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|
(************************************************************************)
(* 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 Errors
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 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 Feedback.msg_warning
(strbrk "Implicit arguments declaration relies on type." ++ spc () ++
strbrk "The term declares more implicits than the type here.");
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 get_locality id = function
| Discharge ->
(** If a Let is defined outside a section, then we consider it as a local definition *)
let msg = pr_id id ++ strbrk " is declared as a local definition" in
let () = Feedback.msg_warning msg in
true
| Local -> true
| Global -> false
let declare_global_definition ident ce local k pl imps =
let local = get_locality ident 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 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
let msg = strbrk "Section definition " ++
pr_id ident ++ strbrk " is not visible from current goals" in
Feedback.msg_warning msg
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_warning (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 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
let ty, impls = interp_type_evars_impls env evdref ~impls c in
let evd, nf = nf_evars_and_universes !evdref in
let ctx = Evd.universe_context_set evd in
((nf ty, ctx), impls)
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
let _,l = List.fold_map (fun (env,ienv) (is_coe,(idl,c)) ->
let (t,ctx),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,(ctx,imps))))
(env,empty_internalization_env) l
in
let evd = solve_remaining_evars all_and_fail_flags env !evdref (Evd.empty,!evdref) in
let l = List.map (on_pi2 (nf_evar evd)) l in
snd (List.fold_left (fun (subst,status) ((is_coe,idl),t,(ctx,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)) ([],true) 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_betadeltaiota 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) && Evd.check_eq evd cu duu then
if is_flexible_sort evd duu then
if Evd.check_leq evd Univ.type0_univ duu then
evd
else 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 _, _) -> ()
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 ++ str " but not conversely"
else if Id.List.mem y xge then
pr_id x ++ str " depends on " ++ pr_id y ++ str " but not conversely"
else
pr_id y ++ str " and " ++ pr_id x ++ str " are not mutually dependent" in
let e = if List.is_empty rest then reason else str "e.g., " ++ reason in
let k = if isfix then "fixpoint" else "cofixpoint" in
let w =
if isfix
then str "Well-foundedness check may fail unexpectedly." ++ fnl()
else mt () in
str "Not a fully mutually defined " ++ str k ++ fnl () ++
str "(" ++ e ++ str ")." ++ fnl () ++ w
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 ->
Feedback.msg_warning (non_full_mutual_message 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 () = check_evars_are_solved env !evdref (Evd.empty,!evdref) 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 Errors.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 (ls @ 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 Errors.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 = consider_remaining_unif_problems 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 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 evars, _, def, typ =
Obligations.eterm_obligations env id evd
(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 ()
|