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inductiveops.ml
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(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * Copyright INRIA, CNRS and contributors *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(* \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 CErrors
open Util
open Names
open Term
open Constr
open Vars
open Context
open Declarations
open Declareops
open Environ
open Reductionops
open Context.Rel.Declaration
(* The following three functions are similar to the ones defined in
Inductive, but they expect an env *)
let type_of_inductive env (ind,u) =
let (mib,_ as specif) = Inductive.lookup_mind_specif env ind in
Typeops.check_hyps_inclusion env (GlobRef.IndRef ind) mib.mind_hyps;
let t = Inductive.type_of_inductive (specif,u) in
Arguments_renaming.rename_type t (IndRef ind)
let e_type_of_inductive env sigma (ind,u) =
let (mib,_ as specif) = Inductive.lookup_mind_specif env ind in
Reductionops.check_hyps_inclusion env sigma (GlobRef.IndRef ind) mib.mind_hyps;
let t = Inductive.type_of_inductive (specif, EConstr.Unsafe.to_instance u) in
EConstr.of_constr (Arguments_renaming.rename_type t (IndRef ind))
(* Return type as quoted by the user *)
let type_of_constructor env (cstr,u) =
let (mib,_ as specif) =
Inductive.lookup_mind_specif env (inductive_of_constructor cstr) in
Typeops.check_hyps_inclusion env (GlobRef.ConstructRef cstr) mib.mind_hyps;
let t = Inductive.type_of_constructor (cstr,u) specif in
Arguments_renaming.rename_type t (ConstructRef cstr)
let e_type_of_constructor env sigma (cstr,u) =
let (mib,_ as specif) =
Inductive.lookup_mind_specif env (inductive_of_constructor cstr) in
Reductionops.check_hyps_inclusion env sigma (GlobRef.ConstructRef cstr) mib.mind_hyps;
let t = Inductive.type_of_constructor (cstr,EConstr.Unsafe.to_instance u) specif in
EConstr.of_constr (Arguments_renaming.rename_type t (ConstructRef cstr))
(* Return constructor types in user form *)
let type_of_constructors env (ind,u as indu) =
let specif = Inductive.lookup_mind_specif env ind in
Inductive.type_of_constructors indu specif
(* Return constructor types in normal form *)
let arities_of_constructors env (ind,u as indu) =
let specif = Inductive.lookup_mind_specif env ind in
Inductive.arities_of_constructors indu specif
(* [inductive_family] = [inductive_instance] applied to global parameters *)
type inductive_family = pinductive * constr list
let make_ind_family (mis, params) = (mis,params)
let dest_ind_family (mis,params) : inductive_family = (mis,params)
let map_ind_family f (mis,params) = (mis, List.map f params)
let liftn_inductive_family n d = map_ind_family (liftn n d)
let lift_inductive_family n = liftn_inductive_family n 1
let substnl_ind_family l n = map_ind_family (substnl l n)
let relevance_of_inductive_family env (ind,_ : inductive_family) =
Inductive.relevance_of_inductive env ind
type inductive_type = IndType of inductive_family * EConstr.constr list
let ind_of_ind_type = function IndType (((ind,_),_),_) -> ind
let make_ind_type (indf, realargs) = IndType (indf,realargs)
let dest_ind_type (IndType (indf,realargs)) = (indf,realargs)
let map_inductive_type f (IndType (indf, realargs)) =
let f' c = EConstr.Unsafe.to_constr (f (EConstr.of_constr c)) in
IndType (map_ind_family f' indf, List.map f realargs)
let liftn_inductive_type n d = map_inductive_type (EConstr.Vars.liftn n d)
let lift_inductive_type n = liftn_inductive_type n 1
let substnl_ind_type l n = map_inductive_type (EConstr.Vars.substnl l n)
