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
|
(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(*i $Id$ i*)
(*i*)
open Term
open Sign
open Evd
open Proof_trees
open Proof_type
open Tacexpr
(*i*)
(* The refiner (handles primitive rules and high-level tactics). *)
val sig_it : 'a sigma -> 'a
val sig_sig : 'a sigma -> evar_map
val project_with_focus : goal sigma -> named_context sigma
val unpackage : 'a sigma -> evar_map ref * 'a
val repackage : evar_map ref -> 'a -> 'a sigma
val apply_sig_tac :
evar_map ref -> ('a sigma -> 'b sigma * 'c) -> 'a -> 'b * 'c
type transformation_tactic = proof_tree -> (goal list * validation)
val add_tactic : string -> (closed_generic_argument list -> tactic) -> unit
val overwriting_add_tactic : string -> (closed_generic_argument list -> tactic) -> unit
val lookup_tactic : string -> (closed_generic_argument list) -> tactic
(*s Hiding the implementation of tactics. *)
(* [abstract_tactic tac] hides the (partial) proof produced by [tac] under
a single proof node *)
val abstract_tactic : atomic_tactic_expr -> tactic -> tactic
val abstract_tactic_expr : tactic_expr -> tactic -> tactic
val abstract_extended_tactic : string -> closed_generic_argument list -> tactic -> tactic
val refiner : rule -> tactic
val vernac_tactic : string * closed_generic_argument list -> tactic
val frontier : transformation_tactic
val list_pf : proof_tree -> goal list
val unTAC : tactic -> goal sigma -> proof_tree sigma
val local_Constraints : tactic
(* [frontier_map f n p] applies f on the n-th open subgoal of p and
rebuilds proof-tree.
n=1 for first goal, n negative counts from the right *)
val frontier_map :
(proof_tree -> proof_tree) -> int -> proof_tree -> proof_tree
(* [frontier_mapi f p] applies (f i) on the i-th open subgoal of p. *)
val frontier_mapi :
(int -> proof_tree -> proof_tree) -> proof_tree -> proof_tree
(*s Tacticals. *)
(* [tclIDTAC] is the identity tactic *)
val tclIDTAC : tactic
(* [tclTHEN tac1 tac2 gls] applies the tactic [tac1] to [gls] and applies
[tac2] to every resulting subgoals *)
val tclTHEN : tactic -> tactic -> tactic
(* [tclTHENLIST [t1;..;tn]] applies [t1] THEN [t2] ... THEN [tn]. More
convenient than [tclTHEN] when [n] is large *)
val tclTHENLIST : tactic list -> tactic
(* [tclTHEN_i tac1 tac2 gls] applies the tactic [tac1] to [gls] and applies
[(tac2 i)] to the [i]$^{th}$ resulting subgoal (starting from 1) *)
val tclTHEN_i : tactic -> (int -> tactic) -> tactic
(* [tclTHENLAST tac1 tac2 gls] applies the tactic [tac1] to [gls] and [tac2]
to the last resulting subgoal (previously called [tclTHENL]) *)
val tclTHENLAST : tactic -> tactic -> tactic
(* [tclTHENFIRST tac1 tac2 gls] applies the tactic [tac1] to [gls] and [tac2]
to the first resulting subgoal *)
val tclTHENFIRST : tactic -> tactic -> tactic
(* [tclTHENS tac1 [|t1 ; ... ; tn|] gls] applies the tactic [tac1] to
[gls] and applies [t1],..., [tn] to the [n] resulting subgoals. Raises
an error if the number of resulting subgoals is not [n] *)
val tclTHENSV : tactic -> tactic array -> tactic
(* Same with a list of tactics *)
val tclTHENS : tactic -> tactic list -> tactic
(* [tclTHENST] is renamed [tclTHENSFIRSTn]
val tclTHENST : tactic -> tactic array -> tactic -> tactic
*)
(* [tclTHENSLASTn tac1 [t1 ; ... ; tn] tac2 gls] applies [t1],...,[tn] on the
last [n] resulting subgoals and [tac2] on the remaining first subgoals *)
val tclTHENSLASTn : tactic -> tactic -> tactic array -> tactic
(* [tclTHENSFIRSTn tac1 [t1 ; ... ; tn] tac2 gls] first applies [tac1], then
applies [t1],...,[tn] on the first [n] resulting subgoals and
[tac2] for the remaining last subgoals (previously called tclTHENST) *)
val tclTHENSFIRSTn : tactic -> tactic array -> tactic -> tactic
