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Diffstat (limited to 'vernac/comInductive.ml')
| -rw-r--r-- | vernac/comInductive.ml | 581 |
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diff --git a/vernac/comInductive.ml b/vernac/comInductive.ml new file mode 100644 index 0000000000..977e804da2 --- /dev/null +++ b/vernac/comInductive.ml @@ -0,0 +1,581 @@ +(************************************************************************) +(* * The Coq Proof Assistant / The Coq Development Team *) +(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *) +(* <O___,, * (see CREDITS file for the list of authors) *) +(* \VV/ **************************************************************) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(* * (see LICENSE file for the text of the license) *) +(************************************************************************) + +open Pp +open CErrors +open Sorts +open Util +open Constr +open Context +open Environ +open Declare +open Names +open Libnames +open Globnames +open Nameops +open Constrexpr +open Constrexpr_ops +open Constrintern +open Impargs +open Reductionops +open Type_errors +open Pretyping +open Indschemes +open Context.Rel.Declaration +open Entries + +module RelDecl = Context.Rel.Declaration + +(* 3b| Mutual inductive definitions *) + +let warn_auto_template = + CWarnings.create ~name:"auto-template" ~category:"vernacular" ~default:CWarnings.Disabled + (fun id -> + Pp.(strbrk "Automatically declaring " ++ Id.print id ++ + strbrk " as template polymorphic. Use attributes or " ++ + strbrk "disable Auto Template Polymorphism to avoid this warning.")) + +let should_auto_template = + let open Goptions in + let auto = ref true in + let () = declare_bool_option + { optdepr = false; + optname = "Automatically make some inductive types template polymorphic"; + optkey = ["Auto";"Template";"Polymorphism"]; + optread = (fun () -> !auto); + optwrite = (fun b -> auto := b); } + in + fun id would_auto -> + let b = !auto && would_auto in + if b then warn_auto_template id; + b + +let rec complete_conclusion a cs = CAst.map_with_loc (fun ?loc -> function + | CProdN (bl,c) -> CProdN (bl,complete_conclusion a cs c) + | CLetIn (na,b,t,c) -> CLetIn (na,b,t,complete_conclusion a cs c) + | CHole (k, _, _) -> + let (has_no_args,name,params) = a in + if not has_no_args then + user_err ?loc + (strbrk"Cannot infer the non constant arguments of the conclusion of " + ++ Id.print cs ++ str "."); + let args = List.map (fun id -> CAst.(make ?loc @@ CRef(qualid_of_ident ?loc id,None))) params in + CAppExpl ((None,qualid_of_ident ?loc name,None),List.rev args) + | c -> c + ) + +let push_types env idl rl tl = + List.fold_left3 (fun env id r t -> EConstr.push_rel (LocalAssum (make_annot (Name id) r,t)) env) + env idl rl tl + +type structured_one_inductive_expr = { + ind_name : Id.t; + ind_arity : constr_expr; + ind_lc : (Id.t * constr_expr) list +} + +type structured_inductive_expr = + local_binder_expr list * structured_one_inductive_expr list + +let minductive_message = function + | [] -> user_err Pp.(str "No inductive definition.") + | [x] -> (Id.print x ++ str " is defined") + | l -> hov 0 (prlist_with_sep pr_comma Id.print 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 sigma env assums arity indname = + let is_ml_type = is_sort env sigma arity in + (is_ml_type,indname,assums) + +(** 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 DAst.get ind with + | GSort (GType []) -> true + | GProd ( _, _, _, e) + | GLetIn (_, _, _, e) + | GLambda (_, _, _, e) + | GApp (e, _) + | GCast (e, _) -> check_anonymous_type e + | _ -> false + +let make_conclusion_flexible sigma = function + | None -> sigma + | Some s -> + (match EConstr.ESorts.kind sigma s with + | Type u -> + (match Univ.universe_level u with + | Some u -> + Evd.make_flexible_variable sigma ~algebraic:true u + | None -> sigma) + | _ -> sigma) + +let interp_ind_arity env sigma ind = + let c = intern_gen IsType env sigma ind.ind_arity in + let impls = Implicit_quantifiers.implicits_of_glob_constr ~with_products:true c in + let sigma,t = understand_tcc env sigma ~expected_type:IsType c in + let pseudo_poly = check_anonymous_type c in + match Reductionops.sort_of_arity env sigma t with + | exception Invalid_argument _ -> + user_err ?loc:(constr_loc ind.ind_arity) (str "Not an arity") + | s -> + let concl = if pseudo_poly then Some s else None in + sigma, (t, Retyping.relevance_of_sort