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Diffstat (limited to 'toplevel/command.ml')
| -rw-r--r-- | toplevel/command.ml | 1355 |
1 files changed, 0 insertions, 1355 deletions
diff --git a/toplevel/command.ml b/toplevel/command.ml deleted file mode 100644 index a9f2598e..00000000 --- a/toplevel/command.ml +++ /dev/null @@ -1,1355 +0,0 @@ -(************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) -(* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) -(************************************************************************) - -open Pp -open CErrors -open Util -open Flags -open Term -open Vars -open Termops -open Environ -open Redexpr -open Declare -open Names -open Libnames -open Globnames -open Nameops -open Constrexpr -open Constrexpr_ops -open Topconstr -open Constrintern -open Nametab -open Impargs -open Reductionops -open Indtypes -open Decl_kinds -open Pretyping -open Evarutil -open Evarconv -open Indschemes -open Misctypes -open Vernacexpr -open Sigma.Notations -open Context.Rel.Declaration -open Entries - -let do_universe poly l = Declare.do_universe poly l -let do_constraint poly l = Declare.do_constraint poly l - -let rec under_binders env sigma f n c = - if Int.equal n 0 then f env sigma c else - match kind_of_term c with - | Lambda (x,t,c) -> - mkLambda (x,t,under_binders (push_rel (LocalAssum (x,t)) env) sigma f (n-1) c) - | LetIn (x,b,t,c) -> - mkLetIn (x,b,t,under_binders (push_rel (LocalDef (x,b,t)) env) sigma f (n-1) c) - | _ -> assert false - -let rec complete_conclusion a cs = function - | CProdN (loc,bl,c) -> CProdN (loc,bl,complete_conclusion a cs c) - | CLetIn (loc,b,t,c) -> CLetIn (loc,b,t,complete_conclusion a cs c) - | CHole (loc, k, _, _) -> - let (has_no_args,name,params) = a in - if not has_no_args then - user_err_loc (loc,"", - strbrk"Cannot infer the non constant arguments of the conclusion of " - ++ pr_id cs ++ str "."); - let args = List.map (fun id -> CRef(Ident(loc,id),None)) params in - CAppExpl (loc,(None,Ident(loc,name),None),List.rev args) - | c -> c - -(* Commands of the interface *) - -(* 1| Constant definitions *) - -let red_constant_entry n ce sigma = function - | None -> ce - | Some red -> - let proof_out = ce.const_entry_body in - let env = Global.env () in - let (redfun, _) = reduction_of_red_expr env red in - let redfun env sigma c = - let sigma = Sigma.Unsafe.of_evar_map sigma in - let Sigma (c, _, _) = redfun.e_redfun env sigma c in - c - in - { ce with const_entry_body = Future.chain ~greedy:true ~pure:true proof_out - (fun ((body,ctx),eff) -> (under_binders env sigma redfun n body,ctx),eff) } - -let warn_implicits_in_term = - CWarnings.create ~name:"implicits-in-term" ~category:"implicits" - (fun () -> - strbrk "Implicit arguments declaration relies on type." ++ spc () ++ - strbrk "The term declares more implicits than the type here.") - -let interp_definition pl bl p red_option c ctypopt = - let env = Global.env() in - let ctx = Evd.make_evar_universe_context env pl in - let evdref = ref (Evd.from_ctx ctx) in - let impls, ((env_bl, ctx), imps1) = interp_context_evars env evdref bl in - let nb_args = List.length ctx in - let imps,pl,ce = - match ctypopt with - None -> - let subst = evd_comb0 Evd.nf_univ_variables evdref in - let ctx = Context.Rel.map (Vars.subst_univs_constr subst) ctx in - let env_bl = push_rel_context ctx env in - let c, imps2 = interp_constr_evars_impls ~impls env_bl evdref c in - let nf,subst = Evarutil.e_nf_evars_and_universes evdref in - let body = nf (it_mkLambda_or_LetIn c ctx) in - let vars = Universes.universes_of_constr body in - let evd = Evd.restrict_universe_context !evdref vars in - let pl, uctx = Evd.universe_context ?names:pl evd in - imps1@(Impargs.lift_implicits nb_args imps2), pl, - definition_entry ~univs:uctx ~poly:p body - | Some ctyp -> - let ty, impsty = interp_type_evars_impls ~impls env_bl evdref ctyp in - let subst = evd_comb0 Evd.nf_univ_variables evdref in - let ctx = Context.Rel.map (Vars.subst_univs_constr subst) ctx in - let env_bl = push_rel_context ctx env in - let c, imps2 = interp_casted_constr_evars_impls ~impls env_bl evdref c ty in - let nf, subst = Evarutil.e_nf_evars_and_universes evdref in - let body = nf (it_mkLambda_or_LetIn c ctx) in - let typ = nf (it_mkProd_or_LetIn ty ctx) in - let beq b1 b2 = if b1 then b2 else not b2 in - let impl_eq (x,y,z) (x',y',z') = beq x x' && beq y y' && beq z z' in - (* Check that all implicit arguments inferable from the term - are inferable from the type *) - let chk (key,va) = - impl_eq (List.assoc_f Pervasives.(=) key impsty) va (* FIXME *) - in - if not (try List.for_all chk imps2 with Not_found -> false) - then warn_implicits_in_term (); - let vars = Univ.LSet.union (Universes.universes_of_constr body) - (Universes.universes_of_constr typ) in - let ctx = Evd.restrict_universe_context !evdref vars in - let pl, uctx = Evd.universe_context ?names:pl ctx in - imps1@(Impargs.lift_implicits nb_args impsty), pl, - definition_entry ~types:typ ~poly:p - ~univs:uctx body - in - red_constant_entry (Context.Rel.length ctx) ce !evdref red_option, !evdref, pl, imps - -let check_definition (ce, evd, _, imps) = - check_evars_are_solved (Global.env ()) evd (Evd.empty,evd); - ce - -let warn_local_declaration = - CWarnings.create ~name:"local-declaration" ~category:"scope" - (fun (id,kind) -> - pr_id id ++ strbrk " is declared as a local " ++ str kind) - -let get_locality id ~kind = function -| Discharge -> - (** If a Let is defined outside a section, then we consider it as a local definition *) - warn_local_declaration (id,kind); - true -| Local -> true -| Global -> false - -let declare_global_definition ident ce local k pl imps = - let local = get_locality ident ~kind:"definition" local in - let kn = declare_constant ident ~local (DefinitionEntry ce, IsDefinition k) in - let gr = ConstRef kn in - let () = maybe_declare_manual_implicits false gr imps in - let () = Universes.register_universe_binders gr pl in - let () = definition_message ident in - gr - -let declare_definition_hook = ref ignore -let set_declare_definition_hook = (:=) declare_definition_hook -let get_declare_definition_hook () = !declare_definition_hook - -let warn_definition_not_visible = - CWarnings.create ~name:"definition-not-visible" ~category:"implicits" - (fun