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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 Pp
open Errors
open Util
open Term
open Vars
open Inductive
open Inductiveops
open Names
open Reductionops
open Environ
open Declarations
open Termops
type retype_error =
| NotASort
| NotAnArity
| NotAType
| BadVariable of Id.t
| BadMeta of int
| BadRecursiveType
| NonFunctionalConstruction
let print_retype_error = function
| NotASort -> str "Not a sort"
| NotAnArity -> str "Not an arity"
| NotAType -> str "Not a type (1)"
| BadVariable id -> str "variable " ++ Id.print id ++ str " unbound"
| BadMeta n -> str "unknown meta " ++ int n
| BadRecursiveType -> str "Bad recursive type"
| NonFunctionalConstruction -> str "Non-functional construction"
exception RetypeError of retype_error
let retype_error re = raise (RetypeError re)
let anomaly_on_error f x =
try f x
with RetypeError e -> anomaly ~label:"retyping" (print_retype_error e)
let get_type_from_constraints env sigma t =
if isEvar (fst (decompose_app t)) then
match
List.map_filter (fun (pbty,env,t1,t2) ->
if is_fconv Reduction.CONV env sigma t t1 then Some t2
else if is_fconv Reduction.CONV env sigma t t2 then Some t1
else None)
(snd (Evd.extract_all_conv_pbs sigma))
with
| t::l -> t
| _ -> raise Not_found
else raise Not_found
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
| _ -> retype_error NonFunctionalConstruction
(* If ft is the type of f which itself is applied to args, *)
(* [sort_of_atomic_type] computes ft[args] which has to be a sort *)
let sort_of_atomic_type env sigma ft args =
let rec concl_of_arity env n 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 (lift n h),t) env) (n + 1) b l
| Sort s, [] -> s
| _ -> retype_error NotASort
in concl_of_arity env 0 ft (Array.to_list args)
let type_of_var env id =
try let (_,_,ty) = lookup_named id env in ty
with Not_found -> retype_error (BadVariable id)
let decomp_sort env sigma t =
match kind_of_term (whd_betadeltaiota env sigma t) with
| Sort s -> s
| _ -> retype_error NotASort
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 -> retype_error (BadMeta 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_in 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) =
let t = type_of env c in
try Inductiveops.find_rectype env sigma t
with Not_found ->
try
let t = get_type_from_constraints env sigma t in
Inductiveops.find_rectype env sigma t
with Not_found -> retype_error BadRecursiveType
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 is_template_polymorphic env 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))
| Proj (p,c) ->
let Inductiveops.IndType(pars,realargs) =
try Inductiveops.find_rectype env sigma (type_of env c)
with Not_found -> anomaly ~label:"type_of" (str "Bad recursive type")
in
let (_,u), pars = dest_ind_family pars in
substl (c :: List.rev pars) (Typeops.type_of_projection env (p,u))
| 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 is_impredicative_set env -> s
| 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 is_template_polymorphic env 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 _ -> retype_error NotAType
| _ -> 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 not (is_impredicative_set env) &&
s2 == InSet && sort_family_of env t == InType then InType else s2
| App(f,args) when is_template_polymorphic env 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 _ -> retype_error NotAType
| _ ->
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 -> lazy (nf_evar sigma (type_of env c))) args in
match kind_of_term c with
| Ind ind ->
let mip = lookup_mind_specif env (fst ind) in
(try Inductive.type_of_inductive_knowing_parameters
~polyprop env (mip,snd ind) argtyps
with Reduction.NotArity -> retype_error NotAnArity)
| Const cst ->
let t = constant_type_in env cst in
(try Typeops.type_of_constant_type_knowing_parameters env t argtyps
with Reduction.NotArity -> retype_error NotAnArity)
| 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 anomaly_on_error (f env) t
let get_sort_family_of ?(polyprop=true) env sigma c =
let _,_,f,_ = retype ~polyprop sigma in anomaly_on_error (f env) c
let type_of_global_reference_knowing_parameters env sigma c args =
let _,_,_,f = retype sigma in anomaly_on_error (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,u) ->
let spec = Inductive.lookup_mind_specif env ind in
type_of_inductive_knowing_conclusion env sigma (spec,u) conclty
| Const cst ->
let t = constant_type_in env cst in
(* TODO *)
sigma, Typeops.type_of_constant_type_knowing_parameters env t [||]
| Var id -> sigma, type_of_var env id
| Construct cstr -> sigma, type_of_constructor env cstr
| _ -> assert false
(* Profiling *)
(* let get_type_of polyprop lax env sigma c = *)
(* let f,_,_,_ = retype ~polyprop sigma in *)
(* if lax then f env c else anomaly_on_error (f env) c *)
(* let get_type_of_key = Profile.declare_profile "get_type_of" *)
(* let get_type_of = Profile.profile5 get_type_of_key get_type_of *)
(* let get_type_of ?(polyprop=true) ?(lax=false) env sigma c = *)
(* get_type_of polyprop lax env sigma c *)
let get_type_of ?(polyprop=true) ?(lax=false) env sigma c =
let f,_,_,_ = retype ~polyprop sigma in
if lax then f env c else anomaly_on_error (f env) 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 }
(* Returns sorts of a context *)
let sorts_of_context env evc ctxt =
let rec aux = function
| [] -> env,[]
| (_,_,t as d)::ctxt ->
let env,sorts = aux ctxt in
let s = get_sort_of env evc t in
(push_rel d env,s::sorts) in
snd (aux ctxt)
|