s, concl, impls) + +let interp_cstrs env sigma 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 sigma, (ctyps'', cimpls) = + on_snd List.split @@ + List.fold_left_map (fun sigma l -> + interp_type_evars_impls ~program_mode:false env sigma ~impls l) sigma ctyps' in + sigma, (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 + (EConstr.to_constr evd (Retyping.get_type_of env evd (EConstr.of_constr (RelDecl.get_type d))))) + in + let u = univ_of_sort s in + (Univ.sup u lev, push_rel d env)) + sign (Univ.Universe.sprop,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 (make_annot Anonymous Sorts.Relevant, 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 + +(**********************************************************************) +(* Tools for template polymorphic inductive types *) + +(* Miscellaneous functions to remove or test local univ assumed to + occur only in the le constraints *) + +(* + Solve a system of universe constraint of the form + + u_s11, ..., u_s1p1, w1 <= u1 + ... + u_sn1, ..., u_snpn, wn <= un + +where + + - the ui (1 <= i <= n) are universe variables, + - the sjk select subsets of the ui for each equations, + - the wi are arbitrary complex universes that do not mention the ui. +*) + +let is_direct_sort_constraint s v = match s with + | Some u -> Univ.univ_level_mem u v + | None -> false + +let solve_constraints_system levels level_bounds = + let open Univ in + let levels = + Array.mapi (fun i o -> + match o with + | Some u -> + (match Universe.level u with + | Some u -> Some u + | _ -> level_bounds.(i) <- Universe.sup level_bounds.(i) u; None) + | None -> None) + levels in + let v = Array.copy level_bounds in + let nind = Array.length v in + let clos = Array.map (fun _ -> Int.Set.empty) levels in + (* First compute the transitive closure of the levels dependencies *) + for i=0 to nind-1 do + for j=0 to nind-1 do + if not (Int.equal i j) && is_direct_sort_constraint levels.(j) v.(i) then + clos.(i) <- Int.Set.add j clos.(i); + done; + done; + let rec closure () = + let continue = ref false in + Array.iteri (fun i deps -> + let deps' = + Int.Set.fold (fun j acc -> Int.Set.union acc clos.(j)) deps deps + in + if Int.Set.equal deps deps' then () + else (clos.(i) <- deps'; continue := true)) + clos; + if !continue then closure () + else () + in + closure (); + for i=0 to nind-1 do + for j=0 to nind-1 do + if not (Int.equal i j) && Int.Set.mem j clos.(i) then + (v.(i) <- Universe.sup v.(i) level_bounds.(j)); + done; + done; + v + +let inductive_levels env evd 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 Sorts.is_prop a || Sorts.is_sprop a 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_sort env du) then + Univ.sup minlev Univ.type0_univ + else minlev + in + let minlev = + (* Indices contribute. *) + if indices_matter env && List.length ctx > 0 then ( + let ilev = sign_level env evd ctx in + Univ.sup ilev minlev) + else minlev + in + let clev = extract_level env evd 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' = solve_constraints_system (Array.of_list levels) + (Array.of_list cstrs_levels) + in + let evd, arities = + CList.fold_left3 (fun (evd, arities) cu (arity,(ctx,du)) len -> + if is_impredicative_sort 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 (InductiveError 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 Sorts.set 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 Sorts.prop du + else evd + else Evd.set_eq_sort env evd (sort_of_univ cu) du + in + (evd, arity :: arities)) + (evd,[]) (Array.to_list levels') destarities sizes + in evd, List.rev arities + +let check_named {CAst.loc;v=na} = match na with +| Name _ -> () +| Anonymous -> + let msg = str "Parameters must be named." in + user_err ?loc msg + + +let check_param = function +| CLocalDef (na, _, _) -> check_named na +| CLocalAssum (nas, Default _, _) -> List.iter check_named nas +| CLocalAssum (nas, Generalized _, _) -> () +| CLocalPattern {CAst.loc} -> + Loc.raise ?loc (Stream.Error "pattern with quote not allowed here") + +let restrict_inductive_universes sigma ctx_params arities constructors = + let merge_universes_of_constr c = + Univ.LSet.union (EConstr.universes_of_constr sigma (EConstr.of_constr c)) in + let uvars = Univ.LSet.empty in + let uvars = Context.Rel.