2 (* ********************************************************************** *)
3 (* Module: EXAMPLE_ENGINE (instance of CTL_ENGINE) *)
4 (* ********************************************************************** *)
6 (* Simple env.: meta.vars and values are strings *)
11 let eq_mvar x x'
= x
= x'
;;
12 let eq_val v v'
= v
= v'
;;
13 let merge_val v v'
= v
;;
17 (* Simple predicates *)
20 type predicate
= string
23 module EXAMPLE_ENGINE
=
24 Wrapper_ctl.CTL_ENGINE_BIS
(SIMPLE_ENV
) (Ctl_engine.OGRAPHEXT_GRAPH
) (WRAPPER_PRED
)
28 (* ******************************************************************** *)
32 (* ******************************************************************** *)
34 (* For convenience in the examples *)
36 open Ctl_engine.OGRAPHEXT_GRAPH
;;
40 (* ---------------------------------------------------------------------- *)
42 (* ---------------------------------------------------------------------- *)
44 (* FIX ME: move to ENGINE module *)
45 let (-->) x v
= Subst
(x
,v
);;
47 (* FIX ME: move to ENGINE module *)
48 let (-/->) x v
= NegSubst
(x
,v
);;
50 let mkgraph nodes edges
=
51 let g = ref (new Ograph_extended.ograph_extended
) in
53 (* let (g',i) = (!g)#add_node x in *)
54 (* now I need to force the nodei of a node, because of the state(vx) predicates
55 hence add_node -> add_nodei
57 let (g'
, i
) = !g#add_nodei n x
in
60 let adde anodes
(n1
,n2
,x
) =
61 let g'
= (!g)#add_arc
((List.assoc n1 anodes
,List.assoc n2 anodes
),x
) in
63 let add_nodes = List.map
addn nodes
in
64 let _add_edges = List.map
(adde add_nodes) edges
in
69 (* CTL parameterised on basic predicates and metavar's*)
70 type ('pred
,'mvar
) old_gen_ctl
=
74 | Not_
of ('pred
,'mvar
) old_gen_ctl
75 | Exists_
of 'mvar
* ('pred
,'mvar
) old_gen_ctl
(* !!! *)
76 | And_
of ('pred
,'mvar
) old_gen_ctl
* ('pred
,'mvar
) old_gen_ctl
77 | Or_
of ('pred
,'mvar
) old_gen_ctl
* ('pred
,'mvar
) old_gen_ctl
78 | Implies_
of ('pred
,'mvar
) old_gen_ctl
* ('pred
,'mvar
) old_gen_ctl
79 | AF_
of ('pred
,'mvar
) old_gen_ctl
80 | AX_
of ('pred
,'mvar
) old_gen_ctl
81 | AG_
of ('pred
,'mvar
) old_gen_ctl
82 | AU_
of ('pred
,'mvar
) old_gen_ctl
* ('pred
,'mvar
) old_gen_ctl
83 | EF_
of ('pred
,'mvar
) old_gen_ctl
84 | EX_
of ('pred
,'mvar
) old_gen_ctl
85 | EG_
of ('pred
,'mvar
) old_gen_ctl
86 | EU_
of ('pred
,'mvar
) old_gen_ctl
* ('pred
,'mvar
) old_gen_ctl
87 | Let_
of string * ('pred
,'mvar
) old_gen_ctl
* ('pred
,'mvar
) old_gen_ctl
91 let anno phi
= (phi
,None
) in
93 | False_
-> anno False
95 | Pred_
(p
) -> anno (Pred
(p
))
96 | Not_
(phi
) -> anno (Not
(mkanno phi
))
97 | Exists_
(v
,phi
) -> anno (Exists
(v
,mkanno phi
))
98 | And_
(phi1
,phi2
) -> anno (And
(mkanno phi1
,mkanno phi2
))
99 | Or_
(phi1
,phi2
) -> anno (Or
(mkanno phi1
,mkanno phi2
))
100 | Implies_
(phi1
,phi2
) -> anno (Implies
(mkanno phi1
,mkanno phi2
))
101 | AF_
(phi1
) -> anno (AF
(mkanno phi1
))
102 | AX_
(phi1
) -> anno (AX
(mkanno phi1
))
103 | AG_
(phi1
) -> anno (AG
(mkanno phi1
))
104 | AU_
(phi1
,phi2
) -> anno (AU
(mkanno phi1
,mkanno phi2
))
105 | EF_
(phi1
) -> anno (EF
(mkanno phi1
))
106 | EX_
(phi1
) -> anno (EX
(mkanno phi1
))
107 | EG_
(phi1
) -> anno (EG
(mkanno phi1
))
108 | EU_
(phi1
,phi2
) -> anno (EU
(mkanno phi1
,mkanno phi2
))
109 | Let_
(x
,phi1
,phi2
) -> anno (Let
(x
,mkanno phi1
,mkanno phi2
))
110 | Ref_
(s
) -> anno (Ref
(s
))
113 (* ******************************************************************** *)
115 (* CTL: f(x) /\ AF(Ey.g(y)) *)
116 (* ******************************************************************** *)
120 | "f(x)" -> [(0,["x" --> "1"]); (1,["x" --> "2"])]
121 | "g(y)" -> [(3,["y" --> "1"]); (4,["y" --> "2"])]
131 [(0,"f(1)");(1,"f(2)");(2,"< >");(3,"g(1)");(4,"g(2)");(5,"<exit>")] in
