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
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
|
(*
* This file is part of Coccinelle, licensed under the terms of the GPL v2.
* See copyright.txt in the Coccinelle source code for more information.
* The Coccinelle source code can be obtained at http://coccinelle.lip6.fr
*)
(* ********************************************************************** *)
(* Module: EXAMPLE_ENGINE (instance of CTL_ENGINE) *)
(* ********************************************************************** *)
(* Simple env.: meta.vars and values are strings *)
module SIMPLE_ENV =
struct
type value = string;;
type mvar = string;;
let eq_mvar x x' = x = x';;
let eq_val v v' = v = v';;
let merge_val v v' = v;;
end
;;
(* Simple predicates *)
module WRAPPER_PRED =
struct
type predicate = string
end
module EXAMPLE_ENGINE =
Wrapper_ctl.CTL_ENGINE_BIS (SIMPLE_ENV) (Ctl_engine.OGRAPHEXT_GRAPH) (WRAPPER_PRED)
let top_wit = []
(* ******************************************************************** *)
(* *)
(* EXAMPLES *)
(* *)
(* ******************************************************************** *)
(* For convenience in the examples *)
(* FIX ME: remove *)
open Ctl_engine.OGRAPHEXT_GRAPH;;
open EXAMPLE_ENGINE;;
open Ast_ctl;;
(* ---------------------------------------------------------------------- *)
(* Helpers *)
(* ---------------------------------------------------------------------- *)
(* FIX ME: move to ENGINE module *)
let (-->) x v = Subst (x,v);;
(* FIX ME: move to ENGINE module *)
let (-/->) x v = NegSubst(x,v);;
let mkgraph nodes edges =
let g = ref (new Ograph_extended.ograph_extended) in
let addn (n,x) =
(* let (g',i) = (!g)#add_node x in *)
(* now I need to force the nodei of a node, because of the state(vx) predicates
hence add_node -> add_nodei
*)
let (g', i) = !g#add_nodei n x in
assert (i = n);
g := g'; (n,i) in
let adde anodes (n1,n2,x) =
let g' = (!g)#add_arc ((List.assoc n1 anodes,List.assoc n2 anodes),x) in
g := g'; () in
let add_nodes = List.map addn nodes in
let _add_edges = List.map (adde add_nodes) edges in
!g
;;
(* CTL parameterised on basic predicates and metavar's*)
type ('pred,'mvar) old_gen_ctl =
| False_
| True_
| Pred_ of 'pred
| Not_ of ('pred,'mvar) old_gen_ctl
| Exists_ of 'mvar * ('pred,'mvar) old_gen_ctl (* !!! *)
| And_ of ('pred,'mvar) old_gen_ctl * ('pred,'mvar) old_gen_ctl
| Or_ of ('pred,'mvar) old_gen_ctl * ('pred,'mvar) old_gen_ctl
| Implies_ of ('pred,'mvar) old_gen_ctl * ('pred,'mvar) old_gen_ctl
| AF_ of ('pred,'mvar) old_gen_ctl
| AX_ of ('pred,'mvar) old_gen_ctl
| AG_ of ('pred,'mvar) old_gen_ctl
| AU_ of ('pred,'mvar) old_gen_ctl * ('pred,'mvar) old_gen_ctl
