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34e49164 C |
1 | (* ---------------------------------------------------------------- *) |
2 | (* code to check for ambiguities *) | |
3 | ||
4 | (* Idea: for each node that is said to be modified in any witness tree, we | |
5 | check that all backward paths end up at the root of some witness tree | |
6 | that says that the node should be modified. We then give a warning, if | |
7 | the node itself appears more than once in such a path, because then there | |
8 | could be some instances that are modified and some that are not. An | |
9 | example is as follows: | |
10 | ||
11 | f(); ... g(); ... - h(); | |
12 | ||
13 | with C code: f(); while(E) { h(); g(); } g(); h(); | |
14 | ||
15 | Then the h() in the while loop matches both the first ... and the - h(); | |
16 | ||
17 | Concretely, if a node 47 is in the witness tree rooted at 1 and the | |
18 | witness tree rooted at 2, then we give an error if 47 is not in the set | |
19 | of nodes satisfying AF[1v2] and give a warning if 47 is in the set of | |
20 | nodes satisfying EXEF(47 & EXEF(1v2)). (Note that the root of a witness | |
21 | tree here is the node causing the pattern to match; there might not be | |
22 | any witnesses associated with this node.) | |
23 | ||
24 | Another try on the exists formula: | |
25 | !(1v2) & EXE[!(1v2) U 47] | |
26 | The first !(1v2) is to discard immediately cases where the beginning and | |
27 | end of the path are the same. Afterwards, it would only seem necessary to | |
28 | serach up to the next occurrence of 47 (leaf), ensuring that there are not | |
29 | 1s or 2s (starting points) along the way. Then the second 47 would be in | |
30 | the path, but possible not transformed. | |
31 | *) | |
32 | ||
33 | module G = Ograph_extended | |
34 | module CTL = Ast_ctl | |
35 | ||
36 | (* Step 1: for each tree, make a mapping from the modified nodes to the root | |
37 | of the tree *) | |
38 | ||
39 | let modified = (Hashtbl.create(25) : (G.nodei, G.nodei list ref) Hashtbl.t) | |
40 | ||
41 | let build_modified (n,_,wits) = | |
42 | let rec loop = function | |
43 | CTL.Wit(st,[CTL.Subst(x,Wrapper_ctl.PredVal(CTL.Modif(v)))],anno,wit) -> | |
44 | let cell = | |
45 | try Hashtbl.find modified st | |
46 | with Not_found -> | |
47 | let cell = ref [] in Hashtbl.add modified st cell; cell in | |
48 | cell := n :: !cell; | |
49 | List.iter loop wit | |
50 | | CTL.Wit(st,_,anno,wit) -> List.iter loop wit | |
51 | | CTL.NegWit(wit) -> () in | |
52 | List.iter loop wits | |
53 | ||
54 | (* Step 2: For each node in the hash table, create the error and warning | |
55 | formulas *) | |
56 | ||
57 | type 'a nodes = Node of 'a | After | |
58 | ||
59 | let create_formulas _ = | |
60 | Hashtbl.fold | |
61 | (function node -> | |
62 | function roots -> | |
63 | function acc -> | |
64 | (*let exef f = | |
65 | wrap | |
66 | (Ast_ctl.EX | |
67 | (Ast_ctl.BACKWARD,wrap(Ast_ctl.EF(Ast_ctl.BACKWARD,f)))) in*) | |
68 | let match_node = Ast_ctl.Pred(Node(node)) in | |
69 | let match_roots = | |
70 | List.map (function n -> Ast_ctl.Pred(Node(n))) | |
71 | (List.sort compare !roots) in | |
72 | let roots = | |
73 | List.fold_left | |
74 | (function prev -> function cur -> Ast_ctl.Or(prev,cur)) | |
75 | (List.hd match_roots) (List.tl match_roots) in | |
76 | (node, | |
77 | Ast_ctl.AF(Ast_ctl.BACKWARD,Ast_ctl.NONSTRICT, | |
78 | Ast_ctl.Or(roots,Ast_ctl.Pred(After))), | |
79 | Ast_ctl.And | |
80 | (Ast_ctl.NONSTRICT, | |
81 | Ast_ctl.Not(roots), | |
82 | Ast_ctl.EX | |
83 | (Ast_ctl.BACKWARD, | |
84 | Ast_ctl.EU(Ast_ctl.BACKWARD,roots,match_node)))) | |
85 | (*exef | |
86 | (wrap(Ast_ctl.And(Ast_ctl.NONSTRICT,match_node,exef(roots))))*) | |
87 | :: acc) | |
88 | modified [] | |
89 | ||
90 | (* Step 3: check the formula on the control-flow graph *) | |
91 | ||
92 | module PRED = | |
93 | struct | |