ident -> - strbrk "Section definition " ++ - pr_id ident ++ strbrk " is not visible from current goals") - -let declare_definition ident (local, p, k) ce pl imps hook = - let fix_exn = Future.fix_exn_of ce.const_entry_body in - let () = !declare_definition_hook ce in - let r = match local with - | Discharge when Lib.sections_are_opened () -> - let c = SectionLocalDef ce in - let _ = declare_variable ident (Lib.cwd(), c, IsDefinition k) in - let () = definition_message ident in - let gr = VarRef ident in - let () = maybe_declare_manual_implicits false gr imps in - let () = if Pfedit.refining () then - warn_definition_not_visible ident - in - gr - | Discharge | Local | Global -> - declare_global_definition ident ce local k pl imps in - Lemmas.call_hook fix_exn hook local r - -let _ = Obligations.declare_definition_ref := - (fun i k c imps hook -> declare_definition i k c [] imps hook) - -let do_definition ident k pl bl red_option c ctypopt hook = - let (ce, evd, pl', imps as def) = - interp_definition pl bl (pi2 k) red_option c ctypopt - in - if Flags.is_program_mode () then - let env = Global.env () in - let (c,ctx), sideff = Future.force ce.const_entry_body in - assert(Safe_typing.empty_private_constants = sideff); - assert(Univ.ContextSet.is_empty ctx); - let typ = match ce.const_entry_type with - | Some t -> t - | None -> Retyping.get_type_of env evd c - in - Obligations.check_evars env evd; - let obls, _, c, cty = - Obligations.eterm_obligations env ident evd 0 c typ - in - let ctx = Evd.evar_universe_context evd in - let hook = Lemmas.mk_hook (fun l r _ -> Lemmas.call_hook (fun exn -> exn) hook l r) in - ignore(Obligations.add_definition - ident ~term:c cty ctx ?pl ~implicits:imps ~kind:k ~hook obls) - else let ce = check_definition def in - ignore(declare_definition ident k ce pl' imps - (Lemmas.mk_hook - (fun l r -> Lemmas.call_hook (fun exn -> exn) hook l r;r))) - -(* 2| Variable/Hypothesis/Parameter/Axiom declarations *) - -let declare_assumption is_coe (local,p,kind) (c,ctx) pl imps impl nl (_,ident) = -match local with -| Discharge when Lib.sections_are_opened () -> - let decl = (Lib.cwd(), SectionLocalAssum ((c,ctx),p,impl), IsAssumption kind) in - let _ = declare_variable ident decl in - let () = assumption_message ident in - let () = - if is_verbose () && Pfedit.refining () then - Feedback.msg_info (str"Variable" ++ spc () ++ pr_id ident ++ - strbrk " is not visible from current goals") - in - let r = VarRef ident in - let () = Typeclasses.declare_instance None true r in - let () = if is_coe then Class.try_add_new_coercion r ~local:true false in - (r,Univ.Instance.empty,true) - -| Global | Local | Discharge -> - let local = get_locality ident ~kind:"axiom" local in - let inl = match nl with - | NoInline -> None - | DefaultInline -> Some (Flags.get_inline_level()) - | InlineAt i -> Some i - in - let ctx = Univ.ContextSet.to_context ctx in - let decl = (ParameterEntry (None,p,(c,ctx),inl), IsAssumption kind) in - let kn = declare_constant ident ~local decl in - let gr = ConstRef kn in - let () = maybe_declare_manual_implicits false gr imps in - let () = Universes.register_universe_binders gr pl in - let () = assumption_message ident in - let () = Typeclasses.declare_instance None false gr in - let () = if is_coe then Class.try_add_new_coercion gr local p in - let inst = - if p (* polymorphic *) then Univ.UContext.instance ctx - else Univ.Instance.empty - in - (gr,inst,Lib.is_modtype_strict ()) - -let interp_assumption evdref env impls bl c = - let c = prod_constr_expr c bl in - interp_type_evars_impls env evdref ~impls c - -let declare_assumptions idl is_coe k (c,ctx) pl imps impl_is_on nl = - let refs, status, _ = - List.fold_left (fun (refs,status,ctx) id -> - let ref',u',status' = - declare_assumption is_coe k (c,ctx) pl imps impl_is_on nl id in - (ref',u')::refs, status' && status, Univ.ContextSet.empty) - ([],true,ctx) idl - in - List.rev refs, status - -let do_assumptions_unbound_univs (_, poly, _ as kind) nl l = - let open Context.Named.Declaration in - let env = Global.env () in - let evdref = ref (Evd.from_env env) in - let l = - if poly then - (* Separate declarations so that A B : Type puts A and B in different levels. *) - List.fold_right (fun (is_coe,(idl,c)) acc -> - List.fold_right (fun id acc -> - (is_coe, ([id], c)) :: acc) idl acc) - l [] - else l - in - (* We intepret all declarations in the same evar_map, i.e. as a telescope. *) - let _,l = List.fold_map (fun (env,ienv) (is_coe,(idl,c)) -> - let t,imps = interp_assumption evdref env ienv [] c in - let env = - push_named_context (List.map (fun (_,id) -> LocalAssum (id,t)) idl) env in - let ienv = List.fold_right (fun (_,id) ienv -> - let impls = compute_internalization_data env Variable t imps in - Id.Map.add id impls ienv) idl ienv in - ((env,ienv),((is_coe,idl),t,imps))) - (env,empty_internalization_env) l - in - let evd = solve_remaining_evars all_and_fail_flags env !evdref (Evd.empty,!evdref) in - (* The universe constraints come from the whole telescope. *) - let evd = Evd.nf_constraints evd in - let ctx = Evd.universe_context_set evd in - let l = List.map (on_pi2 (nf_evar evd)) l in - pi2 (List.fold_left (fun (subst,status,ctx) ((is_coe,idl),t,imps) -> - let t = replace_vars subst t in - let (refs,status') = declare_assumptions idl is_coe kind (t,ctx) [] imps false nl in - let subst' = List.map2 - (fun (_,id) (c,u) -> (id,Universes.constr_of_global_univ (c,u))) - idl refs - in - (subst'@subst, status' && status, - (* The universe constraints are declared with the first declaration only. *) - Univ.ContextSet.empty)) ([],true,ctx) l) - -let do_assumptions_bound_univs coe kind nl id pl c = - let env = Global.env () in - let ctx = Evd.make_evar_universe_context env pl in - let evdref = ref (Evd.from_ctx ctx) in - let ty, impls = interp_type_evars_impls env evdref c in - let nf, subst = Evarutil.e_nf_evars_and_universes evdref in - let ty = nf ty in - let vars = Universes.universes_of_constr ty in - let evd = Evd.restrict_universe_context !evdref vars in - let pl, uctx = Evd.universe_context ?names:pl evd in - let uctx = Univ.ContextSet.of_context uctx in - let (_, _, st) = declare_assumption coe kind (ty, uctx) pl impls false nl id in - st - -let do_assumptions