let relevance_of_inductive_type env (IndType (indf, _)) =
relevance_of_inductive_family env indf
let mkAppliedInd (IndType ((ind,params), realargs)) =
let open EConstr in
let ind = on_snd EInstance.make ind in
applist (mkIndU ind, (List.map EConstr.of_constr params)@realargs)
(* Does not consider imbricated or mutually recursive types *)
let mis_is_recursive_subset listind rarg =
let one_is_rec rvec =
List.exists
(fun ra ->
match dest_recarg ra with
| Mrec (_,i) -> Int.List.mem i listind
| _ -> false) rvec
in
Array.exists one_is_rec (dest_subterms rarg)
let mis_is_recursive (ind,mib,mip) =
mis_is_recursive_subset (List.interval 0 (mib.mind_ntypes - 1))
mip.mind_recargs
let mis_nf_constructor_type ((_,j),u) (mib,mip) =
let nconstr = Array.length mip.mind_consnames in
if j > nconstr then user_err Pp.(str "Not enough constructors in the type.");
let (ctx, cty) = mip.mind_nf_lc.(j - 1) in
subst_instance_constr u (Term.it_mkProd_or_LetIn cty ctx)
(* Number of constructors *)
let nconstructors env ind =
let (_,mip) = Inductive.lookup_mind_specif env ind in
Array.length mip.mind_consnames
(* Arity of constructors excluding parameters, excluding local defs *)
let constructors_nrealargs env ind =
let (_,mip) = Inductive.lookup_mind_specif env ind in
mip.mind_consnrealargs
(* Arity of constructors excluding parameters, including local defs *)
let constructors_nrealdecls env ind =
let (_,mip) = Inductive.lookup_mind_specif env ind in
mip.mind_consnrealdecls
(* Arity of constructors including parameters, excluding local defs *)
let constructor_nallargs env (ind,j) =
let (mib,mip) = Inductive.lookup_mind_specif env ind in
mip.mind_consnrealargs.(j-1) + mib.mind_nparams
(* Arity of constructors including params, including local defs *)
let constructor_nalldecls env (ind,j) = (* TOCHANGE en decls *)
let (mib,mip) = Inductive.lookup_mind_specif env ind in
mip.mind_consnrealdecls.(j-1) + Context.Rel.length (mib.mind_params_ctxt)
(* Arity of constructors excluding params, excluding local defs *)
let constructor_nrealargs env (ind,j) =
let (_,mip) = Inductive.lookup_mind_specif env ind in
mip.mind_consnrealargs.(j-1)
(* Arity of constructors excluding params, including local defs *)
let constructor_nrealdecls env (ind,j) = (* TOCHANGE en decls *)
let (_,mip) = Inductive.lookup_mind_specif env ind in
mip.mind_consnrealdecls.(j-1)
(* Length of arity, excluding params, excluding local defs *)
let inductive_nrealargs env ind =
let (_,mip) = Inductive.lookup_mind_specif env ind in
mip.mind_nrealargs
(* Length of arity, excluding params, including local defs *)
let inductive_nrealdecls env ind =
let (_,mip) = Inductive.lookup_mind_specif env ind in
mip.mind_nrealdecls
(* Full length of arity (w/o local defs) *)
let inductive_nallargs env ind =
let (mib,mip) = Inductive.lookup_mind_specif env ind in
mib.mind_nparams + mip.mind_nrealargs
(* Length of arity (w/o local defs) *)
let inductive_nparams env ind =
let (mib,mip) = Inductive.lookup_mind_specif env ind in
mib.mind_nparams
(* Length of arity (with local defs) *)
let inductive_nparamdecls env ind =
let (mib,mip) = Inductive.lookup_mind_specif env ind in
Context.Rel.length mib.mind_params_ctxt
(* Full length of arity (with local defs) *)
let inductive_nalldecls env ind =
let (mib,mip) = Inductive.lookup_mind_specif env ind in
Context.Rel.length (mib.mind_params_ctxt) + mip.mind_nrealdecls
(* Others *)
let inductive_paramdecls env (ind,u) =
let (mib,mip) = Inductive.lookup_mind_specif env ind in
