nametab
+open Pfedit
+open Proof_type
+open Refiner
+open Tacmach
+open Tactic_debug
+open Topconstr
+open Term
+open Termops
+open Tacexpr
+open Safe_typing
+open Typing
+open Hiddentac
+open Genarg
+open Decl_kinds
+open Mod_subst
+open Printer
+open Inductiveops
+open Syntax_def
+open Environ
+open Tactics
+open Tacticals
+open Tacinterp
+open Vernacexpr
+open Notation
+open Evd
+open Evarutil
+
+module SPretyping = Subtac_pretyping.Pretyping
+open Subtac_utils
+open Pretyping
+open Subtac_obligations
+
+(*********************************************************************)
+(* Functions to parse and interpret constructions *)
+
+let evar_nf isevars c =
+  Evarutil.nf_evar !isevars c
+
+let interp_gen kind isevars env
+               ?(impls=([],[])) ?(allow_patvar=false) ?(ltacvars=([],[]))
+               c =
+  let c' = Constrintern.intern_gen (kind=IsType) ~impls ~allow_patvar ~ltacvars ( !isevars) env c in
+  let c' = SPretyping.understand_tcc_evars isevars env kind c' in
+    evar_nf isevars c'
+
+let interp_constr isevars env c =
+  interp_gen (OfType None) isevars env c
+
+let interp_type_evars isevars env ?(impls=([],[])) c =
+  interp_gen IsType isevars env ~impls c
+
+let interp_casted_constr isevars env ?(impls=([],[])) c typ =
+  interp_gen (OfType (Some typ)) isevars env ~impls c
+
+let interp_casted_constr_evars isevars env ?(impls=([],[])) c typ =
+  interp_gen (OfType (Some typ)) isevars env ~impls c
+
+let interp_open_constr isevars env c =
+    msgnl (str "Pretyping " ++ my_print_constr_expr c);
+  let c = Constrintern.intern_constr ( !isevars) env c in
+  let c' = SPretyping.understand_tcc_evars isevars env (OfType None) c in
+    evar_nf isevars c'
+
+let interp_constr_judgment isevars env c =
+  let j =
+    SPretyping.understand_judgment_tcc isevars env
+      (Constrintern.intern_constr ( !isevars) env c)
+  in
+    { uj_val = evar_nf isevars j.uj_val; uj_type = evar_nf isevars j.uj_type }
+
+let locate_if_isevar loc na = function
+  | RHole _ ->
+      (try match na with
+	| Name id ->  Reserve.find_reserved_type id
+	| Anonymous -> raise Not_found
+      with Not_found -> RHole (loc, Evd.BinderType na))
+  | x -> x
+
+let interp_binder sigma env na t =
+  let t = Constrintern.intern_gen true ( !sigma) env t in
+    SPretyping.understand_tcc_evars sigma env IsType (locate_if_isevar (loc_of_rawconstr t) na t)
+
+let interp_context_evars evdref env params =
+  let bl = Constrintern.intern_context false ( !evdref) env params in
+  let (env, par, _, impls) =
+    List.fold_left
+      (fun (env,params,n,impls) (na, k, b, t) ->
+	match b with
+	    None ->
+	      let t' = locate_if_isevar (loc_of_rawconstr t) na t in
+	      let t = SPretyping.understand_tcc_evars evdref env IsType t' in
+	      let d = (na,None,t) in
+	      let impls =
+		if k = Implicit then
+		  let na = match na with Name n -> Some n | Anonymous -> None in
+		    (ExplByPos (n, na), (true, true, true)) :: impls
+		else impls
+	      in
+		(push_rel d env, d::params, succ n, impls)
+	  | Some b ->
+	      let c = SPretyping.understand_judgment_tcc evdref env b in
+	      let d = (na, Some c.uj_val, c.uj_type) in
+		(push_rel d env,d::params, succ n, impls))
+      (env,[],1,[]) (List.rev bl)
+  in (env, par), impls
+