kind nl l = match l with -| [coe, ([id, Some pl], c)] -> - let () = match kind with - | (Discharge, _, _) when Lib.sections_are_opened () -> - let loc = fst id in - let msg = Pp.str "Section variables cannot be polymorphic." in - user_err_loc (loc, "", msg) - | _ -> () - in - do_assumptions_bound_univs coe kind nl id (Some pl) c -| _ -> - let map (coe, (idl, c)) = - let map (id, univs) = match univs with - | None -> id - | Some _ -> - let loc = fst id in - let msg = - Pp.str "Assumptions with bound universes can only be defined one at a time." in - user_err_loc (loc, "", msg) - in - (coe, (List.map map idl, c)) - in - let l = List.map map l in - do_assumptions_unbound_univs kind nl l - -(* 3a| Elimination schemes for mutual inductive definitions *) - -(* 3b| Mutual inductive definitions *) - -let push_types env idl tl = - List.fold_left2 (fun env id t -> Environ.push_rel (LocalAssum (Name id,t)) env) - env idl tl - -type structured_one_inductive_expr = { - ind_name : Id.t; - ind_univs : lident list option; - ind_arity : constr_expr; - ind_lc : (Id.t * constr_expr) list -} - -type structured_inductive_expr = - local_binder list * structured_one_inductive_expr list - -let minductive_message warn = function - | [] -> error "No inductive definition." - | [x] -> (pr_id x ++ str " is defined" ++ - if warn then str " as a non-primitive record" else mt()) - | l -> hov 0 (prlist_with_sep pr_comma pr_id l ++ - spc () ++ str "are defined") - -let check_all_names_different indl = - let ind_names = List.map (fun ind -> ind.ind_name) indl in - let cstr_names = List.map_append (fun ind -> List.map fst ind.ind_lc) indl in - let l = List.duplicates Id.equal ind_names in - let () = match l with - | [] -> () - | t :: _ -> raise (InductiveError (SameNamesTypes t)) - in - let l = List.duplicates Id.equal cstr_names in - let () = match l with - | [] -> () - | c :: _ -> raise (InductiveError (SameNamesConstructors (List.hd l))) - in - let l = List.intersect Id.equal ind_names cstr_names in - match l with - | [] -> () - | _ -> raise (InductiveError (SameNamesOverlap l)) - -let mk_mltype_data evdref env assums arity indname = - let is_ml_type = is_sort env !evdref arity in - (is_ml_type,indname,assums) - -let prepare_param = function - | LocalAssum (na,t) -> out_name na, LocalAssumEntry t - | LocalDef (na,b,_) -> out_name na, LocalDefEntry b - -(** Make the arity conclusion flexible to avoid generating an upper bound universe now, - only if the universe does not appear anywhere else. - This is really a hack to stay compatible with the semantics of template polymorphic - inductives which are recognized when a "Type" appears at the end of the conlusion in - the source syntax. *) - -let rec check_anonymous_type ind = - let open Glob_term in - match ind with - | GSort (_, GType []) -> true - | GProd (_, _, _, _, e) - | GLetIn (_, _, _, e) - | GLambda (_, _, _, _, e) - | GApp (_, e, _) - | GCast (_, e, _) -> check_anonymous_type e - | _ -> false - -let make_conclusion_flexible evdref ty poly = - if poly && isArity ty then - let _, concl = destArity ty in - match concl with - | Type u -> - (match Univ.universe_level u with - | Some u -> - evdref := Evd.make_flexible_variable !evdref true u - | None -> ()) - | _ -> () - else () - -let is_impredicative env u = - u = Prop Null || (is_impredicative_set env && u = Prop Pos) - -let interp_ind_arity env evdref ind = - let c = intern_gen IsType env ind.ind_arity in - let imps = Implicit_quantifiers.implicits_of_glob_constr ~with_products:true c in - let t, impls = understand_tcc_evars env evdref ~expected_type:IsType c, imps in - let pseudo_poly = check_anonymous_type c in - let () = if not (Reduction.is_arity env t) then - user_err_loc (constr_loc ind.ind_arity, "", str "Not an arity") - in - t, pseudo_poly, impls - -let interp_cstrs evdref env impls mldata arity ind = - let cnames,ctyps = List.split ind.ind_lc in - (* Complete conclusions of constructor types if given in ML-style syntax *) - let ctyps' = List.map2 (complete_conclusion mldata) cnames ctyps in - (* Interpret the constructor types *) - let ctyps'', cimpls = List.split (List.map (interp_type_evars_impls evdref env ~impls) ctyps') in - (cnames, ctyps'', cimpls) - -let sign_level env evd sign = - fst (List.fold_right - (fun d (lev,env) -> - match d with - | LocalDef _ -> lev, push_rel d env - | LocalAssum _ -> - let s = destSort (Reduction.whd_all env - (nf_evar evd (Retyping.get_type_of env evd (get_type d)))) - in - let u = univ_of_sort s in - (Univ.sup u lev, push_rel d env)) - sign (Univ.type0m_univ,env)) - -let sup_list min = List.fold_left Univ.sup min - -let extract_level env evd min tys = - let sorts = List.map (fun ty -> - let ctx, concl = Reduction.dest_prod_assum env ty in - sign_level env evd (LocalAssum (Anonymous, concl) :: ctx)) tys - in sup_list min sorts - -let is_flexible_sort evd u = - match Univ.Universe.level u with - | Some l -> Evd.is_flexible_level evd l - | None -> false - -let inductive_levels env evdref poly arities inds = - let destarities = List.map (fun x -> x, Reduction.dest_arity env x) arities in - let levels = List.map (fun (x,(ctx,a)) -> - if a = Prop Null then None - else Some (univ_of_sort a)) destarities - in - let cstrs_levels, min_levels, sizes = - CList.split3 - (List.map2 (fun (_,tys,_) (arity,(ctx,du)) -> - let len = List.length tys in - let minlev = Sorts.univ_of_sort du in - let minlev = - if len > 1 && not (is_impredicative env du) then - Univ.sup minlev Univ.type0_univ - else minlev - in - let minlev = - (** Indices contribute. *) - if Indtypes.is_indices_matter () && List.length ctx > 0 then ( - let ilev = sign_level env !evdref ctx in - Univ.sup ilev minlev) - else minlev - in - let clev = extract_level env !evdref minlev tys in - (clev, minlev, len)) inds destarities) - in - (* Take the transitive closure of the system of constructors *) - (* level constraints and remove the recursive dependencies *) - let levels' = Universes.solve_constraints_system (Array.of_list levels) - (Array.of_list cstrs_levels) (Array.of_list min_levels) - in - let evd, arities = - CList.fold_left3 (fun (evd, arities) cu (arity,(ctx,du)) len -> - if is_impredicative env du then - (** Any product is allowed here. *) - evd, arity :: arities - else (** If in