Inductive.inductive_paramdecls (mib,u)
let inductive_alldecls env (ind,u) =
let (mib,mip) = Inductive.lookup_mind_specif env ind in
Vars.subst_instance_context u mip.mind_arity_ctxt
let inductive_alltags env ind =
let (mib,mip) = Inductive.lookup_mind_specif env ind in
Context.Rel.to_tags mip.mind_arity_ctxt
let constructor_alltags env (ind,j) =
let (mib,mip) = Inductive.lookup_mind_specif env ind in
Context.Rel.to_tags (fst mip.mind_nf_lc.(j-1))
let constructor_has_local_defs env (indsp,j) =
let (mib,mip) = Inductive.lookup_mind_specif env indsp in
let l1 = mip.mind_consnrealdecls.(j-1) + Context.Rel.length (mib.mind_params_ctxt) in
let l2 = recarg_length mip.mind_recargs j + mib.mind_nparams in
not (Int.equal l1 l2)
let inductive_has_local_defs env ind =
let (mib,mip) = Inductive.lookup_mind_specif env ind in
let l1 = Context.Rel.length (mib.mind_params_ctxt) + mip.mind_nrealdecls in
let l2 = mib.mind_nparams + mip.mind_nrealargs in
not (Int.equal l1 l2)
(* XXX use above_prop from the ustate *)
let quality_leq q q' =
let open Sorts.Quality in
match q, q' with
| QVar q, QVar q' -> Sorts.QVar.equal q q'
| QConstant q, QConstant q' ->
begin match q, q' with
| QSProp, _
| _, QType
| QProp, QProp
-> true
| (QProp|QType), _ -> false
end
| (QVar _|QConstant _), _ -> false
type squash = SquashToSet | SquashToQuality of Sorts.Quality.t
let is_squashed sigma ((_,mip),u) =
match mip.mind_arity with
| TemplateArity _ -> None (* template is never squashed *)
| RegularArity a ->
match mip.mind_squashed with
| None -> None
| Some squash ->
let indq = EConstr.ESorts.quality sigma
(EConstr.ESorts.make @@ UVars.subst_instance_sort u a.mind_sort)
in
match squash with
| AlwaysSquashed -> begin match a.mind_sort with
| Sorts.Set -> Some SquashToSet
| _ -> Some (SquashToQuality indq)
end
| SometimesSquashed squash ->
(* impredicative set squashes are always AlwaysSquashed,
so here if inds=Set it is a sort poly squash (see "foo6" in test sort_poly.v) *)
if Sorts.Quality.Set.for_all (fun q ->
let q = UVars.subst_instance_quality u q in
let q = UState.nf_quality (Evd.evar_universe_context sigma) q in
quality_leq q indq) squash
then None
else Some (SquashToQuality indq)
let is_allowed_elimination sigma ((mib,_),_ as specifu) s =
let open Sorts in
match mib.mind_record with
| PrimRecord _ -> true
| NotRecord | FakeRecord ->
match is_squashed sigma specifu with
| None -> true
| Some SquashToSet ->
begin match EConstr.ESorts.kind sigma s with
| SProp|Prop|Set -> true
| QSort _ | Type _ ->
(* XXX in [Type u] case, should we check [u == set] in the ugraph? *)
false
end
| Some (SquashToQuality indq) -> quality_leq (EConstr.ESorts.quality sigma s) indq
let elim_sort (_,mip) =
if Option.is_empty mip.mind_squashed then Sorts.InType
else Inductive.inductive_sort_family mip
let top_allowed_sort env (kn,i as ind) =
let specif = Inductive.lookup_mind_specif env ind in
elim_sort specif
let sorts_below top =
List.filter (fun s ->
Sorts.family_equal s top
|| match s, top with
| InQSort, _ -> assert false
| _, InQSort -> false
| InSProp, _ -> true
| InProp, InSet -> true
| _, InType -> true
| (InProp|InSet|InType), _ -> false)
Sorts.[InSProp;InProp;InSet;InType]
let sorts_for_schemes specif =
sorts_below (elim_sort specif)
let has_dependent_elim (mib,mip) =
match mib.mind_record with
| PrimRecord _ -> mib.mind_finite == BiFinite || mip.mind_relevance == Irrelevant
| NotRecord | FakeRecord -> true
(* Annotation for cases *)
let make_case_info env ind style =
let (mib,mip) = Inductive.lookup_mind_specif env ind in