+(* try to find non recursive definitions *)
+
+let list_chop_hd i l = match list_chop i l with
+  | (l1,x::l2) -> (l1,x,l2)
+  | (x :: [], l2) -> ([], x, [])
+  | _ -> assert(false)
+
+let collect_non_rec env =
+  let rec searchrec lnonrec lnamerec ldefrec larrec nrec =
+    try
+      let i =
+        list_try_find_i
+          (fun i f ->
+             if List.for_all (fun (_, def) -> not (occur_var env f def)) ldefrec
+             then i else failwith "try_find_i")
+          0 lnamerec
+      in
+      let (lf1,f,lf2) = list_chop_hd i lnamerec in
+      let (ldef1,def,ldef2) = list_chop_hd i ldefrec in
+      let (lar1,ar,lar2) = list_chop_hd i larrec in
+      let newlnv =
+	try
+	  match list_chop i nrec with
+            | (lnv1,_::lnv2) -> (lnv1@lnv2)
+	    | _ -> [] (* nrec=[] for cofixpoints *)
+        with Failure "list_chop" -> []
+      in
+      searchrec ((f,def,ar)::lnonrec)
+	(lf1@lf2) (ldef1@ldef2) (lar1@lar2) newlnv
+    with Failure "try_find_i" ->
+      (List.rev lnonrec,
+       (Array.of_list lnamerec, Array.of_list ldefrec,
+        Array.of_list larrec, Array.of_list nrec))
+  in
+  searchrec []
+
+let list_of_local_binders l =
+  let rec aux acc = function
+      Topconstr.LocalRawDef (n, c) :: tl -> aux ((n, Some c, None) :: acc) tl
+    | Topconstr.LocalRawAssum (nl, k, c) :: tl ->
+	aux (List.fold_left (fun acc n -> (n, None, Some c) :: acc) acc nl) tl
+    | [] -> List.rev acc
+  in aux [] l
+
+let lift_binders k n l =
+  let rec aux n = function
+    | (id, t, c) :: tl -> (id, Option.map (liftn k n) t, liftn k n c) :: aux (pred n) tl
+    | [] -> []
+  in aux n l
+
+let rec gen_rels = function
+    0 -> []
+  | n -> mkRel n :: gen_rels (pred n)
+
+let split_args n rel = match list_chop ((List.length rel) - n) rel with
+    (l1, x :: l2) -> l1, x, l2
+  | _ -> assert(false)
+
+open Coqlib
+
+let sigT = Lazy.lazy_from_fun build_sigma_type
+let sigT_info = lazy
+  { ci_ind       = destInd (Lazy.force sigT).typ;
+    ci_npar      = 2;
+    ci_cstr_nargs = [|2|];
+    ci_pp_info   =  { ind_nargs = 0; style = LetStyle }
+  }
+
+let telescope = function
+  | [] -> assert false
+  | [(n, None, t)] -> t, [n, Some (mkRel 1), t], mkRel 1
+  | (n, None, t) :: tl ->
+      let ty, tys, (k, constr) =
+	List.fold_left
+	  (fun (ty, tys, (k, constr)) (n, b, t) ->
+	    let pred = mkLambda (n, t, ty) in
+	    let sigty = mkApp ((Lazy.force sigT).typ, [|t; pred|]) in
+	    let intro = mkApp ((Lazy.force sigT).intro, [|lift k t; lift k pred; mkRel k; constr|]) in
+	      (sigty, pred :: tys, (succ k, intro)))
+	  (t, [], (2, mkRel 1)) tl
+      in
+      let (last, subst) = List.fold_right2
+	(fun pred (n, b, t) (prev, subst) ->
+	  let proj1 = applistc (Lazy.force sigT).proj1 [t; pred; prev] in
+	  let proj2 = applistc (Lazy.force sigT).proj2 [t; pred; prev] in
+	    (lift 1 proj2, (n, Some proj1, t) :: subst))
+	(List.rev tys) tl (mkRel 1, [])
+      in ty, ((n, Some last, t) :: subst), constr
+
+  | _ -> raise (Invalid_argument "telescope")
+
+let nf_evar_context isevars ctx =
+  List.map (fun (n, b, t) ->
+    (n, Option.map (Evarutil.nf_evar isevars) b, Evarutil.nf_evar isevars t)) ctx
+
+let build_wellfounded (recname,n,bl,arityc,body) r measure notation boxed =
+  Coqlib.check_required_library ["Coq";"Program";"Wf"];