a predicative sort, or asked to infer the type, - we take the max of: - - indices (if in indices-matter mode) - - constructors - - Type(1) if there is more than 1 constructor - *) - (** Constructors contribute. *) - let evd = - if Sorts.is_set du then - if not (Evd.check_leq evd cu Univ.type0_univ) then - raise (Indtypes.InductiveError Indtypes.LargeNonPropInductiveNotInType) - else evd - else evd - (* Evd.set_leq_sort env evd (Type cu) du *) - in - let evd = - if len >= 2 && Univ.is_type0m_univ cu then - (** "Polymorphic" type constraint and more than one constructor, - should not land in Prop. Add constraint only if it would - land in Prop directly (no informative arguments as well). *) - Evd.set_leq_sort env evd (Prop Pos) du - else evd - in - let duu = Sorts.univ_of_sort du in - let evd = - if not (Univ.is_small_univ duu) && Univ.Universe.equal cu duu then - if is_flexible_sort evd duu && not (Evd.check_leq evd Univ.type0_univ duu) then - Evd.set_eq_sort env evd (Prop Null) du - else evd - else Evd.set_eq_sort env evd (Type cu) du - in - (evd, arity :: arities)) - (!evdref,[]) (Array.to_list levels') destarities sizes - in evdref := evd; List.rev arities - -let check_named (loc, na) = match na with -| Name _ -> () -| Anonymous -> - let msg = str "Parameters must be named." in - user_err_loc (loc, "", msg) - - -let check_param = function -| LocalRawDef (na, _) -> check_named na -| LocalRawAssum (nas, Default _, _) -> List.iter check_named nas -| LocalRawAssum (nas, Generalized _, _) -> () -| LocalPattern _ -> assert false - -let interp_mutual_inductive (paramsl,indl) notations poly prv finite = - check_all_names_different indl; - List.iter check_param paramsl; - let env0 = Global.env() in - let pl = (List.hd indl).ind_univs in - let ctx = Evd.make_evar_universe_context env0 pl in - let evdref = ref Evd.(from_ctx ctx) in - let _, ((env_params, ctx_params), userimpls) = - interp_context_evars env0 evdref paramsl - in - let indnames = List.map (fun ind -> ind.ind_name) indl in - - (* Names of parameters as arguments of the inductive type (defs removed) *) - let assums = List.filter is_local_assum ctx_params in - let params = List.map (fun decl -> out_name (get_name decl)) assums in - - (* Interpret the arities *) - let arities = List.map (interp_ind_arity env_params evdref) indl in - - let fullarities = List.map (fun (c, _, _) -> it_mkProd_or_LetIn c ctx_params) arities in - let env_ar = push_types env0 indnames fullarities in - let env_ar_params = push_rel_context ctx_params env_ar in - - (* Compute interpretation metadatas *) - let indimpls = List.map (fun (_, _, impls) -> userimpls @ - lift_implicits (Context.Rel.nhyps ctx_params) impls) arities in - let arities = List.map pi1 arities and aritypoly = List.map pi2 arities in - let impls = compute_internalization_env env0 (Inductive params) indnames fullarities indimpls in - let mldatas = List.map2 (mk_mltype_data evdref env_params params) arities indnames in - - let constructors = - Metasyntax.with_syntax_protection (fun () -> - (* Temporary declaration of notations and scopes *) - List.iter (Metasyntax.set_notation_for_interpretation impls) notations; - (* Interpret the constructor types *) - List.map3 (interp_cstrs env_ar_params evdref impls) mldatas arities indl) - () in - - (* Try further to solve evars, and instantiate them *) - let sigma = solve_remaining_evars all_and_fail_flags env_params !evdref (Evd.empty,!evdref) in - evdref := sigma; - (* Compute renewed arities *) - let nf,_ = e_nf_evars_and_universes evdref in - let arities = List.map nf arities in - let constructors = List.map (fun (idl,cl,impsl) -> (idl,List.map nf cl,impsl)) constructors in - let _ = List.iter2 (fun ty poly -> make_conclusion_flexible evdref ty poly) arities aritypoly in - let arities = inductive_levels env_ar_params evdref poly arities constructors in - let nf',_ = e_nf_evars_and_universes evdref in - let nf x = nf' (nf x) in - let arities = List.map nf' arities in - let constructors = List.map (fun (idl,cl,impsl) -> (idl,List.map nf' cl,impsl)) constructors in - let ctx_params = Context.Rel.map nf ctx_params in - let evd = !evdref in - let pl, uctx = Evd.universe_context ?names:pl evd in - List.iter (check_evars env_params Evd.empty evd) arities; - Context.Rel.iter (check_evars env0 Evd.empty evd) ctx_params; - List.iter (fun (_,ctyps,_) -> - List.iter (check_evars env_ar_params Evd.empty evd) ctyps) - constructors; - - (* Build the inductive entries *) - let entries = List.map4 (fun ind arity template (cnames,ctypes,cimpls) -> { - mind_entry_typename = ind.ind_name; - mind_entry_arity = arity; - mind_entry_template = template; - mind_entry_consnames = cnames; - mind_entry_lc = ctypes - }) indl arities aritypoly constructors in - let impls = - let len = Context.Rel.nhyps ctx_params in - List.map2 (fun indimpls (_,_,cimpls) -> - indimpls, List.map (fun impls -> - userimpls @ (lift_implicits len impls)) cimpls) indimpls constructors - in - (* Build the mutual inductive entry *) - { mind_entry_params = List.map prepare_param ctx_params; - mind_entry_record = None; - mind_entry_finite = finite; - mind_entry_inds = entries; - mind_entry_polymorphic = poly; - mind_entry_private = if prv then Some false else None; - mind_entry_universes = uctx; - }, - pl, impls - -(* Very syntactical equality *) -let eq_local_binders bl1 bl2 = - List.equal local_binder_eq bl1 bl2 - -let extract_coercions indl = - let mkqid (_,((_,id),_)) = qualid_of_ident id in - let extract lc = List.filter (fun (iscoe,_) -> iscoe) lc in - List.map mkqid (List.flatten(List.map (fun (_,_,_,lc) -> extract lc) indl)) - -let extract_params indl = - let paramsl = List.map (fun (_,params,_,_) -> params) indl in - match paramsl with - | [] -> anomaly (Pp.str "empty list of inductive types") - | params::paramsl -> - if not (List.for_all (eq_local_binders params) paramsl) then error - "Parameters should be syntactically the same for each inductive type."; - params - -let extract_inductive indl = - List.map (fun (((_,indname),pl),_,ar,lc) -> { - ind_name = indname; ind_univs = pl; - ind_arity = Option.cata (fun x -> x) (CSort (Loc.ghost,GType [])) ar; - ind_lc = List.map (fun (_,((_,id),t)) -> (id,t)) lc - }) indl - -let extract_mutual_inductive_declaration_components