132 let edges = [(0,2); (1,2); (2,3); (2,4); (3,5); (4,5); (5,5)] in
133 mkgraph nodes (List.map
(fun (x
,y
) -> (x
,y
,())) edges)
136 let ex1states = List.map fst
(ex1graph#
nodes)#tolist
;;
138 let ex1model = (ex1graph,ex1lab,ex1states);;
139 let ex1model_wrapped = (ex1graph,wrap_label
ex1lab,ex1states);;
141 let ex1s0 = Exists_
("v0",Pred_
("f(x)",UnModif
"v0"));;
142 let ex1s1 = Exists_
("v1",Pred_
("g(y)",Modif
"v1"));;
143 let ex1s2 = Exists_
("y",ex1s1);;
144 let ex1s3 = AF_
(ex1s2);;
145 let ex1s4 = And_
(ex1s0,ex1s3);;
147 let ex1s3a = AX_
(ex1s2);;
148 let ex1s4a = AX_
(AX_
(ex1s2));;
149 let ex1s5a = And_
(ex1s0,ex1s4a);;
151 let ex1s0b = Pred_
("g(y)", Modif
"v0");;
152 let ex1s1b = Exists_
("v0",ex1s0b);;
153 let ex1s2b = Exists_
("y",ex1s1b);;
154 let ex1s3b = AF_
(ex1s2b);;
155 let ex1s4b = AX_
(ex1s3b);;
156 let ex1s5b = Pred_
("f(x)", UnModif
"v3");;
157 let ex1s6b = Exists_
("v3", ex1s5b);;
158 let ex1s7b = Exists_
("x", ex1s6b);;
159 let ex1s8b = And_
(ex1s7b,ex1s4b);;
161 let ex1s7c = And_
(ex1s6b,ex1s4b);;
162 let ex1s8c = Exists_
("x",ex1s7c);;
164 let ex1phi1 = ex1s4;;
165 let ex1phi2 = ex1s5a;;
170 Pred_
("f(x)", UnModif
"v3")))),
173 (Exists_
("y", (* change this to Y and have strange behaviour *)
175 Pred_
("g(y)", Modif
"v0")
182 Pred_
("f(x)", UnModif
"v3"))),
185 (Exists_
("y", (* change this to Y and have strange behaviour *)
187 Pred_
("g(y)", Modif
"v0")
191 let ex1phi5 = AU_
(True_
,Exists_
("y", Exists_
("v0",Pred_
("g(y)",Modif
"v0"))));;
195 Not_
(Exists_
("x",Exists_
("v1",Pred_
("f(x)",UnModif
"v1")))),
196 Exists_
("y", Exists_
("v0",Pred_
("g(y)",Modif
"v0")))
202 Not_
(Or_
(Pred_
("f(1)",Control
),Pred_
("f(2)",Control
))),
203 Exists_
("y", Exists_
("v0",Pred_
("g(y)",Modif
"v0")))
206 let ex1 phi
= satbis
ex1model (mkanno phi
);;
207 let ex1nc phi
= satbis_noclean
ex1model (mkanno phi
);;
210 (* ******************************************************************** *)
212 (* ******************************************************************** *)
217 | "{" -> [(1,[]); (2,[])]
218 | "}" -> [(3,[]); (4,[])]
219 | "paren(v)" -> [(1,["v" --> "1"]); (2,["v" --> "2"]);
220 (3,["v" --> "2"]); (4,["v" --> "1"])]
226 [(0,"p");(1,"{");(2,"{");(3,"}");(4,"}");(5,"<exit>")] in
227 let edges = [(0,1); (1,2); (2,3); (3,4); (4,5); (5,5)] in
228 mkgraph nodes (List.map
(fun (x
,y
) -> (x
,y
,())) edges)
231 let ex2states = List.map fst
(ex2graph#
nodes)#tolist
;;
233 let ex2model = (ex2graph,ex2lab,ex2states);;
234 let ex2model_wrapped = (ex2graph,wrap_label
ex2lab,ex2states);;
236 let ex2s0 = Pred_
("p",Control
);;
237 let ex2s1 = Pred_
("{",Control
);;
238 let ex2s2 = Pred_
("paren(v)",Control
);;
239 let ex2s3 = And_
(ex2s1,ex2s2);;
240 let ex2s4 = Pred_
("}",Control
);;
241 let ex2s5 = Pred_
("paren(v)",Control
);;
242 let ex2s6 = And_
(ex2s4,ex2s5);;
243 let ex2s7 = AF_
(ex2s6);;
244 let ex2s8 = And_
(ex2s3,ex2s7);;
245 let ex2s9 = Exists_
("v",ex2s8);;
246 let ex2s10 = AX_
(ex2s9);;
247 let ex2s11 = And_
(ex2s0,ex2s10);;
249 let ex2phi1 = ex2s11;;
251 let ex2 phi
= satbis_noclean
ex2model (mkanno phi
)
260 +---------- s8:& --------+
264 s1:"{" s2:paren(v) +-- s6:& -+
269 s1 : "{" : (1,_,_); (2,_,_)
270 s2 : paren(v) : (1,v=1,_); (2,v=2,_); (3,v=2,_); (4,v=1,_)
271 s3 : "{" & paren(v) : (1,v=1,_); (2,v=2,_)
272 s4 : "}" : (3,_,_); (4,_,_)
273 s5 : paren(v) : (1,v=1,_); (2,v=2,_); (3,v=2,_); (4,v=1,_)
274 s6 : "}" & paren(v) : (3,v=2,_); (4,v=1,_)
275 s7 : AF(...) : (0;1;2;3,v=2,_); (0;1;2;3;4,v=1,_)
276 s8 : (...&...) & AF(...) : (1,v=1,_); (2,v=2,_)
277 s9 : exists ... : (1,_,(1,v=1)); (2,_,(2,v=2))
278 s10 : AX(...) : (0,_,(1,v=1)); (1,_,(2,v=2))
279 s11 : p & AX(...) : (0,_,(1,v=1))