94 | type t = Ograph_extended.nodei nodes | |
95 | let print_predicate = function | |
96 | After -> Format.print_string "after" | |
97 | | Node x -> Format.print_string (string_of_int x) | |
98 | end | |
99 | ||
100 | module ENV = | |
101 | struct | |
102 | type value = unit | |
103 | type mvar = unit | |
104 | let eq_mvar x x' = failwith "should not be invoked" | |
105 | let eq_val v v' = failwith "should not be invoked" | |
106 | let merge_val v v' = failwith "should not be invoked" | |
107 | ||
108 | let print_mvar s = failwith "should not be invoked" | |
109 | let print_value x = failwith "should not be invoked" | |
110 | end | |
111 | ||
112 | ||
113 | module CFG = | |
114 | struct | |
115 | type node = Ograph_extended.nodei | |
116 | type cfg = | |
117 | (Control_flow_c.node, Control_flow_c.edge) | |
118 | Ograph_extended.ograph_mutable | |
119 | let predecessors cfg n = List.map fst ((cfg#predecessors n)#tolist) | |
120 | let successors cfg n = List.map fst ((cfg#successors n)#tolist) | |
121 | let extract_is_loop cfg n = | |
122 | Control_flow_c.extract_is_loop (cfg#nodes#find n) | |
123 | let print_node i = Format.print_string (string_of_int i) | |
124 | let size cfg = cfg#nodes#length | |
485bce71 | 125 | let print_graph cfg label border_nodes fill_nodes filename = () |
34e49164 C |
126 | end |
127 | ||
128 | module ENGINE = Ctl_engine.CTL_ENGINE (ENV) (CFG) (PRED) | |
129 | ||
130 | let test_formula state formula cfg = | |
131 | let label = function | |
132 | Node pred -> [(pred,[],[])] | |
133 | | After -> | |
134 | List.concat | |
135 | (List.map | |
136 | (fun (nodei, node) -> | |
137 | match Control_flow_c.unwrap node with | |
138 | Control_flow_c.AfterNode -> [(nodei,[],[])] | |
139 | | _ -> []) | |
140 | cfg#nodes#tolist) in | |
141 | let verbose = !Flag_ctl.verbose_ctl_engine in | |
142 | let pm = !Flag_ctl.partial_match in | |
485bce71 | 143 | (* let gt = !Flag_ctl.graphical_trace in *) |
34e49164 C |
144 | Flag_ctl.verbose_ctl_engine := false; |
145 | Flag_ctl.partial_match := false; | |
485bce71 C |
146 | Flag_ctl.checking_reachability := true; |
147 | (* Flag_ctl.graphical_trace := ""; *) | |
34e49164 C |
148 | let res = |
149 | ENGINE.sat (cfg,label,List.map fst cfg#nodes#tolist) | |
150 | (CTL.And(CTL.NONSTRICT,CTL.Pred(Node(state)),formula)) | |
151 | [[Node(state)]] in | |
152 | Flag_ctl.verbose_ctl_engine := verbose; | |
153 | Flag_ctl.partial_match := pm; | |
485bce71 C |
154 | Flag_ctl.checking_reachability := false; |
155 | (* Flag_ctl.graphical_trace := gt; *) | |
34e49164 C |
156 | match res with [] -> false | _ -> true |
157 | ||
158 | (* ---------------------------------------------------------------- *) | |
159 | (* Entry point *) | |
160 | ||
161 | (* The argument is a list of triples with a node name, an empty environment | |
162 | and a witness tree *) | |
163 | ||
164 | type witness = | |
165 | (Ograph_extended.nodei, unit, | |
166 | (Ograph_extended.nodei, unit, unit) Ast_ctl.generic_ctl list) | |
167 | Ast_ctl.generic_witnesstree | |
168 | ||
169 | type ('a,'b,'c,'d,'e) triples = | |
170 | (Ograph_extended.nodei * 'a * | |
171 | (Ograph_extended.nodei, | |
172 | ('b, ('c, 'd) Wrapper_ctl.wrapped_binding) CTL.generic_subst list, 'e) | |
173 | CTL.generic_witnesstree list) list | |
174 | ||
175 | let check_reachability triples cfg = | |
176 | Hashtbl.clear modified; | |
177 | List.iter build_modified triples; | |
178 | let formulas = create_formulas() in | |
179 | List.iter | |
180 | (function (node,af_formula,ef_formula) -> | |
181 | if test_formula node af_formula cfg | |
182 | then | |
183 | if test_formula node ef_formula cfg | |
184 | then | |
185 | Printf.printf "warning: node %d may be inconsistently modified\n" | |
186 | node | |
187 | else () | |
188 | else | |
189 | failwith | |
190 | (Printf.sprintf | |
191 | "node %d reachable by inconsistent control-flow paths" node)) | |
192 | formulas |