indl = - let indl,ntnl = List.split indl in - let params = extract_params indl in - let coes = extract_coercions indl in - let indl = extract_inductive indl in - (params,indl), coes, List.flatten ntnl - -let is_recursive mie = - let rec is_recursive_constructor lift typ = - match Term.kind_of_term typ with - | Prod (_,arg,rest) -> - Termops.dependent (mkRel lift) arg || - is_recursive_constructor (lift+1) rest - | LetIn (na,b,t,rest) -> is_recursive_constructor (lift+1) rest - | _ -> false - in - match mie.mind_entry_inds with - | [ind] -> - let nparams = List.length mie.mind_entry_params in - List.exists (fun t -> is_recursive_constructor (nparams+1) t) ind.mind_entry_lc - | _ -> false - -let declare_mutual_inductive_with_eliminations mie pl impls = - (* spiwack: raises an error if the structure is supposed to be non-recursive, - but isn't *) - begin match mie.mind_entry_finite with - | BiFinite when is_recursive mie -> - if Option.has_some mie.mind_entry_record then - error "Records declared with the keywords Record or Structure cannot be recursive. You can, however, define recursive records using the Inductive or CoInductive command." - else - error ("Types declared with the keyword Variant cannot be recursive. Recursive types are defined with the Inductive and CoInductive command.") - | _ -> () - end; - let names = List.map (fun e -> e.mind_entry_typename) mie.mind_entry_inds in - let (_, kn), prim = declare_mind mie in - let mind = Global.mind_of_delta_kn kn in - List.iteri (fun i (indimpls, constrimpls) -> - let ind = (mind,i) in - let gr = IndRef ind in - maybe_declare_manual_implicits false gr indimpls; - Universes.register_universe_binders gr pl; - List.iteri - (fun j impls -> - maybe_declare_manual_implicits false - (ConstructRef (ind, succ j)) impls) - constrimpls) - impls; - let warn_prim = match mie.mind_entry_record with Some (Some _) -> not prim | _ -> false in - if_verbose Feedback.msg_info (minductive_message warn_prim names); - if mie.mind_entry_private == None - then declare_default_schemes mind; - mind - -type one_inductive_impls = - Impargs.manual_explicitation list (* for inds *)* - Impargs.manual_explicitation list list (* for constrs *) - -let do_mutual_inductive indl poly prv finite = - let indl,coes,ntns = extract_mutual_inductive_declaration_components indl in - (* Interpret the types *) - let mie,pl,impls = interp_mutual_inductive indl ntns poly prv finite in - (* Declare the mutual inductive block with its associated schemes *) - ignore (declare_mutual_inductive_with_eliminations mie pl impls); - (* Declare the possible notations of inductive types *) - List.iter Metasyntax.add_notation_interpretation ntns; - (* Declare the coercions *) - List.iter (fun qid -> Class.try_add_new_coercion (locate qid) false poly) coes; - (* If positivity is assumed declares itself as unsafe. *) - if Environ.deactivated_guard (Global.env ()) then Feedback.feedback Feedback.AddedAxiom else () - -(* 3c| Fixpoints and co-fixpoints *) - -(* An (unoptimized) function that maps preorders to partial orders... - - Input: a list of associations (x,[y1;...;yn]), all yi distincts - and different of x, meaning x<=y1, ..., x<=yn - - Output: a list of associations (x,Inr [y1;...;yn]), collecting all - distincts yi greater than x, _or_, (x, Inl y) meaning that - x is in the same class as y (in which case, x occurs - nowhere else in the association map) - - partial_order : ('a * 'a list) list -> ('a * ('a,'a list) union) list -*) - -let rec partial_order cmp = function - | [] -> [] - | (x,xge)::rest -> - let rec browse res xge' = function - | [] -> - let res = List.map (function - | (z, Inr zge) when List.mem_f cmp x zge -> - (z, Inr (List.union cmp zge xge')) - | r -> r) res in - (x,Inr xge')::res - | y::xge -> - let rec link y = - try match List.assoc_f cmp y res with - | Inl z -> link z - | Inr yge -> - if List.mem_f cmp x yge then - let res = List.remove_assoc_f cmp y res in - let res = List.map (function - | (z, Inl t) -> - if cmp t y then (z, Inl x) else (z, Inl t) - | (z, Inr zge) -> - if List.mem_f cmp y zge then - (z, Inr (List.add_set cmp x (List.remove cmp y zge))) - else - (z, Inr zge)) res in - browse ((y,Inl x)::res) xge' (List.union cmp xge (List.remove cmp x yge)) - else - browse res (List.add_set cmp y (List.union cmp xge' yge)) xge - with Not_found -> browse res (List.add_set cmp y xge') xge - in link y - in browse (partial_order cmp rest) [] xge - -let non_full_mutual_message x xge y yge isfix rest = - let reason = - if Id.List.mem x yge then - pr_id y ++ str " depends on " ++ pr_id x ++ strbrk " but not conversely" - else if Id.List.mem y xge then - pr_id x ++ str " depends on " ++ pr_id y ++ strbrk " but not conversely" - else - pr_id y ++ str " and " ++ pr_id x ++ strbrk " are not mutually dependent" in - let e = if List.is_empty rest then reason else strbrk "e.g., " ++ reason in - let k = if isfix then "fixpoint" else "cofixpoint" in - let w = - if isfix - then strbrk "Well-foundedness check may fail unexpectedly." ++ fnl() - else mt () in - strbrk "Not a fully mutually defined " ++ str k ++ fnl () ++ - str "(" ++ e ++ str ")." ++ fnl () ++ w - -let warn_non_full_mutual = - CWarnings.create ~name:"non-full-mutual" ~category:"fixpoints" - (fun (x,xge,y,yge,isfix,rest) -> - non_full_mutual_message x xge y yge isfix rest) - -let check_mutuality env isfix fixl = - let names = List.map fst fixl in - let preorder = - List.map (fun (id,def) -> - (id, List.filter (fun id' -> not (Id.equal id id') && occur_var env id' def) names)) - fixl in - let po = partial_order Id.equal preorder in - match List.filter (function (_,Inr _) -> true | _ -> false) po with - | (x,Inr xge)::(y,Inr yge)::rest -> - warn_non_full_mutual (x,xge,y,yge,isfix,rest) - | _ -> () - -type structured_fixpoint_expr = { - fix_name : Id.t; - fix_univs : lident list option; - fix_annot : Id.t Loc.located option; - fix_binders : local_binder list; - fix_body : constr_expr option; - fix_type : constr_expr -} - -let interp_fix_context env evdref isfix fix = - let before, after = if isfix then split_at_annot fix.fix_binders fix.fix_annot else [], fix.fix_binders in - let impl_env, ((env', ctx), imps) = interp_context_evars env evdref before in - let impl_env', ((env'', ctx'), imps') = interp_context_evars ~impl_env ~shift:(List.length before) env' evdref after in - let annot = Option.map (fun _ -> List.length (assums_of_rel_context ctx)) fix.fix_annot in - ((env'', ctx' @ ctx), (impl_env',imps @ imps'), annot) - -let interp_fix_ccl evdref impls (env,_) fix = - interp_type_evars_impls ~impls env evdref fix.fix_type - -let interp_fix_body env_rec evdref impls (_,ctx) fix ccl = - Option.map (fun body -> - let env = push_rel_context ctx env_rec in - let body = interp_casted_constr_evars env evdref ~impls body ccl in - it_mkLambda_or_LetIn body ctx) fix.fix_body - -let build_fix_type (_,ctx) ccl = it_mkProd_or_LetIn ccl ctx - -let declare_fix ?