(fold_outside (Declaration.fold_constr merge_universes_of_constr) ctx_params ~init:uvars) in + let uvars = List.fold_right merge_universes_of_constr arities uvars in + let uvars = List.fold_right (fun (_,ctypes,_) -> List.fold_right merge_universes_of_constr ctypes) constructors uvars in + Evd.restrict_universe_context sigma uvars + +let interp_mutual_inductive_gen env0 ~template udecl (uparamsl,paramsl,indl) notations cum poly prv finite = + check_all_names_different indl; + List.iter check_param paramsl; + if not (List.is_empty uparamsl) && not (List.is_empty notations) + then user_err (str "Inductives with uniform parameters may not have attached notations."); + let sigma, udecl = interp_univ_decl_opt env0 udecl in + let sigma, (uimpls, ((env_uparams, ctx_uparams), useruimpls)) = + interp_context_evars ~program_mode:false env0 sigma uparamsl in + let sigma, (impls, ((env_params, ctx_params), userimpls)) = + interp_context_evars ~program_mode:false ~impl_env:uimpls env_uparams sigma 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 (RelDecl.get_name %> Name.get_id) assums in + + (* Interpret the arities *) + let sigma, arities = List.fold_left_map (fun sigma -> interp_ind_arity env_params sigma) sigma indl in + let arities, relevances, arityconcl, indimpls = List.split4 arities in + + let fullarities = List.map (fun c -> EConstr.it_mkProd_or_LetIn c ctx_params) arities in + let env_ar = push_types env_uparams indnames relevances fullarities in + let env_ar_params = EConstr.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) indimpls in + let impls = compute_internalization_env env_uparams sigma ~impls (Inductive (params,true)) indnames fullarities indimpls in + let ntn_impls = compute_internalization_env env_uparams sigma (Inductive (params,true)) indnames fullarities indimpls in + let mldatas = List.map2 (mk_mltype_data sigma env_params params) arities indnames in + + let sigma, constructors = + Metasyntax.with_syntax_protection (fun () -> + (* Temporary declaration of notations and scopes *) + List.iter (Metasyntax.set_notation_for_interpretation env_params ntn_impls) notations; + (* Interpret the constructor types *) + List.fold_left3_map (fun sigma -> interp_cstrs env_ar_params sigma impls) sigma mldatas arities indl) + () in + + (* generalize over the uniform parameters *) + let nparams = Context.Rel.length ctx_params in + let nuparams = Context.Rel.length ctx_uparams in + let uargs = Context.Rel.to_extended_vect EConstr.mkRel 0 ctx_uparams in + let uparam_subst = + List.init (List.length indl) EConstr.(fun i -> mkApp (mkRel (i + 1 + nuparams), uargs)) + @ List.init nuparams EConstr.(fun i -> mkRel (i + 1)) in + let generalize_constructor c = EConstr.Unsafe.to_constr (EConstr.Vars.substnl uparam_subst nparams c) in + let constructors = List.map (fun (cnames,ctypes,cimpls) -> + (cnames,List.map generalize_constructor ctypes,cimpls)) + constructors + in + let ctx_params = ctx_params @ ctx_uparams in + let userimpls = useruimpls @ (lift_implicits (Context.Rel.nhyps ctx_uparams) userimpls) in + let indimpls = List.map (fun iimpl -> useruimpls @ (lift_implicits (Context.Rel.nhyps ctx_uparams) iimpl)) indimpls in + let fullarities = List.map (fun c -> EConstr.it_mkProd_or_LetIn c ctx_uparams) fullarities in + let env_ar = push_types env0 indnames relevances fullarities in + let env_ar_params = EConstr.push_rel_context ctx_params env_ar in + + (* Try further to solve evars, and instantiate them *) + let sigma = solve_remaining_evars all_and_fail_flags env_params sigma in + (* Compute renewed arities *) + let sigma = Evd.minimize_universes sigma in + let nf = Evarutil.nf_evars_universes sigma in + let constructors = List.map (fun (idl,cl,impsl) -> (idl,List.map nf cl,impsl)) constructors in + let arities = List.map EConstr.(to_constr sigma) arities in + let sigma = List.fold_left make_conclusion_flexible sigma arityconcl in + let sigma, arities = inductive_levels env_ar_params sigma poly arities constructors in + let sigma = Evd.minimize_universes sigma in + let nf = Evarutil.nf_evars_universes sigma 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 = List.map Termops.(map_rel_decl (EConstr.to_constr sigma)) ctx_params in + let arityconcl = List.map (Option.map (EConstr.ESorts.kind sigma)) arityconcl in + let sigma = restrict_inductive_universes sigma ctx_params arities constructors in + let uctx = Evd.check_univ_decl ~poly sigma udecl in + List.iter (fun c -> check_evars env_params (Evd.from_env env_params) sigma (EConstr.of_constr c)) arities; + Context.Rel.iter (fun c -> check_evars env0 (Evd.from_env env0) sigma (EConstr.of_constr c)) ctx_params; + List.iter (fun (_,ctyps,_) -> + List.iter (fun c -> check_evars env_ar_params (Evd.from_env env_ar_params) sigma (EConstr.of_constr c)) ctyps) + constructors; + + (* Build the inductive entries *) + let entries = List.map4 (fun ind arity concl (cnames,ctypes,cimpls) -> + let template = match template with + | Some template -> + if poly && template then user_err Pp.