+  let sigma = Evd.empty in
+  let isevars = ref (Evd.create_evar_defs sigma) in
+  let env = Global.env() in
+  let _pr c = my_print_constr env c in
+  let _prr = Printer.pr_rel_context env in
+  let _prn = Printer.pr_named_context env in
+  let _pr_rel env = Printer.pr_rel_context env in
+  let (env', binders_rel), impls = interp_context_evars isevars env bl in
+  let len = List.length binders_rel in
+  let top_env = push_rel_context binders_rel env in
+  let top_arity = interp_type_evars isevars top_env arityc in
+  let full_arity = it_mkProd_or_LetIn top_arity binders_rel in
+  let argtyp, letbinders, make = telescope binders_rel in
+  let argname = id_of_string "recarg" in
+  let arg = (Name argname, None, argtyp) in
+  let binders = letbinders @ [arg] in
+  let binders_env = push_rel_context binders_rel env in
+  let rel = interp_constr isevars env r in
+  let relty = type_of env !isevars rel in
+  let relargty =
+    let ctx, ar = Reductionops.splay_prod_n env !isevars 2 relty in
+      match ctx, kind_of_term ar with
+      | [(_, None, t); (_, None, u)], Sort (Prop Null)
+	  when Reductionops.is_conv env !isevars t u -> t
+      | _, _ ->
+	  user_err_loc (constr_loc r,
+		       "Subtac_command.build_wellfounded",
+		       my_print_constr env rel ++ str " is not an homogeneous binary relation.")
+  in
+  let measure = interp_casted_constr isevars binders_env measure relargty in
+  let wf_rel, wf_rel_fun, measure_fn =
+    let measure_body, measure =
+      it_mkLambda_or_LetIn measure letbinders,
+      it_mkLambda_or_LetIn measure binders
+    in
+    let comb = constr_of_global (Lazy.force measure_on_R_ref) in
+    let wf_rel = mkApp (comb, [| argtyp; relargty; rel; measure |]) in
+    let wf_rel_fun x y =
+      mkApp (rel, [| subst1 x measure_body;
+ 		     subst1 y measure_body |])
+    in wf_rel, wf_rel_fun, measure
+  in
+  let wf_proof = mkApp (Lazy.force well_founded, [| argtyp ; wf_rel |]) in
+  let argid' = id_of_string (string_of_id argname ^ "'") in
+  let wfarg len = (Name argid', None,
+  		  mkSubset (Name argid') argtyp
+		    (wf_rel_fun (mkRel 1) (mkRel (len + 1))))
+  in
+  let intern_bl = wfarg 1 :: [arg] in
+  let _intern_env = push_rel_context intern_bl env in
+  let proj = (Lazy.force sig_).Coqlib.proj1 in
+  let wfargpred = mkLambda (Name argid', argtyp, wf_rel_fun (mkRel 1) (mkRel 3)) in
+  let projection = (* in wfarg :: arg :: before *)
+    mkApp (proj, [| argtyp ; wfargpred ; mkRel 1 |])
+  in
+  let top_arity_let = it_mkLambda_or_LetIn top_arity letbinders in
+  let intern_arity = substl [projection] top_arity_let in
+  (* substitute the projection of wfarg for something,
+     now intern_arity is in wfarg :: arg *)
+  let intern_fun_arity_prod = it_mkProd_or_LetIn intern_arity [wfarg 1] in
+  let intern_fun_binder = (Name (add_suffix recname "'"), None, intern_fun_arity_prod) in
+  let curry_fun =
+    let wfpred = mkLambda (Name argid', argtyp, wf_rel_fun (mkRel 1) (mkRel (2 * len + 4))) in
+    let arg = mkApp ((Lazy.force sig_).intro, [| argtyp; wfpred; lift 1 make; mkRel 1 |]) in
+    let app = mkApp (mkRel (2 * len + 2 (* recproof + orig binders + current binders *)), [| arg |]) in
+    let rcurry = mkApp (rel, [| measure; lift len measure |]) in
+    let lam = (Name (id_of_string "recproof"), None, rcurry) in
