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
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
open Names
open Term
open Environ
open Esubst
(** Flags for profiling reductions. *)
val stats : bool ref
val share : bool ref
val with_stats: 'a Lazy.t -> 'a
(** {6 ... } *)
(** Delta implies all consts (both global (= by
[kernel_name]) and local (= by [Rel] or [Var])), all evars, and letin's.
Rem: reduction of a Rel/Var bound to a term is Delta, but reduction of
a LetIn expression is Letin reduction *)
val all_opaque : transparent_state
val all_transparent : transparent_state
val is_transparent_variable : transparent_state -> variable -> bool
val is_transparent_constant : transparent_state -> constant -> bool
(** Sets of reduction kinds. *)
module type RedFlagsSig = sig
type reds
type red_kind
(** {7 The different kinds of reduction } *)
val fBETA : red_kind
val fDELTA : red_kind
val fETA : red_kind
(** This flag is never used by the kernel reduction but pretyping does *)
val fIOTA : red_kind
val fZETA : red_kind
val fCONST : constant -> red_kind
val fVAR : Id.t -> red_kind
(** No reduction at all *)
val no_red : reds
(** Adds a reduction kind to a set *)
val red_add : reds -> red_kind -> reds
(** Removes a reduction kind to a set *)
val red_sub : reds -> red_kind -> reds
(** Adds a reduction kind to a set *)
val red_add_transparent : reds -> transparent_state -> reds
(** Build a reduction set from scratch = iter [red_add] on [no_red] *)
val mkflags : red_kind list -> reds
(** Tests if a reduction kind is set *)
val red_set : reds -> red_kind -> bool
(** This tests if the projection is in unfolded state already or
is unfodable due to delta. *)
val red_projection : reds -> projection -> bool
end
module RedFlags : RedFlagsSig
open RedFlags
val beta : reds
val betaiota : reds
val betadeltaiota : reds
val betaiotazeta : reds
val betadeltaiotanolet : reds
val unfold_side_red : reds
val unfold_red : evaluable_global_reference -> reds
(***********************************************************************)
type table_key = constant puniverses tableKey
type 'a infos_cache
type 'a infos = {
i_flags : reds;
i_cache : 'a infos_cache }
val ref_value_cache: 'a infos -> table_key -> 'a option
val create: ('a infos -> constr -> 'a) -> reds -> env ->
(existential -> constr option) -> 'a infos
val evar_value : 'a infos_cache -> existential -> constr option
val info_env : 'a infos -> env
val info_flags: 'a infos -> reds
(***********************************************************************
s Lazy reduction. *)
(** [fconstr] is the type of frozen constr *)
type fconstr
(** [fconstr] can be accessed by using the function [fterm_of] and by
matching on type [fterm] *)
type fterm =
| FRel of int
| FAtom of constr (** Metas and Sorts *)
| FCast of fconstr * cast_kind * fconstr
| FFlex of table_key
| FInd of inductive puniverses
| FConstruct of constructor puniverses
| FApp of fconstr * fconstr array
| FProj of projection * fconstr
| FFix of fixpoint * fconstr subs
| FCoFix of cofixpoint * fconstr subs
| FCaseT of case_info * constr * fconstr * constr array * fconstr subs (* predicate and branches are closures *)
| FLambda of int * (Name.t * constr) list * constr * fconstr subs
| FProd of Name.t * fconstr * fconstr
| FLetIn of Name.t * fconstr * fconstr * constr * fconstr subs
| FEvar of existential * fconstr subs
| FLIFT of int * fconstr
| FCLOS of constr * fconstr subs
| FLOCKED
(***********************************************************************
s A [stack] is a context of arguments, arguments are pushed by
[append_stack] one array at a time but popped with [decomp_stack]
one by one *)
type stack_member =
| Zapp of fconstr array
| ZcaseT of case_info * constr * constr array * fconstr subs
| Zproj of int * int * constant
| Zfix of fconstr * stack
| Zshift of int
| Zupdate of fconstr
and stack = stack_member list
val empty_stack : stack
val append_stack : fconstr array -> stack -> stack
val decomp_stack : stack -> (fconstr * stack) option
val array_of_stack : stack -> fconstr array
val stack_assign : stack -> int -> fconstr -> stack
val stack_args_size : stack -> int
val stack_tail : int -> stack -> stack
val stack_nth : stack -> int -> fconstr
val zip_term : (fconstr -> constr) -> constr -> stack -> constr
val eta_expand_stack : stack -> stack
(** To lazy reduce a constr, create a [clos_infos] with
[create_clos_infos], inject the term to reduce with [inject]; then use
a reduction function *)
val inject : constr -> fconstr
(** mk_atom: prevents a term from being evaluated *)
val mk_atom : constr -> fconstr
(** mk_red: makes a reducible term (used in newring) *)
val mk_red : fterm -> fconstr
val fterm_of : fconstr -> fterm
val term_of_fconstr : fconstr -> constr
val destFLambda :
(fconstr subs -> constr -> fconstr) -> fconstr -> Name.t * fconstr * fconstr
(** Global and local constant cache *)
type clos_infos = fconstr infos
val create_clos_infos :
?evars:(existential->constr option) -> reds -> env -> clos_infos
val oracle_of_infos : clos_infos -> Conv_oracle.oracle
val env_of_infos : clos_infos -> env
val infos_with_reds : clos_infos -> reds -> clos_infos
(** Reduction function *)
(** [norm_val] is for strong normalization *)
val norm_val : clos_infos -> fconstr -> constr
(** [whd_val] is for weak head normalization *)
val whd_val : clos_infos -> fconstr -> constr
(** [whd_stack] performs weak head normalization in a given stack. It
stops whenever a reduction is blocked. *)
val whd_stack :
clos_infos -> fconstr -> stack -> fconstr * stack
(** [eta_expand_ind_stack env ind c s t] computes stacks correspoding
to the conversion of the eta expansion of t, considered as an inhabitant
of ind, and the Constructor c of this inductive type applied to arguments
s.
@assumes [t] is a rigid term, and not a constructor. [ind] is the inductive
of the constructor term [c]
@raises Not_found if the inductive is not a primitive record, or if the
constructor is partially applied.
*)
val eta_expand_ind_stack : env -> inductive -> fconstr -> stack ->
(fconstr * stack) -> stack * stack
(** Conversion auxiliary functions to do step by step normalisation *)
(** [unfold_reference] unfolds references in a [fconstr] *)
val unfold_reference : clos_infos -> table_key -> fconstr option
val eq_table_key : table_key -> table_key -> bool
(***********************************************************************
i This is for lazy debug *)
val lift_fconstr : int -> fconstr -> fconstr
val lift_fconstr_vect : int -> fconstr array -> fconstr array
val mk_clos : fconstr subs -> constr -> fconstr
val mk_clos_vect : fconstr subs -> constr array -> fconstr array
val mk_clos_deep :
(fconstr subs -> constr -> fconstr) ->
fconstr subs -> constr -> fconstr
val kni: clos_infos -> fconstr -> stack -> fconstr * stack
val knr: clos_infos -> fconstr -> stack -> fconstr * stack
val kl : clos_infos -> fconstr -> constr
val to_constr : (lift -> fconstr -> constr) -> lift -> fconstr -> constr
(** End of cbn debug section i*)
|