| EF_ of ('pred,'mvar) old_gen_ctl
| EX_ of ('pred,'mvar) old_gen_ctl
| EG_ of ('pred,'mvar) old_gen_ctl
| EU_ of ('pred,'mvar) old_gen_ctl * ('pred,'mvar) old_gen_ctl
| Let_ of string * ('pred,'mvar) old_gen_ctl * ('pred,'mvar) old_gen_ctl
| Ref_ of string
let rec mkanno phi0 =
let anno phi = (phi,None) in
match phi0 with
| False_ -> anno False
| True_ -> anno True
| Pred_(p) -> anno (Pred(p))
| Not_(phi) -> anno (Not(mkanno phi))
| Exists_(v,phi) -> anno (Exists(v,mkanno phi))
| And_(phi1,phi2) -> anno (And(mkanno phi1,mkanno phi2))
| Or_(phi1,phi2) -> anno (Or(mkanno phi1,mkanno phi2))
| Implies_(phi1,phi2) -> anno (Implies(mkanno phi1,mkanno phi2))
| AF_(phi1) -> anno (AF(mkanno phi1))
| AX_(phi1) -> anno (AX(mkanno phi1))
| AG_(phi1) -> anno (AG(mkanno phi1))
| AU_(phi1,phi2) -> anno (AU(mkanno phi1,mkanno phi2))
| EF_(phi1) -> anno (EF(mkanno phi1))
| EX_(phi1) -> anno (EX(mkanno phi1))
| EG_(phi1) -> anno (EG(mkanno phi1))
| EU_(phi1,phi2) -> anno (EU(mkanno phi1,mkanno phi2))
| Let_ (x,phi1,phi2) -> anno (Let(x,mkanno phi1,mkanno phi2))
| Ref_(s) -> anno (Ref(s))
(* ******************************************************************** *)
(* Example 1 *)
(* CTL: f(x) /\ AF(Ey.g(y)) *)
(* ******************************************************************** *)
let ex1lab s =
match s with
| "f(x)" -> [(0,["x" --> "1"]); (1,["x" --> "2"])]
| "g(y)" -> [(3,["y" --> "1"]); (4,["y" --> "2"])]
| "f(1)" -> [(0,[])]
| "f(2)" -> [(1,[])]
| "g(1)" -> [(3,[])]
| "g(2)" -> [(4,[])]
| _ -> []
;;
let ex1graph =
let nodes =
[(0,"f(1)");(1,"f(2)");(2,"< >");(3,"g(1)");(4,"g(2)");(5,"<exit>")] in
let edges = [(0,2); (1,2); (2,3); (2,4); (3,5); (4,5); (5,5)] in
mkgraph nodes (List.map (fun (x,y) -> (x,y,())) edges)
;;
let ex1states = List.map fst (ex1graph#nodes)#tolist;;
let ex1model = (ex1graph,ex1lab,ex1states);;
let ex1model_wrapped = (ex1graph,wrap_label ex1lab,ex1states);;
let ex1s0 = Exists_("v0",Pred_ ("f(x)",UnModif "v0"));;
let ex1s1 = Exists_("v1",Pred_ ("g(y)",Modif "v1"));;
let ex1s2 = Exists_("y",ex1s1);;
let ex1s3 = AF_(ex1s2);;
let ex1s4 = And_(ex1s0,ex1s3);;
let ex1s3a = AX_(ex1s2);;
let ex1s4a = AX_(AX_(ex1s2));;
let ex1s5a = And_(ex1s0,ex1s4a);;
let ex1s0b = Pred_ ("g(y)", Modif "v0");;
let ex1s1b = Exists_ ("v0",ex1s0b);;
let ex1s2b = Exists_ ("y",ex1s1b);;
let ex1s3b = AF_(ex1s2b);;
let ex1s4b = AX_(ex1s3b);;
let ex1s5b = Pred_ ("f(x)", UnModif "v3");;
let ex1s6b = Exists_ ("v3", ex1s5b);;
let ex1s7b = Exists_ ("x", ex1s6b);;
let ex1s8b = And_(ex1s7b,ex1s4b);;
let ex1s7c = And_(ex1s6b,ex1s4b);;
let ex1s8c = Exists_("x",ex1s7c);;
let ex1phi1 = ex1s4;;
let ex1phi2 = ex1s5a;;
let ex1phi3 =
And_
(Exists_ ("x",
(Exists_ ("v3",
Pred_ ("f(x)", UnModif "v3")))),