(opaque = false) (_,poly,_ as kind) pl ctx f ((def,_),eff) t imps = - let ce = definition_entry ~opaque ~types:t ~poly ~univs:ctx ~eff def in - declare_definition f kind ce pl imps (Lemmas.mk_hook (fun _ r -> r)) - -let _ = Obligations.declare_fix_ref := - (fun ?opaque k ctx f d t imps -> declare_fix ?opaque k [] ctx f d t imps) - -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) - -(* Jump over let-bindings. *) - -let compute_possible_guardness_evidences (ids,_,na) = - match na with - | Some i -> [i] - | 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 ?) *) - List.interval 0 (List.length ids - 1) - -type recursive_preentry = - Id.t list * constr option list * types list - -(* Wellfounded definition *) - -open Coqlib - -let contrib_name = "Program" -let subtac_dir = [contrib_name] -let fixsub_module = subtac_dir @ ["Wf"] -let tactics_module = subtac_dir @ ["Tactics"] - -let init_reference dir s () = Coqlib.gen_reference "Command" dir s -let init_constant dir s () = Coqlib.gen_constant "Command" dir s -let make_ref l s = init_reference l s -let fix_proto = init_constant tactics_module "fix_proto" -let fix_sub_ref = make_ref fixsub_module "Fix_sub" -let measure_on_R_ref = make_ref fixsub_module "MR" -let well_founded = init_constant ["Init"; "Wf"] "well_founded" -let mkSubset name typ prop = - mkApp (Universes.constr_of_global (delayed_force build_sigma).typ, - [| typ; mkLambda (name, typ, prop) |]) -let sigT = Lazy.from_fun build_sigma_type - -let make_qref s = Qualid (Loc.ghost, qualid_of_string s) -let lt_ref = make_qref "Init.Peano.lt" - -let rec telescope = function - | [] -> assert false - | [LocalAssum (n, t)] -> t, [LocalDef (n, mkRel 1, t)], mkRel 1 - | LocalAssum (n, t) :: tl -> - let ty, tys, (k, constr) = - List.fold_left - (fun (ty, tys, (k, constr)) decl -> - let t = get_type decl in - let pred = mkLambda (get_name decl, t, ty) in - let ty = Universes.constr_of_global (Lazy.force sigT).typ in - let intro = Universes.constr_of_global (Lazy.force sigT).intro in - let sigty = mkApp (ty, [|t; pred|]) in - let intro = mkApp (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 decl (prev, subst) -> - let t = get_type decl in - let p1 = Universes.constr_of_global (Lazy.force sigT).proj1 in - let p2 = Universes.constr_of_global (Lazy.force sigT).proj2 in - let proj1 = applistc p1 [t; pred; prev] in - let proj2 = applistc p2 [t; pred; prev] in - (lift 1 proj2, LocalDef (get_name decl, proj1, t) :: subst)) - (List.rev tys) tl (mkRel 1, []) - in ty, (LocalDef (n, last, t) :: subst), constr - - | LocalDef (n, b, t) :: tl -> let ty, subst, term = telescope tl in - ty, (LocalDef (n, b, t) :: subst), lift 1 term - -let nf_evar_context sigma ctx = - List.map (map_constr (Evarutil.nf_evar sigma)) ctx - -let build_wellfounded (recname,pl,n,bl,arityc,body) poly r measure notation = - Coqlib.check_required_library ["Coq";"Program";"Wf"]; - let env = Global.env() in - let ctx = Evd.make_evar_universe_context env pl in - let evdref = ref (Evd.from_ctx ctx) in - let _, ((env', binders_rel), impls) = interp_context_evars env evdref 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 top_env evdref 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 = LocalAssum (Name argname, argtyp) in - let binders = letbinders @ [arg] in - let binders_env = push_rel_context binders_rel env in - let rel, _ = interp_constr_evars_impls env evdref r in - let relty = Typing.unsafe_type_of env !evdref rel in - let relargty = - let error () = - user_err_loc (constr_loc r, - "Command.build_wellfounded", - Printer.pr_constr_env env !evdref rel ++ str " is not an homogeneous binary relation.") - in - try - let ctx, ar = Reductionops.splay_prod_n env !evdref 2 relty in - match ctx, kind_of_term ar with - | [LocalAssum (_,t); LocalAssum (_,u)], Sort (Prop Null) - when Reductionops.is_conv env !evdref t u -> t - | _, _ -> error () - with e when CErrors.noncritical e -> error () - in - let measure = interp_casted_constr_evars binders_env evdref 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 = Universes.constr_of_global (delayed_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 (delayed_force well_founded, [| argtyp ; wf_rel |]) in - let argid' = Id.of_string (Id.to_string argname ^ "'") in - let wfarg len = LocalAssum (Name argid', - 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 = (*FIXME*)Universes.constr_of_global (delayed_force build_sigma).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 = LocalAssum (Name (add_suffix recname "'"), 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 intro = (*FIXME*)Universes.constr_of_global (delayed_force build_sigma).Coqlib.intro in - let arg = mkApp (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 = LocalAssum (Name (Id.of_string "recproof"), 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 - LocalDef (Name recname, 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 = LocalAssum (Name recname, get_type curry_fun) :: binders_rel in - let (r, l, impls, scopes) = - Constrintern.compute_internalization_data env - Constrintern.Recursive full_arity impls - in - let newimpls = Id.Map.singleton recname - (r, l, impls @ [(Some (Id.of_string "recproof", Impargs.Manual, (true, false)))], - scopes @ [None]) in - interp_casted_constr_evars (push_rel_context ctx env) evdref - ~impls:newimpls 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 (Universes.constr_of_global (delayed_force fix_sub_ref), - [| argtyp ; wf_rel ; - Evarutil.e_new_evar env evdref - ~src:(Loc.ghost, Evar_kinds.QuestionMark (Evar_kinds.Define false)) wf_proof; - prop |]) - in - let def = Typing.e_solve_evars