(strbrk "template and polymorphism not compatible"); + template + | None -> + should_auto_template ind.ind_name (not poly && + Option.cata (fun s -> not (Sorts.is_small s)) false concl) + in + { mind_entry_typename = ind.ind_name; + mind_entry_arity = arity; + mind_entry_template = template; + mind_entry_consnames = cnames; + mind_entry_lc = ctypes + }) + indl arities arityconcl 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 + let variance = if poly && cum then Some (InferCumulativity.dummy_variance uctx) else None in + (* Build the mutual inductive entry *) + let mind_ent = + { mind_entry_params = ctx_params; + mind_entry_record = None; + mind_entry_finite = finite; + mind_entry_inds = entries; + mind_entry_private = if prv then Some false else None; + mind_entry_universes = uctx; + mind_entry_variance = variance; + } + in + (if poly && cum then + InferCumulativity.infer_inductive env_ar mind_ent + else mind_ent), Evd.universe_binders sigma, impls + +let interp_mutual_inductive ~template udecl (paramsl,indl) notations cum poly prv finite = + interp_mutual_inductive_gen (Global.env()) ~template udecl ([],paramsl,indl) notations cum poly prv finite + +(* Very syntactical equality *) +let eq_local_binders bl1 bl2 = + List.equal local_binder_eq bl1 bl2 + +let extract_coercions indl = + let mkqid (_,({CAst.v=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 user_err Pp.(str + "Parameters should be syntactically the same for each inductive type."); + params + +let extract_inductive indl = + List.map (fun ({CAst.v=indname},_,ar,lc) -> { + ind_name = indname; + ind_arity = Option.cata (fun x -> x) (CAst.make @@ CSort (Glob_term.GType [])) ar; + ind_lc = List.map (fun (_,({CAst.v=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 Constr.kind typ with + | Prod (_,arg,rest) -> + not (EConstr.Vars.noccurn Evd.empty (* FIXME *) lift (EConstr.of_constr 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 warn_non_primitive_record = + CWarnings.create ~name:"non-primitive-record" ~category:"record" + (fun indsp -> + (hov 0 (str "The record " ++ Nametab.pr_global_env Id.Set.empty (IndRef indsp) ++ + strbrk" could not be defined as a primitive record"))) + +let declare_mutual_inductive_with_eliminations ?(primitive_expected=false) 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 + | Declarations.BiFinite when is_recursive mie -> + if Option.has_some mie.mind_entry_record then + user_err Pp.(str "Records declared with the keywords Record or Structure cannot be recursive. You can, however, define recursive records using the Inductive or CoInductive command.") + else + user_err Pp.(str ("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 + if primitive_expected && not prim then warn_non_primitive_record (mind,0); + Declare.declare_univ_binders (IndRef (mind,0)) pl; + List.iteri (fun i (indimpls, constrimpls) -> + let ind = (mind,i) in + let gr = IndRef ind in + maybe_declare_manual_implicits false gr indimpls; + List.iteri + (fun j impls -> + maybe_declare_manual_implicits false + (ConstructRef (ind, succ j)) impls) + constrimpls) + impls; + Flags.if_verbose Feedback.msg_info (minductive_message 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 *) + +type uniform_inductive_flag = + | UniformParameters + | NonUniformParameters + +let do_mutual_inductive ~template udecl indl cum poly prv ~uniform finite = + let (params,indl),coes,ntns = extract_mutual_inductive_declaration_components indl in + (* Interpret the types *) + let indl = match uniform with UniformParameters -> (params, [], indl) | NonUniformParameters -> ([], params, indl) in + let mie,pl,impls = interp_mutual_inductive_gen (Global.env()) ~template udecl indl ntns cum 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 (Global.env ())) ntns; + (* Declare the coercions *) + List.iter (fun qid -> Class.try_add_new_coercion (Nametab.locate qid) ~local:false poly) coes; + (* If positivity is assumed declares itself as unsafe. *) + if Environ.deactivated_guard (Global.env ()) then Feedback.feedback Feedback.AddedAxiom else () |