(* [tclTHENLASTn tac1 [t1 ; ... ; tn] gls] first applies [tac1] then,
applies [t1],...,[tn] on the last [n] resulting subgoals and leaves
unchanged the other subgoals *)
val tclTHENLASTn : tactic -> tactic array -> tactic
(* [tclTHENFIRSTn tac1 [t1 ; ... ; tn] gls] first applies [tac1] then,
applies [t1],...,[tn] on the first [n] resulting subgoals and leaves
unchanged the other subgoals (previously called [tclTHENSI]) *)
val tclTHENFIRSTn : tactic -> tactic array -> tactic
(* A special exception for levels for the Fail tactic *)
exception FailError of int * string
val tclORELSE : tactic -> tactic -> tactic
val tclREPEAT : tactic -> tactic
val tclREPEAT_MAIN : tactic -> tactic
val tclFIRST : tactic list -> tactic
val tclSOLVE : tactic list -> tactic
val tclTRY : tactic -> tactic
val tclTHENTRY : tactic -> tactic -> tactic
val tclCOMPLETE : tactic -> tactic
val tclAT_LEAST_ONCE : tactic -> tactic
val tclFAIL : int -> string -> tactic
val tclDO : int -> tactic -> tactic
val tclPROGRESS : tactic -> tactic
val tclWEAK_PROGRESS : tactic -> tactic
val tclNOTSAMEGOAL : tactic -> tactic
val tclINFO : tactic -> tactic
(* [tclIFTHENELSE tac1 tac2 tac3 gls] first applies [tac1] to [gls] then,
if it succeeds, applies [tac2] to the resulting subgoals,
and if not applies [tac3] to the initial goal [gls] *)
val tclIFTHENELSE : tactic -> tactic -> tactic -> tactic
val tclIFTHENSELSE : tactic -> tactic list -> tactic ->tactic
val tclIFTHENSVELSE : tactic -> tactic array -> tactic ->tactic
(*s Tactics handling a list of goals. *)
type validation_list = proof_tree list -> proof_tree list
type tactic_list = (goal list sigma) -> (goal list sigma) * validation_list
val tclFIRSTLIST : tactic_list list -> tactic_list
val tclIDTAC_list : tactic_list
val first_goal : 'a list sigma -> 'a sigma
val apply_tac_list : tactic -> tactic_list
val then_tactic_list : tactic_list -> tactic_list -> tactic_list
val tactic_list_tactic : tactic_list -> tactic
val goal_goal_list : 'a sigma -> 'a list sigma
(*s Functions for handling the state of the proof editor. *)
type pftreestate
val proof_of_pftreestate : pftreestate -> proof_tree
val cursor_of_pftreestate : pftreestate -> int list
val is_top_pftreestate : pftreestate -> bool
val evc_of_pftreestate : pftreestate -> evar_map
val top_goal_of_pftreestate : pftreestate -> goal sigma
val nth_goal_of_pftreestate : int -> pftreestate -> goal sigma
val traverse : int -> pftreestate -> pftreestate
val solve_nth_pftreestate : int -> tactic -> pftreestate -> pftreestate
val solve_pftreestate : tactic -> pftreestate -> pftreestate
(* a weak version of logical undoing, that is really correct only *)
(* if there are no existential variables. *)
val weak_undo_pftreestate : pftreestate -> pftreestate
val mk_pftreestate : goal -> pftreestate
val extract_open_pftreestate : pftreestate -> constr * Termops.metamap
val extract_pftreestate : pftreestate -> constr
val first_unproven : pftreestate -> pftreestate
val last_unproven : pftreestate -> pftreestate
val nth_unproven : int -> pftreestate -> pftreestate
val node_prev_unproven : int -> pftreestate -> pftreestate
val node_next_unproven : int -> pftreestate -> pftreestate
val next_unproven : pftreestate -> pftreestate
val prev_unproven : pftreestate -> pftreestate
val top_of_tree : pftreestate -> pftreestate
val change_constraints_pftreestate
: evar_map -> pftreestate -> pftreestate
(*s Pretty-printers. *)
(*i*)
open Pp
(*i*)
val print_proof : evar_map -> named_context -> proof_tree -> std_ppcmds
val pr_rule : rule -> std_ppcmds
val pr_tactic : tactic_expr -> std_ppcmds
val print_script :
bool -> evar_map -> named_context -> proof_tree -> std_ppcmds
val print_treescript :
bool -> evar_map -> named_context -> proof_tree -> std_ppcmds
|