let ind_tags =
Context.Rel.to_tags (List.firstn mip.mind_nrealdecls mip.mind_arity_ctxt) in
let cstr_tags =
Array.map2 (fun (d, _) n ->
Context.Rel.to_tags (List.firstn n d))
mip.mind_nf_lc mip.mind_consnrealdecls in
let print_info = { ind_tags; cstr_tags; style } in
{ ci_ind = ind;
ci_npar = mib.mind_nparams;
ci_cstr_ndecls = mip.mind_consnrealdecls;
ci_cstr_nargs = mip.mind_consnrealargs;
ci_pp_info = print_info }
(*s Useful functions *)
type constructor_summary = {
cs_cstr : pconstructor;
cs_params : constr list;
cs_nargs : int;
cs_args : Constr.rel_context;
cs_concl_realargs : constr array
}
let lift_constructor n cs = {
cs_cstr = cs.cs_cstr;
cs_params = List.map (lift n) cs.cs_params;
cs_nargs = cs.cs_nargs;
cs_args = Vars.lift_rel_context n cs.cs_args;
cs_concl_realargs = Array.map (liftn n (cs.cs_nargs+1)) cs.cs_concl_realargs
}
(* Accept either all parameters or only recursively uniform ones *)
let instantiate_params t params sign =
let nnonrecpar = Context.Rel.nhyps sign - List.length params in
(* Adjust the signature if recursively non-uniform parameters are not here *)
let _,sign = Context.Rel.chop_nhyps nnonrecpar sign in
let _,t = decompose_prod_n_decls (Context.Rel.length sign) t in
let subst = subst_of_rel_context_instance_list sign params in
substl subst t
let instantiate_constructor_params (_,u as cstru) (mib,_ as mind_specif) params =
let typi = mis_nf_constructor_type cstru mind_specif in
let ctx = Vars.subst_instance_context u mib.mind_params_ctxt in
instantiate_params typi params ctx
let get_constructor ((ind,u),mib,mip,params) j =
assert (j <= Array.length mip.mind_consnames);
let typi = instantiate_constructor_params ((ind,j),u) (mib,mip) params in
let (args,ccl) = decompose_prod_decls typi in
let (_,allargs) = decompose_app_list ccl in
let vargs = List.skipn (List.length params) allargs in
{ cs_cstr = (ith_constructor_of_inductive ind j,u);
cs_params = params;
cs_nargs = Context.Rel.length args;
cs_args = args;
cs_concl_realargs = Array.of_list vargs }
let get_constructors env (ind,params) =
let (mib,mip) = Inductive.lookup_mind_specif env (fst ind) in
Array.init (Array.length mip.mind_consnames)
(fun j -> get_constructor (ind,mib,mip,params) (j+1))
let get_projections = Environ.get_projections
let make_case_invert env (IndType (((ind,u),params),indices)) ~case_relevance:r ci =
if Typeops.should_invert_case env r ci
then CaseInvert {indices=Array.of_list indices}
else NoInvert
let make_project env sigma ind pred c branches ps =
let open EConstr in
assert(Array.length branches == 1);
let na, ty, t = destLambda sigma pred in
let mib, mip as specif = Inductive.lookup_mind_specif env ind in
let () =
if (* dependent *) not (Vars.noccurn sigma 1 t) &&
not (has_dependent_elim specif) then
user_err
Pp.(str"Dependent case analysis not allowed" ++
str" on inductive type " ++ Termops.pr_global_env env (IndRef ind) ++ str ".")
in
let branch = branches.(0) in
let ctx, br = decompose_lambda_n_decls sigma mip.mind_consnrealdecls.(0) branch in
let _, u = destInd sigma (fst (decompose_app sigma ty)) in
let u = Unsafe.to_instance u in
let mkProj i c =
let p, r = ps.(i) in
let r = UVars.subst_instance_relevance u r in
mkProj (Projection.make p true, r, c)
in
let proj = match EConstr.destRel sigma br with
| exception DestKO -> None
| i ->
begin match List.skipn (i-1) ctx with
| exception Failure _ -> None
| ctx -> match ctx with
| [] -> None
| LocalDef _ :: _ ->
(* XXX Maybe we should produce the applied constant for this letin pseudoprojection?
