1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(* $Id: retyping.ml 13323 2010-07-24 15:57:30Z herbelin $ *)
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 =
match kind_of_term (whd_betadeltaiota env sigma ar) with
| Prod (na, t, b) -> concl_of_arity (push_rel (na,None,t) env) b
| Sort s -> s
| _ -> decomp_sort env sigma (subst_type env sigma ft (Array.to_list args))
in concl_of_arity env ft
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 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
Inductive.type_of_inductive_knowing_parameters env mip argtyps
| Const cst ->
let t = constant_type env cst in
Typeops.type_of_constant_knowing_parameters env t argtyps
| 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 env sigma t = let _,f,_,_ = retype sigma in f env t
let get_sort_family_of env sigma c = let _,_,f,_ = retype 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 ?(refresh=true) env sigma c =
let f,_,_,_ = retype 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 }
|