+    let body = it_mkLambda_or_LetIn app (lam :: binders_rel) in
+    let ty = it_mkProd_or_LetIn (lift 1 top_arity) (lam :: binders_rel) in
+      (Name recname, Some body, ty)
+  in
+  let fun_bl = intern_fun_binder :: [arg] in
+  let lift_lets = Termops.lift_rel_context 1 letbinders in
+  let intern_body =
+    let ctx = (Name recname, None, pi3 curry_fun) :: binders_rel in
+    let (r, l, impls, scopes) = 
+      Constrintern.compute_internalization_data env
+	Constrintern.Recursive full_arity impls 
+    in
+    let newimpls = [(recname, (r, l, impls @ 
+      [Some (id_of_string "recproof", Impargs.Manual, (true, false))], 
+			      scopes @ [None]))] in
+    let newimpls = Constrintern.set_internalization_env_params newimpls [] in
+    interp_casted_constr isevars ~impls:newimpls
+      (push_rel_context ctx env) body (lift 1 top_arity)
+  in
+  let intern_body_lam = it_mkLambda_or_LetIn intern_body (curry_fun :: lift_lets @ fun_bl) in
+  let prop = mkLambda (Name argname, argtyp, top_arity_let) in
+  let def =
+    mkApp (constr_of_global (Lazy.force fix_sub_ref),
+	  [| argtyp ; wf_rel ;
+	     make_existential dummy_loc ~opaque:(Define false) env isevars wf_proof ;
+	     prop ; intern_body_lam |])
+  in
+  let _ = isevars := Evarutil.nf_evar_map !isevars in
+  let binders_rel = nf_evar_context !isevars binders_rel in
+  let binders = nf_evar_context !isevars binders in
+  let top_arity = Evarutil.nf_evar !isevars top_arity in
+  let hook, recname, typ = 
+    if List.length binders_rel > 1 then
+      let name = add_suffix recname "_func" in
+      let hook l gr = 
+	let body = it_mkLambda_or_LetIn (mkApp (constr_of_global gr, [|make|])) binders_rel in
+	let ty = it_mkProd_or_LetIn top_arity binders_rel in
+	let ce =
+	  { const_entry_body = Evarutil.nf_evar !isevars body;
+	    const_entry_type = Some ty;
+	    const_entry_opaque = false;
+	    const_entry_boxed = false} 
+	in 
+	let c = Declare.declare_constant recname (DefinitionEntry ce, IsDefinition Definition) in
+	let gr = ConstRef c in
+	  if Impargs.is_implicit_args () || impls <> [] then
+	    Impargs.declare_manual_implicits false gr impls
+      in
+      let typ = it_mkProd_or_LetIn top_arity binders in
+	hook, name, typ
+    else 
+      let typ = it_mkProd_or_LetIn top_arity binders_rel in
+      let hook l gr = 
+	if Impargs.is_implicit_args () || impls <> [] then
+	  Impargs.declare_manual_implicits false gr impls
+      in hook, recname, typ
+  in
+  let fullcoqc = Evarutil.nf_evar !isevars def in
+  let fullctyp = Evarutil.nf_evar !isevars typ in
+  let evm = evars_of_term !isevars Evd.empty fullctyp in
+  let evm = evars_of_term !isevars evm fullcoqc in
+  let evm = non_instanciated_map env isevars evm in
+  let evars, _, evars_def, evars_typ = 
+    Eterm.eterm_obligations env recname !isevars evm 0 fullcoqc fullctyp 
+  in
+    Subtac_obligations.add_definition recname ~term:evars_def evars_typ evars ~hook
+
+let interp_fix_context evdref env fix =
+  interp_context_evars evdref env fix.Command.fix_binders
+
+let interp_fix_ccl evdref (env,_) fix =
+  interp_type_evars evdref env fix.Command.fix_type
+
+let interp_fix_body evdref env_rec impls (_,ctx) fix ccl =
+  let env = push_rel_context ctx env_rec in