We would have to get the params etc*)
None
| LocalAssum _ :: ctx ->
(* This match is just a projection *)
Some (mkProj (Context.Rel.nhyps ctx) c)
end
in
match proj with
| Some proj -> proj
| None ->
let n, len, ctx =
List.fold_right
(fun decl (i, j, ctx) ->
match decl with
| LocalAssum (na, ty) ->
let t = mkProj i (mkRel j) in
(i + 1, j + 1, LocalDef (na, t, Vars.liftn 1 j ty) :: ctx)
| LocalDef (na, b, ty) ->
(i, j + 1, LocalDef (na, Vars.liftn 1 j b, Vars.liftn 1 j ty) :: ctx))
ctx (0, 1, [])
in
mkLetIn (na, c, ty, it_mkLambda_or_LetIn (Vars.liftn 1 (Array.length ps + 1) br) ctx)
let simple_make_case_or_project env sigma ci pred invert c branches =
let open EConstr in
let ind = ci.ci_ind in
let projs = get_projections env ind in
match projs with
| None -> mkCase (EConstr.contract_case env sigma (ci, pred, invert, c, branches))
| Some ps -> make_project env sigma ind (fst pred) c branches ps
let make_case_or_project env sigma indt ci pred c branches =
let open EConstr in
let IndType (((ind,_),_),_) = indt in
let projs = get_projections env ind in
match projs with
| None ->
let invert = make_case_invert env indt ~case_relevance:(snd pred) ci in
mkCase (EConstr.contract_case env sigma (ci, pred, invert, c, branches))
| Some ps -> make_project env sigma ind (fst pred) c branches ps
(* substitution in a signature *)
let substnl_rel_context subst n sign =
let rec aux n = function
| d::sign -> substnl_decl subst n d :: aux (n+1) sign
| [] -> []
in List.rev (aux n (List.rev sign))
let substl_rel_context subst = substnl_rel_context subst 0
let get_arity env ((ind,u),params) =
let (mib,mip) = Inductive.lookup_mind_specif env ind in
let parsign =
(* Dynamically detect if called with an instance of recursively
uniform parameter only or also of recursively non-uniform
parameters *)
let nparams = List.length params in
if Int.equal nparams mib.mind_nparams then
Inductive.inductive_paramdecls (mib,u)
else begin
assert (Int.equal nparams mib.mind_nparams_rec);
snd (Inductive.inductive_nonrec_rec_paramdecls (mib,u))
end in
let arproperlength = List.length mip.mind_arity_ctxt - List.length parsign in
let arsign,_ = List.chop arproperlength mip.mind_arity_ctxt in
let subst = subst_of_rel_context_instance_list parsign params in
let arsign = Vars.subst_instance_context u arsign in
substl_rel_context subst arsign
(* Functions to build standard types related to inductive *)
let build_dependent_constructor cs =
applist
(mkConstructU cs.cs_cstr,
(List.map (lift cs.cs_nargs) cs.cs_params)
@(Context.Rel.instance_list mkRel 0 cs.cs_args))
let build_dependent_inductive env ((ind, params) as indf) =
let arsign = get_arity env indf in
let nrealargs = List.length arsign in
applist
(mkIndU ind,
(List.map (lift nrealargs) params)@(Context.Rel.instance_list mkRel 0 arsign))
(* builds the arity of an elimination predicate in sort [s] *)
let make_arity_signature env sigma dep (ind, _ as indf) =
let arsign = get_arity env indf in
let r = Inductive.relevance_of_inductive env ind in
let anon = make_annot Anonymous r in
let arsign = List.map (fun d -> Termops.map_rel_decl EConstr.of_constr d) arsign in
if dep then
(* We need names everywhere *)
Namegen.name_context env sigma
((LocalAssum (anon,EConstr.of_constr (build_dependent_inductive env indf)))::arsign)
(* Costly: would be better to name once for all at definition time *)
else
(* No need to enforce names *)
arsign
let make_arity env sigma dep indf s =
let open EConstr in
it_mkProd_or_LetIn (mkSort s) (make_arity_signature env sigma dep indf)
(**************************************************)
(** From a rel context describing the constructor arguments,
build an expansion function.
