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
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
|
(************************************************************************)
(* 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 *)
(************************************************************************)
open Pp
open Util
open Names
open Term
open Mod_subst
open Environ
open Libnames
open Nameops
open Libobject
open Lib
(** Characterization of the head of a term *)
(* We only compute an approximation to ensure the computation is not
arbitrary long (e.g. the head constant of [h] defined to be
[g (fun x -> phi(x))] where [g] is [fun f => g O] does not launch
the evaluation of [phi(0)] and the head of [h] is declared unknown). *)
type rigid_head_kind =
| RigidParameter of constant (* a Const without body *)
| RigidVar of variable (* a Var without body *)
| RigidType (* an inductive, a product or a sort *)
type head_approximation =
| RigidHead of rigid_head_kind
| ConstructorHead
| FlexibleHead of int * int * int * bool (* [true] if a surrounding case *)
| NotImmediatelyComputableHead
(** Registration as global tables and rollback. *)
module Evalreford = struct
type t = evaluable_global_reference
let compare x y =
let make_name = function
| EvalConstRef con ->
EvalConstRef(constant_of_kn(canonical_con con))
| k -> k
in
Pervasives.compare (make_name x) (make_name y)
end
module Evalrefmap =
Map.Make (Evalreford)
let head_map = ref Evalrefmap.empty
let init () = head_map := Evalrefmap.empty
let freeze () = !head_map
let unfreeze hm = head_map := hm
let _ =
Summary.declare_summary "Head_decl"
{ Summary.freeze_function = freeze;
Summary.unfreeze_function = unfreeze;
Summary.init_function = init }
let variable_head id = Evalrefmap.find (EvalVarRef id) !head_map
let constant_head cst = Evalrefmap.find (EvalConstRef cst) !head_map
let kind_of_head env t =
let rec aux k l t b = match kind_of_term (Reduction.whd_betaiotazeta t) with
| Rel n when n > k -> NotImmediatelyComputableHead
| Rel n -> FlexibleHead (k,k+1-n,List.length l,b)
| Var id ->
(try on_subterm k l b (variable_head id)
with Not_found ->
(* a goal variable *)
match pi2 (lookup_named id env) with
| Some c -> aux k l c b
| None -> NotImmediatelyComputableHead)
| Const cst ->
(try on_subterm k l b (constant_head cst)
with Not_found -> assert false)
| Construct _ | CoFix _ ->
if b then NotImmediatelyComputableHead else ConstructorHead
| Sort _ | Ind _ | Prod _ -> RigidHead RigidType
| Cast (c,_,_) -> aux k l c b
| Lambda (_,_,c) when l = [] -> assert (not b); aux (k+1) [] c b
| Lambda (_,_,c) -> aux (k+1) (List.tl l) (subst1 (List.hd l) c) b
| LetIn _ -> assert false
| Meta _ | Evar _ -> NotImmediatelyComputableHead
| App (c,al) -> aux k (Array.to_list al @ l) c b
| Case (_,_,c,_) -> aux k [] c true
| Fix ((i,j),_) ->
let n = i.(j) in
try aux k [] (List.nth l n) true
with Failure _ -> FlexibleHead (k + n + 1, k + n + 1, 0, true)
and on_subterm k l with_case = function
| FlexibleHead (n,i,q,with_subcase) ->
let m = List.length l in
let k',rest,a =
if n > m then
(* eta-expansion *)
let a =
if i <= m then
(* we pick the head in the existing arguments *)
lift (n-m) (List.nth l (i-1))
else
(* we pick the head in the added arguments *)
mkRel (n-i+1) in
k+n-m,[],a
else
(* enough arguments to [cst] *)
k,list_skipn n l,List.nth l (i-1) in
let l' = list_tabulate (fun _ -> mkMeta 0) q @ rest in
aux k' l' a (with_subcase or with_case)
| ConstructorHead when with_case -> NotImmediatelyComputableHead
| x -> x
in aux 0 [] t false
let compute_head = function
| EvalConstRef cst ->
(match constant_opt_value (Global.env()) cst with
| None -> RigidHead (RigidParameter cst)
| Some c -> kind_of_head (Global.env()) c)
| EvalVarRef id ->
(match pi2 (Global.lookup_named id) with
| Some c when not (Decls.variable_opacity id) ->
kind_of_head (Global.env()) c
| _ ->
RigidHead (RigidVar id))
let is_rigid env t =
match kind_of_head env t with
| RigidHead _ | ConstructorHead -> true
| _ -> false
(** Registration of heads as an object *)
let load_head _ (_,(ref,(k:head_approximation))) =
head_map := Evalrefmap.add ref k !head_map
let cache_head o =
load_head 1 o
let subst_head_approximation subst = function
| RigidHead (RigidParameter cst) as k ->
let cst,c = subst_con subst cst in
if isConst c && eq_constant (destConst c) cst then
(* A change of the prefix of the constant *)
k
else
(* A substitution of the constant by a functor argument *)
kind_of_head (Global.env()) c
| x -> x
let subst_head (subst,(ref,k)) =
(subst_evaluable_reference subst ref, subst_head_approximation subst k)
let discharge_head (_,(ref,k)) =
match ref with
| EvalConstRef cst -> Some (EvalConstRef (pop_con cst), k)
| EvalVarRef id -> None
let rebuild_head (ref,k) =
(ref, compute_head ref)
type head_obj = evaluable_global_reference * head_approximation
let inHead : head_obj -> obj =
declare_object {(default_object "HEAD") with
cache_function = cache_head;
load_function = load_head;
subst_function = subst_head;
classify_function = (fun x -> Substitute x);
discharge_function = discharge_head;
rebuild_function = rebuild_head }
let declare_head c =
let hd = compute_head c in
add_anonymous_leaf (inHead (c,hd))
(** Printing *)
let pr_head = function
| RigidHead (RigidParameter cst) -> str "rigid constant " ++ pr_con cst
| RigidHead (RigidType) -> str "rigid type"
| RigidHead (RigidVar id) -> str "rigid variable " ++ pr_id id
| ConstructorHead -> str "constructor"
| FlexibleHead (k,n,p,b) -> int n ++ str "th of " ++ int k ++ str " binders applied to " ++ int p ++ str " arguments" ++ (if b then str " (with case)" else mt())
| NotImmediatelyComputableHead -> str "unknown"
|