+  let body = Option.map (fun c -> interp_casted_constr_evars evdref env ~impls c ccl) fix.Command.fix_body in
+  Option.map (fun c -> it_mkLambda_or_LetIn c ctx) body
+
+let build_fix_type (_,ctx) ccl = it_mkProd_or_LetIn ccl ctx
+
+let prepare_recursive_declaration fixnames fixtypes fixdefs =
+  let defs = List.map (subst_vars (List.rev fixnames)) fixdefs in
+  let names = List.map (fun id -> Name id) fixnames in
+  (Array.of_list names, Array.of_list fixtypes, Array.of_list defs)
+
+let rel_index n ctx =
+  list_index0 (Name n) (List.rev_map pi1 (List.filter (fun x -> pi2 x = None) ctx))
+
+let rec unfold f b =
+  match f b with
+    | Some (x, b') -> x :: unfold f b'
+    | None -> []
+
+let compute_possible_guardness_evidences (n,_) (_, fixctx) fixtype =
+  match n with
+  | Some (loc, n) -> [rel_index n fixctx]
+  | 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 len = List.length fixctx in
+	unfold (function x when x = len -> None
+	  | n -> Some (n, succ n)) 0
+
+let push_named_context = List.fold_right push_named
+
+let check_evars env initial_sigma evd c =
+  let sigma =  evd in
+  let c = nf_evar sigma c in
+  let rec proc_rec c =
+    match kind_of_term c with
+      | Evar (evk,args) ->
+          assert (Evd.mem sigma evk);
+	  if not (Evd.mem initial_sigma evk) then
+            let (loc,k) = evar_source evk evd in
+	      (match k with
+	      | QuestionMark _
+	      | ImplicitArg (_, _, false) -> ()
+	      | _ ->
+		  let evi = nf_evar_info sigma (Evd.find sigma evk) in
+		    Pretype_errors.error_unsolvable_implicit loc env sigma evi k None)
+      | _ -> iter_constr proc_rec c
+  in proc_rec c
+
+let out_def = function
+  | Some def -> def
+  | None -> error "Program Fixpoint needs defined bodies."
+
+let interp_recursive fixkind l boxed =
+  let env = Global.env() in
+  let fixl, ntnl = List.split l in
+  let kind = fixkind <> IsCoFixpoint in
+  let fixnames = List.map (fun fix -> fix.Command.fix_name) fixl in
+
+  (* Interp arities allowing for unresolved types *)
+  let evdref = ref Evd.empty in
+  let fixctxs, fiximps = List.split (List.map (interp_fix_context evdref env) fixl) in
+  let fixccls = List.map2 (interp_fix_ccl evdref) fixctxs fixl in
+  let fixtypes = List.map2 build_fix_type fixctxs fixccls in
+  let rec_sign =
+    List.fold_left2 (fun env' id t ->
+      let sort = Retyping.get_type_of env !evdref t in
+      let fixprot =
+	try mkApp (Lazy.force Subtac_utils.fix_proto, [|sort; t|])
+	with e -> t
+      in
+	(id,None,fixprot) :: env')
+      [] fixnames fixtypes
+  in
+  let env_rec = push_named_context rec_sign env in
+
+  (* Get interpretation metadatas *)
+  let impls = Constrintern.compute_full_internalization_env env 
+    Constrintern.Recursive [] fixnames fixtypes fiximps 
+  in
+  let notations = List.flatten ntnl in
+
+  (* Interp bodies with rollback because temp use of notations/implicit *)
+  let fixdefs =
+    States.with_state_protection (fun () ->
+      List.iter (Metasyntax.set_notation_for_interpretation impls) notations;
+      list_map3 (interp_fix_body evdref env_rec impls) fixctxs fixl fixccls)
+      () in
+
+  let fixdefs = List.map out_def fixdefs in
+
+  (* Instantiate evars and check all are resolved *)
+  let evd,_ = Evarconv.consider_remaining_unif_problems env_rec !evdref in