The term built is expecting to be substituted first by
a substitution of the form [params, x : ind params] *)
let compute_projections env (kn, i as ind) =
let open Term in
let mib = Environ.lookup_mind kn env in
let u = UVars.make_abstract_instance (Declareops.inductive_polymorphic_context mib) in
let x = match mib.mind_record with
| NotRecord | FakeRecord ->
anomaly Pp.(str "Trying to build primitive projections for a non-primitive record")
| PrimRecord info ->
let id, _, _, _ = info.(i) in
make_annot (Name id) mib.mind_packets.(i).mind_relevance
in
let pkt = mib.mind_packets.(i) in
let { mind_nparams = nparamargs; mind_params_ctxt = params } = mib in
let ctx, _ = pkt.mind_nf_lc.(0) in
let ctx, paramslet = List.chop pkt.mind_consnrealdecls.(0) ctx in
(* We build a substitution smashing the lets in the record parameters so
that typechecking projections requires just a substitution and not
matching with a parameter context. *)
let indty =
(* [ty] = [Ind inst] is typed in context [params] *)
let inst = Context.Rel.instance mkRel 0 paramslet in
let indu = mkIndU (ind, u) in
let ty = mkApp (indu, inst) in
(* [Ind inst] is typed in context [params-wo-let] *)
ty
in
let projections decl (proj_arg, j, pbs, subst) =
match decl with
| LocalDef (na,c,t) ->
(* From [params, field1,..,fieldj |- c(params,field1,..,fieldj)]
to [params, x:I, field1,..,fieldj |- c(params,field1,..,fieldj)] *)
let c = liftn 1 j c in
(* From [params, x:I, field1,..,fieldj |- c(params,field1,..,fieldj)]
to [params, x:I |- c(params,proj1 x,..,projj x)] *)
let c1 = substl subst c in
(* From [params, x:I |- subst:field1,..,fieldj]
to [params, x:I |- subst:field1,..,fieldj+1] where [subst]
is represented with instance of field1 last *)
let subst = c1 :: subst in
(proj_arg, j+1, pbs, subst)
| LocalAssum (na,t) ->
match na.binder_name with
| Name id ->
let lab = Label.of_id id in
let proj_relevant = na.binder_relevance in
let kn = Projection.Repr.make ind ~proj_npars:mib.mind_nparams ~proj_arg lab in
(* from [params, field1,..,fieldj |- t(params,field1,..,fieldj)]
to [params, x:I, field1,..,fieldj |- t(params,field1,..,fieldj] *)
let t = liftn 1 j t in
(* from [params, x:I, field1,..,fieldj |- t(params,field1,..,fieldj)]
to [params-wo-let, x:I |- t(params,proj1 x,..,projj x)] *)
(* from [params, x:I, field1,..,fieldj |- t(field1,..,fieldj)]
to [params, x:I |- t(proj1 x,..,projj x)] *)
let ty = substl subst t in
let term = mkProj (Projection.make kn true, proj_relevant, mkRel 1) in
let fterm = mkProj (Projection.make kn false, proj_relevant, mkRel 1) in
let etab = it_mkLambda_or_LetIn (mkLambda (x, indty, term)) params in
let etat = it_mkProd_or_LetIn (mkProd (x, indty, ty)) params in
let body = (etab, etat) in
(proj_arg + 1, j + 1, body :: pbs, fterm :: subst)
| Anonymous ->
anomaly Pp.(str "Trying to build primitive projections for a non-primitive record")
in
let (_, _, pbs, subst) =
List.fold_right projections ctx (0, 1, [], [])
in
Array.rev_of_list pbs
(**************************************************)
let extract_mrectype sigma t =
let open EConstr in
let (t, l) = decompose_app_list sigma t in
match EConstr.kind sigma t with
| Ind ind -> (ind, l)
| _ -> raise Not_found
let find_mrectype_vect env sigma c =
let (t, l) = EConstr.decompose_app sigma (whd_all env sigma c) in
match EConstr.kind sigma t with
| Ind ind -> (ind, l)
| _ -> raise Not_found
let find_mrectype env sigma c =
let (ind, v) = find_mrectype_vect env sigma c in (ind, Array.to_list v)
let find_rectype env sigma c =
let open EConstr in
let (t, l) = decompose_app_list sigma (whd_all env sigma c) in
match EConstr.kind sigma t with
| Ind (ind,u) ->
let (mib,mip) = Inductive.lookup_mind_specif env ind in
if mib.mind_nparams > List.length l then raise Not_found;
let l = List.map EConstr.Unsafe.to_constr l in
let (par,rargs) = List.chop mib.mind_nparams l in
let indu = (ind, EInstance.kind sigma u) in
IndType((indu, par),List.map EConstr.of_constr rargs)
| _ -> raise Not_found
let find_inductive env sigma c =
let open EConstr in
let (t, l) = decompose_app_list sigma (whd_all env sigma c) in
match EConstr.kind sigma t with
| Ind ind
