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|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
open Util
open Term
open Inductive
open Inductiveops
open Names
open Reductionops
open Environ
open Typeops
open Declarations
open Termops
let rec subst_type env sigma typ = function
| [] -> typ
| h::rest ->
match kind_of_term (whd_betadeltaiota env sigma typ) with
| Prod (na,c1,c2) -> subst_type env sigma (subst1 h c2) rest
| _ -> anomaly "Non-functional construction"
(* Si ft est le type d'un terme f, lequel est appliqué à args, *)
(* [sort_of_atomic_ty] calcule ft[args] qui doit être une sorte *)
(* On suit une méthode paresseuse, en espèrant que ft est une arité *)
(* et sinon on substitue *)
let sort_of_atomic_type env sigma ft args =
let rec concl_of_arity env ar args =
match kind_of_term (whd_betadeltaiota env sigma ar), args with
| Prod (na, t, b), h::l -> concl_of_arity (push_rel (na,Some h,t) env) b l
| Sort s, [] -> s
| _ -> anomaly "Not a sort"
in concl_of_arity env ft (Array.to_list args)
let type_of_var env id =
try let (_,_,ty) = lookup_named id env in ty
with Not_found ->
anomaly ("type_of: variable "^(string_of_id id)^" unbound")
let retype ?(polyprop=true) sigma =
let rec type_of env cstr=
match kind_of_term cstr with
| Meta n ->
(try strip_outer_cast (Evd.meta_ftype sigma n).Evd.rebus
with Not_found -> anomaly ("type_of: unknown meta " ^ string_of_int n))
| Rel n ->
let (_,_,ty) = lookup_rel n env in
lift n ty
| Var id -> type_of_var env id
| Const cst -> Typeops.type_of_constant env cst
| Evar ev -> Evd.existential_type sigma ev
| Ind ind -> type_of_inductive env ind
| Construct cstr -> type_of_constructor env cstr
| Case (_,p,c,lf) ->
let Inductiveops.IndType(_,realargs) =
try Inductiveops.find_rectype env sigma (type_of env c)
with Not_found -> anomaly "type_of: Bad recursive type" in
let t = whd_beta sigma (applist (p, realargs)) in
(match kind_of_term (whd_betadeltaiota env sigma (type_of env t)) with
| Prod _ -> whd_beta sigma (applist (t, [c]))
| _ -> t)
| Lambda (name,c1,c2) ->
mkProd (name, c1, type_of (push_rel (name,None,c1) env) c2)
| LetIn (name,b,c1,c2) ->
subst1 b (type_of (push_rel (name,Some b,c1) env) c2)
| Fix ((_,i),(_,tys,_)) -> tys.(i)
| CoFix (i,(_,tys,_)) -> tys.(i)
| App(f,args) when isGlobalRef f ->
let t = type_of_global_reference_knowing_parameters env f args in
strip_outer_cast (subst_type env sigma t (Array.to_list args))
| App(f,args) ->
strip_outer_cast
(subst_type env sigma (type_of env f) (Array.to_list args))
| Cast (c,_, t) -> t
| Sort _ | Prod _ -> mkSort (sort_of env cstr)
and sort_of env t =
match kind_of_term t with
| Cast (c,_, s) when isSort s -> destSort s
| Sort (Prop c) -> type1_sort
| Sort (Type u) -> Type (Univ.super u)
| Prod (name,t,c2) ->
(match (sort_of env t, sort_of (push_rel (name,None,t) env) c2) with
| _, (Prop Null as s) -> s
| Prop _, (Prop Pos as s) -> s
| Type _, (Prop Pos as s) when
Environ.engagement env = Some ImpredicativeSet -> s
| (Type _, _) | (_, Type _) -> new_Type_sort ()
(*
| Type u1, Prop Pos -> Type (Univ.sup u1 Univ.type0_univ)
| Prop Pos, (Type u2) -> Type (Univ.sup Univ.type0_univ u2)
| Prop Null, (Type _ as s) -> s
| Type u1, Type u2 -> Type (Univ.sup u1 u2)*))
| App(f,args) when isGlobalRef f ->
let t = type_of_global_reference_knowing_parameters env f args in
sort_of_atomic_type env sigma t args
| App(f,args) -> sort_of_atomic_type env sigma (type_of env f) args
| Lambda _ | Fix _ | Construct _ ->
anomaly "sort_of: Not a type (1)"
| _ -> decomp_sort env sigma (type_of env t)
and sort_family_of env t =
match kind_of_term t with
| Cast (c,_, s) when isSort s -> family_of_sort (destSort s)
| Sort (Prop c) -> InType
| Sort (Type u) -> InType
| Prod (name,t,c2) ->
let s2 = sort_family_of (push_rel (name,None,t) env) c2 in
if Environ.engagement env <> Some ImpredicativeSet &&
s2 = InSet & sort_family_of env t = InType then InType else s2
| App(f,args) when isGlobalRef f ->
let t = type_of_global_reference_knowing_parameters env f args in
family_of_sort (sort_of_atomic_type env sigma t args)
| App(f,args) ->
family_of_sort (sort_of_atomic_type env sigma (type_of env f) args)
| Lambda _ | Fix _ | Construct _ ->
anomaly "sort_of: Not a type (1)"
| _ -> family_of_sort (decomp_sort env sigma (type_of env t))
and type_of_global_reference_knowing_parameters env c args =
let argtyps = Array.map (fun c -> nf_evar sigma (type_of env c)) args in
match kind_of_term c with
| Ind ind ->
let (_,mip) = lookup_mind_specif env ind in
(try Inductive.type_of_inductive_knowing_parameters
~polyprop env mip argtyps
with Reduction.NotArity -> anomaly "type_of: Not an arity")
| Const cst ->
let t = constant_type env cst in
(try Typeops.type_of_constant_knowing_parameters env t argtyps
with Reduction.NotArity -> anomaly "type_of: Not an arity")
| Var id -> type_of_var env id
| Construct cstr -> type_of_constructor env cstr
| _ -> assert false
in type_of, sort_of, sort_family_of,
type_of_global_reference_knowing_parameters
let get_sort_of ?(polyprop=true) env sigma t =
let _,f,_,_ = retype ~polyprop sigma in f env t
let get_sort_family_of ?(polyprop=true) env sigma c =
let _,_,f,_ = retype ~polyprop sigma in f env c
let type_of_global_reference_knowing_parameters env sigma c args =
let _,_,_,f = retype sigma in f env c args
let type_of_global_reference_knowing_conclusion env sigma c conclty =
let conclty = nf_evar sigma conclty in
match kind_of_term c with
| Ind ind ->
let (_,mip) = Inductive.lookup_mind_specif env ind in
type_of_inductive_knowing_conclusion env mip conclty
| Const cst ->
let t = constant_type env cst in
(* TODO *)
Typeops.type_of_constant_knowing_parameters env t [||]
| Var id -> type_of_var env id
| Construct cstr -> type_of_constructor env cstr
| _ -> assert false
(* We are outside the kernel: we take fresh universes *)
(* to avoid tactics and co to refresh universes themselves *)
let get_type_of ?(polyprop=true) ?(refresh=true) env sigma c =
let f,_,_,_ = retype ~polyprop sigma in
let t = f env c in
if refresh then refresh_universes t else t
(* Makes an assumption from a constr *)
let get_assumption_of env evc c = c
(* Makes an unsafe judgment from a constr *)
let get_judgment_of env evc c = { uj_val = c; uj_type = get_type_of env evc c }
|