env evdref def in - let _ = evdref := Evarutil.nf_evar_map !evdref in - let def = mkApp (def, [|intern_body_lam|]) in - let binders_rel = nf_evar_context !evdref binders_rel in - let binders = nf_evar_context !evdref binders in - let top_arity = Evarutil.nf_evar !evdref 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 (Universes.constr_of_global gr, [|make|])) binders_rel in - let ty = it_mkProd_or_LetIn top_arity binders_rel in - let pl, univs = Evd.universe_context ?names:pl !evdref in - (*FIXME poly? *) - let ce = definition_entry ~poly ~types:ty ~univs (Evarutil.nf_evar !evdref body) in - (** FIXME: include locality *) - let c = Declare.declare_constant recname (DefinitionEntry ce, IsDefinition Definition) in - let gr = ConstRef c in - if Impargs.is_implicit_args () || not (List.is_empty 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 () || not (List.is_empty impls) then - Impargs.declare_manual_implicits false gr [impls] - in hook, recname, typ - in - let hook = Lemmas.mk_hook hook in - let fullcoqc = Evarutil.nf_evar !evdref def in - let fullctyp = Evarutil.nf_evar !evdref typ in - Obligations.check_evars env !evdref; - let evars, _, evars_def, evars_typ = - Obligations.eterm_obligations env recname !evdref 0 fullcoqc fullctyp - in - let ctx = Evd.evar_universe_context !evdref in - ignore(Obligations.add_definition recname ~term:evars_def ?pl - evars_typ ctx evars ~hook) - -let interp_recursive isfix fixl notations = - let open Context.Named.Declaration in - let env = Global.env() in - let fixnames = List.map (fun fix -> fix.fix_name) fixl in - - (* Interp arities allowing for unresolved types *) - let all_universes = - List.fold_right (fun sfe acc -> - match sfe.fix_univs , acc with - | None , acc -> acc - | x , None -> x - | Some ls , Some us -> - if not (CList.for_all2eq (fun x y -> Id.equal (snd x) (snd y)) ls us) then - error "(co)-recursive definitions should all have the same universe binders"; - Some us) fixl None in - let ctx = Evd.make_evar_universe_context env all_universes in - let evdref = ref (Evd.from_ctx ctx) in - let fixctxs, fiximppairs, fixannots = - List.split3 (List.map (interp_fix_context env evdref isfix) fixl) in - let fixctximpenvs, fixctximps = List.split fiximppairs in - let fixccls,fixcclimps = List.split (List.map3 (interp_fix_ccl evdref) fixctximpenvs fixctxs fixl) in - let fixtypes = List.map2 build_fix_type fixctxs fixccls in - let fixtypes = List.map (nf_evar !evdref) fixtypes in - let fiximps = List.map3 - (fun ctximps cclimps (_,ctx) -> ctximps@(Impargs.lift_implicits (List.length ctx) cclimps)) - fixctximps fixcclimps fixctxs in - let rec_sign = - List.fold_left2 - (fun env' id t -> - if Flags.is_program_mode () then - let sort = Evarutil.evd_comb1 (Typing.type_of ~refresh:true env) evdref t in - let fixprot = - try - let app = mkApp (delayed_force fix_proto, [|sort; t|]) in - Typing.e_solve_evars env evdref app - with e when CErrors.noncritical e -> t - in - LocalAssum (id,fixprot) :: env' - else LocalAssum (id,t) :: env') - [] fixnames fixtypes - in - let env_rec = push_named_context rec_sign env in - - (* Get interpretation metadatas *) - let impls = compute_internalization_env env Recursive fixnames fixtypes fiximps in - - (* Interp bodies with rollback because temp use of notations/implicit *) - let fixdefs = - Metasyntax.with_syntax_protection (fun () -> - List.iter (Metasyntax.set_notation_for_interpretation impls) notations; - List.map4 - (fun fixctximpenv -> interp_fix_body env_rec evdref (Id.Map.fold Id.Map.add fixctximpenv impls)) - fixctximpenvs fixctxs fixl fixccls) - () in - - (* Instantiate evars and check all are resolved *) - let evd = solve_unif_constraints_with_heuristics env_rec !evdref in - let evd, nf = nf_evars_and_universes evd in - let fixdefs = List.map (Option.map nf) fixdefs in - let fixtypes = List.map nf fixtypes in - let fixctxnames = List.map (fun (_,ctx) -> List.map get_name ctx) fixctxs in - - (* Build the fix declaration block *) - (env,rec_sign,all_universes,evd), (fixnames,fixdefs,fixtypes), List.combine3 fixctxnames fiximps fixannots - -let check_recursive isfix env evd (fixnames,fixdefs,_) = - check_evars_are_solved env evd (Evd.empty,evd); - if List.for_all Option.has_some fixdefs then begin - let fixdefs = List.map Option.get fixdefs in - check_mutuality env isfix (List.combine fixnames fixdefs) - end - -let interp_fixpoint l ntns = - let (env,_,pl,evd),fix,info = interp_recursive true l ntns in - check_recursive true env evd fix; - (fix,pl,Evd.evar_universe_context evd,info) - -let interp_cofixpoint l ntns = - let (env,_,pl,evd),fix,info = interp_recursive false l ntns in - check_recursive false env evd fix; - (fix,pl,Evd.evar_universe_context evd,info) - -let declare_fixpoint local poly ((fixnames,fixdefs,fixtypes),pl,ctx,fiximps) indexes ntns = - if List.exists Option.is_empty fixdefs then - (* Some bodies to define by proof *) - let thms = - List.map3 (fun id t (len,imps,_) -> ((id,pl),(t,(len,imps)))) - fixnames fixtypes fiximps in - let init_tac = - Some (List.map (Option.cata Tacmach.refine_no_check Tacticals.tclIDTAC) - fixdefs) in - let init_tac = - Option.map (List.map Proofview.V82.tactic) init_tac - in - let evd = Evd.from_ctx ctx in - Lemmas.start_proof_with_initialization (Global,poly,DefinitionBody Fixpoint) - evd (Some(false,indexes,init_tac)) thms None (Lemmas.mk_hook (fun _ _ -> ())) - else begin - (* We shortcut the proof process *) - let fixdefs = List.map Option.get fixdefs in - let fixdecls = prepare_recursive_declaration fixnames fixtypes fixdefs in - let env = Global.env() in - let indexes = search_guard Loc.ghost env indexes fixdecls in - let fiximps = List.map (fun (n,r,p) -> r) fiximps in - let vars = Universes.universes_of_constr (mkFix ((indexes,0),fixdecls)) in - let fixdecls = - List.map_i (fun i _ -> mkFix ((indexes,i),fixdecls)) 0 fixnames in - let evd = Evd.from_ctx ctx in - let evd = Evd.restrict_universe_context evd vars in - let fixdecls = List.map Safe_typing.mk_pure_proof fixdecls in - let pl, ctx = Evd.universe_context ?names:pl evd in - ignore (List.map4 (declare_fix (local, poly, Fixpoint) pl ctx) - fixnames fixdecls fixtypes fiximps); - (* Declare the recursive definitions *) - fixpoint_message (Some