when (fst (Inductive.lookup_mind_specif env (fst ind))).mind_finite <> CoFinite ->
let l = List.map EConstr.Unsafe.to_constr l in
(ind, l)
| _ -> raise Not_found
let find_coinductive env sigma c =
let open EConstr in
let (t, l) = decompose_app_list sigma (whd_all env sigma c) in
match EConstr.kind sigma t with
| Ind ind
when (fst (Inductive.lookup_mind_specif env (fst ind))).mind_finite == CoFinite ->
let l = List.map EConstr.Unsafe.to_constr l in
(ind, l)
| _ -> raise Not_found
(* Type of Case predicates *)
let arity_of_case_predicate env (ind,params) dep k =
let arsign = get_arity env (ind,params) in
let r = Inductive.relevance_of_inductive env ind in
let mind = build_dependent_inductive env (ind,params) in
let concl = if dep then mkArrow mind r (mkSort k) else mkSort k in
Term.it_mkProd_or_LetIn concl arsign
(***********************************************)
(* Inferring the sort of parameters of a polymorphic inductive type
knowing the sort of the conclusion *)
let univ_level_mem l s = match s with
| Prop | Set | SProp -> false
| Type u -> Univ.univ_level_mem l u
| QSort (_, u) -> assert false (* template cannot contain sort variables *)
(* Compute the inductive argument types: replace the sorts
that appear in the type of the inductive by the sort of the
conclusion, and the other ones by fresh universes. *)
let rec instantiate_universes env evdref scl is = function
| (LocalDef _ as d)::sign, exp ->
d :: instantiate_universes env evdref scl is (sign, exp)
| d::sign, None::exp ->
d :: instantiate_universes env evdref scl is (sign, exp)
| (LocalAssum (na,ty))::sign, Some l::exp ->
let ctx,_ = Reduction.dest_arity env ty in
let u = Univ.Universe.make l in
let s =
(* Does the sort of parameter [u] appear in (or equal)
the sort of inductive [is] ? *)
if univ_level_mem l is then
scl (* constrained sort: replace by scl *)
else
(* unconstrained sort: replace by fresh universe *)
let evm, s = Evd.new_sort_variable Evd.univ_flexible !evdref in
let evm = Evd.set_leq_sort env evm s (EConstr.ESorts.make (Sorts.sort_of_univ u)) in
evdref := evm; s
in
let s = EConstr.ESorts.kind !evdref s in
(LocalAssum (na,mkArity(ctx,s))) :: instantiate_universes env evdref scl is (sign, exp)
| sign, [] -> sign (* Uniform parameters are exhausted *)
| [], _ -> assert false
let type_of_inductive_knowing_conclusion env sigma ((mib,mip),u) conclty =
match mip.mind_arity with
| RegularArity s -> sigma, EConstr.of_constr (subst_instance_constr u s.mind_user_arity)
| TemplateArity ar ->
let templ = match mib.mind_template with
| None -> assert false
| Some t -> t
in
let _,scl = splay_arity env sigma conclty in
let ctx = List.rev mip.mind_arity_ctxt in
let evdref = ref sigma in
let ctx =
instantiate_universes
env evdref scl ar.template_level (ctx,templ.template_param_levels) in
let scl = EConstr.ESorts.kind !evdref scl in
!evdref, EConstr.of_constr (mkArity (List.rev ctx,scl))
let type_of_projection_constant env (p,u) =
let _, pty = lookup_projection p env in
Vars.subst_instance_constr u pty
let type_of_projection_knowing_arg env sigma p c ty =
let c = EConstr.Unsafe.to_constr c in
let IndType(pars,realargs) =
try find_rectype env sigma ty
with Not_found ->
raise (Invalid_argument "type_of_projection_knowing_arg_type: not an inductive type")
in
let (_,u), pars = dest_ind_family pars in
substl (c :: List.rev pars) (type_of_projection_constant env (p,u))
(***********************************************)
(* Guard condition *)
(* A function which checks that a term well typed verifies both
syntactic conditions *)
let control_only_guard env sigma c =
let c = Evarutil.nf_evar sigma c in
let check_fix_cofix e c =
(* [c] has already been normalized upfront *)
let c = EConstr.Unsafe.to_constr c in
match kind c with
| CoFix (_,(_,_,_) as cofix) ->
Inductive.check_cofix e cofix
| Fix fix ->
Inductive.check_fix e fix
| _ -> ()
in
let rec iter env c =
check_fix_cofix env c;
EConstr.iter_with_full_binders env sigma EConstr.push_rel iter env c
in
try iter env c
with Type_errors.TypeError (env, e) ->
raise (Pretype_errors.PretypeError (env, sigma, TypingError (Type_errors.map_ptype_error EConstr.of_constr e)))