AX_
(AF_
(Exists_ ("y", (* change this to Y and have strange behaviour *)
(Exists_ ("v0",
Pred_ ("g(y)", Modif "v0")
))))));;
let ex1phi4 =
Exists_ ("x",
And_ (
(Exists_ ("v3",
Pred_ ("f(x)", UnModif "v3"))),
AX_
(AF_
(Exists_ ("y", (* change this to Y and have strange behaviour *)
(Exists_ ("v0",
Pred_ ("g(y)", Modif "v0")
)))))));;
let ex1phi5 = AU_(True_,Exists_("y", Exists_("v0",Pred_("g(y)",Modif "v0"))));;
let ex1phi6 =
AU_(
Not_(Exists_("x",Exists_("v1",Pred_("f(x)",UnModif "v1")))),
Exists_("y", Exists_("v0",Pred_("g(y)",Modif "v0")))
);;
(* use with ex1nc *)
let ex1phi7 =
AU_(
Not_(Or_(Pred_("f(1)",Control),Pred_("f(2)",Control))),
Exists_("y", Exists_("v0",Pred_("g(y)",Modif "v0")))
);;
let ex1 phi = satbis ex1model (mkanno phi);;
let ex1nc phi = satbis_noclean ex1model (mkanno phi);;
(* ******************************************************************** *)
(* Example 2 *)
(* ******************************************************************** *)
let ex2lab s =
match s with
| "p" -> [0,[]]
| "{" -> [(1,[]); (2,[])]
| "}" -> [(3,[]); (4,[])]
| "paren(v)" -> [(1,["v" --> "1"]); (2,["v" --> "2"]);
(3,["v" --> "2"]); (4,["v" --> "1"])]
| _ -> []
;;
let ex2graph =
let nodes =
[(0,"p");(1,"{");(2,"{");(3,"}");(4,"}");(5,"<exit>")] in
let edges = [(0,1); (1,2); (2,3); (3,4); (4,5); (5,5)] in
mkgraph nodes (List.map (fun (x,y) -> (x,y,())) edges)
;;
let ex2states = List.map fst (ex2graph#nodes)#tolist;;
let ex2model = (ex2graph,ex2lab,ex2states);;
let ex2model_wrapped = (ex2graph,wrap_label ex2lab,ex2states);;
let ex2s0 = Pred_("p",Control);;
let ex2s1 = Pred_("{",Control);;
let ex2s2 = Pred_("paren(v)",Control);;
let ex2s3 = And_(ex2s1,ex2s2);;
let ex2s4 = Pred_("}",Control);;
let ex2s5 = Pred_("paren(v)",Control);;
let ex2s6 = And_(ex2s4,ex2s5);;
let ex2s7 = AF_(ex2s6);;
let ex2s8 = And_(ex2s3,ex2s7);;
let ex2s9 = Exists_("v",ex2s8);;
let ex2s10 = AX_(ex2s9);;
let ex2s11 = And_(ex2s0,ex2s10);;
let ex2phi1 = ex2s11;;
let ex2 phi = satbis_noclean ex2model (mkanno phi)
(*
+--- s11:& ---+
| |
s0:p s10:AX
|
s9:exists v
|
+---------- s8:& --------+
| |
+-- s3:& --+ s7:AF
| | |
s1:"{" s2:paren(v) +-- s6:& -+
| |
s4:"}" s5:paren(v)
s0 : p : (0,_,_)
s1 : "{" : (1,_,_); (2,_,_)
s2 : paren(v) : (1,v=1,_); (2,v=2,_); (3,v=2,_); (4,v=1,_)
s3 : "{" & paren(v) : (1,v=1,_); (2,v=2,_)
s4 : "}" : (3,_,_); (4,_,_)
s5 : paren(v) : (1,v=1,_); (2,v=2,_); (3,v=2,_); (4,v=1,_)
s6 : "}" & paren(v) : (3,v=2,_); (4,v=1,_)
s7 : AF(...) : (0;1;2;3,v=2,_); (0;1;2;3;4,v=1,_)
s8 : (...&...) & AF(...) : (1,v=1,_); (2,v=2,_)
s9 : exists ... : (1,_,(1,v=1)); (2,_,(2,v=2))
s10 : AX(...) : (0,_,(1,v=1)); (1,_,(2,v=2))
s11 : p & AX(...) : (0,_,(1,v=1))
*)
|