+  let evd = Typeclasses.resolve_typeclasses
+    ~onlyargs:true ~split:true ~fail:false env_rec evd
+  in
+  let evd = Evarutil.nf_evar_map evd in
+  let fixdefs = List.map (nf_evar evd) fixdefs in
+  let fixtypes = List.map (nf_evar evd) fixtypes in
+  let rec_sign = nf_named_context_evar evd rec_sign in
+
+  let recdefs = List.length rec_sign in
+  List.iter (check_evars env_rec Evd.empty evd) fixdefs;
+  List.iter (check_evars env Evd.empty evd) fixtypes;
+  Command.check_mutuality env kind (List.combine fixnames fixdefs);
+
+  (* Russell-specific code *)
+
+  (* Get the interesting evars, those that were not instanciated *)
+  let isevars = Evd.undefined_evars evd in
+  let evm =  isevars in
+  (* Solve remaining evars *)
+  let rec collect_evars id def typ imps =
+      (* Generalize by the recursive prototypes  *)
+    let def =
+      Termops.it_mkNamedLambda_or_LetIn def rec_sign
+    and typ =
+      Termops.it_mkNamedProd_or_LetIn typ rec_sign
+    in
+    let evm' = Subtac_utils.evars_of_term evm Evd.empty def in
+    let evm' = Subtac_utils.evars_of_term evm evm' typ in
+    let evars, _, def, typ = Eterm.eterm_obligations env id isevars evm' recdefs def typ in
+      (id, def, typ, imps, evars)
+  in
+  let defs = list_map4 collect_evars fixnames fixdefs fixtypes fiximps in
+    (match fixkind with
+      | IsFixpoint wfl ->
+	  let possible_indexes =
+	    list_map3 compute_possible_guardness_evidences wfl fixctxs fixtypes in
+	  let fixdecls = Array.of_list (List.map (fun x -> Name x) fixnames),
+	    Array.of_list fixtypes,
+	    Array.of_list (List.map (subst_vars (List.rev fixnames)) fixdefs)
+	  in
+	  let indexes = Pretyping.search_guard dummy_loc (Global.env ()) possible_indexes fixdecls in
+	    list_iter_i (fun i _ -> Inductive.check_fix env ((indexes,i),fixdecls)) l
+      | IsCoFixpoint -> ());
+    Subtac_obligations.add_mutual_definitions defs notations fixkind
+
+let out_n = function
+    Some n -> n
+  | None -> raise Not_found
+
+let build_recursive l b =
+  let g = List.map (fun ((_,wf,_,_,_),_) -> wf) l in
+    match g, l with
+	[(n, CWfRec r)], [(((_,id),_,bl,typ,def),ntn)] ->
+	  ignore(build_wellfounded (id, n, bl, typ, out_def def) r
+		    (match n with Some n -> mkIdentC (snd n) | None ->
+		      errorlabstrm "Subtac_command.build_recursive"
+			(str "Recursive argument required for well-founded fixpoints"))
+		    ntn false)
+
+      | [(n, CMeasureRec (m, r))], [(((_,id),_,bl,typ,def),ntn)] ->
+	  ignore(build_wellfounded (id, n, bl, typ, out_def def) (Option.default (CRef lt_ref) r)
+		    m ntn false)
+
+      | _, _ when List.for_all (fun (n, ro) -> ro = CStructRec) g ->
+	  let fixl = List.map (fun (((_,id),_,bl,typ,def),ntn) ->
+	    ({Command.fix_name = id; Command.fix_binders = bl; 
+	      Command.fix_body = def; Command.fix_type = typ},ntn)) l
+	  in interp_recursive (IsFixpoint g) fixl b
+      | _, _ ->
+	  errorlabstrm "Subtac_command.build_recursive"
+	    (str "Well-founded fixpoints not allowed in mutually recursive blocks")
+
+let build_corecursive l b =
+  let fixl = List.map (fun (((_,id),bl,typ,def),ntn) ->
+    ({Command.fix_name = id; Command.fix_binders = bl; 
+      Command.fix_body = def; Command.fix_type = typ},ntn))
+    l in
+  interp_recursive IsCoFixpoint fixl b