indexes) fixnames; - end; - (* Declare notations *) - List.iter Metasyntax.add_notation_interpretation ntns - -let declare_cofixpoint local poly ((fixnames,fixdefs,fixtypes),pl,ctx,fiximps) ntns = - if List.exists Option.is_empty fixdefs then - (* Some bodies to define by proof *) - let thms = - List.map3 (fun id t (len,imps,_) -> ((id,pl),(t,(len,imps)))) - fixnames fixtypes fiximps in - let init_tac = - Some (List.map (Option.cata Tacmach.refine_no_check Tacticals.tclIDTAC) - fixdefs) in - let init_tac = - Option.map (List.map Proofview.V82.tactic) init_tac - in - let evd = Evd.from_ctx ctx in - Lemmas.start_proof_with_initialization (Global,poly, DefinitionBody CoFixpoint) - evd (Some(true,[],init_tac)) thms None (Lemmas.mk_hook (fun _ _ -> ())) - else begin - (* We shortcut the proof process *) - let fixdefs = List.map Option.get fixdefs in - let fixdecls = prepare_recursive_declaration fixnames fixtypes fixdefs in - let fixdecls = List.map_i (fun i _ -> mkCoFix (i,fixdecls)) 0 fixnames in - let vars = Universes.universes_of_constr (List.hd fixdecls) in - let fixdecls = List.map Safe_typing.mk_pure_proof fixdecls in - let fiximps = List.map (fun (len,imps,idx) -> imps) fiximps in - let evd = Evd.from_ctx ctx in - let evd = Evd.restrict_universe_context evd vars in - let pl, ctx = Evd.universe_context ?names:pl evd in - ignore (List.map4 (declare_fix (local, poly, CoFixpoint) pl ctx) - fixnames fixdecls fixtypes fiximps); - (* Declare the recursive definitions *) - cofixpoint_message fixnames - end; - (* Declare notations *) - List.iter Metasyntax.add_notation_interpretation ntns - -let extract_decreasing_argument limit = function - | (na,CStructRec) -> na - | (na,_) when not limit -> na - | _ -> error - "Only structural decreasing is supported for a non-Program Fixpoint" - -let extract_fixpoint_components limit l = - let fixl, ntnl = List.split l in - let fixl = List.map (fun (((_,id),pl),ann,bl,typ,def) -> - let ann = extract_decreasing_argument limit ann in - {fix_name = id; fix_annot = ann; fix_univs = pl; - fix_binders = bl; fix_body = def; fix_type = typ}) fixl in - fixl, List.flatten ntnl - -let extract_cofixpoint_components l = - let fixl, ntnl = List.split l in - List.map (fun (((_,id),pl),bl,typ,def) -> - {fix_name = id; fix_annot = None; fix_univs = pl; - fix_binders = bl; fix_body = def; fix_type = typ}) fixl, - List.flatten ntnl - -let out_def = function - | Some def -> def - | None -> error "Program Fixpoint needs defined bodies." - -let collect_evars_of_term evd c ty = - let evars = Evar.Set.union (Evd.evars_of_term c) (Evd.evars_of_term ty) in - Evar.Set.fold (fun ev acc -> Evd.add acc ev (Evd.find_undefined evd ev)) - evars (Evd.from_ctx (Evd.evar_universe_context evd)) - -let do_program_recursive local p fixkind fixl ntns = - let isfix = fixkind != Obligations.IsCoFixpoint in - let (env, rec_sign, pl, evd), fix, info = - interp_recursive isfix fixl ntns - in - (* Program-specific code *) - (* Get the interesting evars, those that were not instanciated *) - let evd = Typeclasses.resolve_typeclasses ~filter:Typeclasses.no_goals ~fail:true env evd in - (* Solve remaining evars *) - let evd = nf_evar_map_undefined evd in - let collect_evars id def typ imps = - (* Generalize by the recursive prototypes *) - let def = - nf_evar evd (Termops.it_mkNamedLambda_or_LetIn def rec_sign) - and typ = - nf_evar evd (Termops.it_mkNamedProd_or_LetIn typ rec_sign) - in - let evm = collect_evars_of_term evd def typ in - let evars, _, def, typ = - Obligations.eterm_obligations env id evm - (List.length rec_sign) def typ - in (id, def, typ, imps, evars) - in - let (fixnames,fixdefs,fixtypes) = fix in - let fiximps = List.map pi2 info in - let fixdefs = List.map out_def fixdefs in - let defs = List.map4 collect_evars fixnames fixdefs fixtypes fiximps in - let () = if isfix then begin - let possible_indexes = List.map compute_possible_guardness_evidences info 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 - Loc.ghost (Global.env ()) possible_indexes fixdecls in - List.iteri (fun i _ -> - Inductive.check_fix env - ((indexes,i),fixdecls)) - fixl - end in - let ctx = Evd.evar_universe_context evd in - let kind = match fixkind with - | Obligations.IsFixpoint _ -> (local, p, Fixpoint) - | Obligations.IsCoFixpoint -> (local, p, CoFixpoint) - in - Obligations.add_mutual_definitions defs ~kind ?pl ctx ntns fixkind - -let do_program_fixpoint local poly l = - let g = List.map (fun ((_,wf,_,_,_),_) -> wf) l in - match g, l with - | [(n, CWfRec r)], [((((_,id),pl),_,bl,typ,def),ntn)] -> - let recarg = - match n with - | Some n -> mkIdentC (snd n) - | None -> - errorlabstrm "do_program_fixpoint" - (str "Recursive argument required for well-founded fixpoints") - in build_wellfounded (id, pl, n, bl, typ, out_def def) poly r recarg ntn - - | [(n, CMeasureRec (m, r))], [((((_,id),pl),_,bl,typ,def),ntn)] -> - build_wellfounded (id, pl, n, bl, typ, out_def def) poly - (Option.default (CRef (lt_ref,None)) r) m ntn - - | _, _ when List.for_all (fun (n, ro) -> ro == CStructRec) g -> - let fixl,ntns = extract_fixpoint_components true l in - let fixkind = Obligations.IsFixpoint g in - do_program_recursive local poly fixkind fixl ntns - - | _, _ -> - errorlabstrm "do_program_fixpoint" - (str "Well-founded fixpoints not allowed in mutually recursive blocks") - -let check_safe () = - let open Declarations in - let flags = Environ.typing_flags (Global.env ()) in - flags.check_universes && flags.check_guarded - -let do_fixpoint local poly l = - if Flags.is_program_mode () then do_program_fixpoint local poly l - else - let fixl, ntns = extract_fixpoint_components true l in - let (_, _, _, info as fix) = interp_fixpoint fixl ntns in - let possible_indexes = - List.map compute_possible_guardness_evidences info in - declare_fixpoint local poly fix possible_indexes ntns; - if not (check_safe ()) then Feedback.feedback Feedback.AddedAxiom else () - -let do_cofixpoint local poly l = - let fixl,ntns = extract_cofixpoint_components l in - if Flags.is_program_mode () then - do_program_recursive local poly Obligations.IsCoFixpoint fixl ntns - else - let cofix = interp_cofixpoint fixl ntns in - declare_cofixpoint local poly cofix ntns; - if not (check_safe ()) then Feedback.feedback Feedback.AddedAxiom else () |