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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 | |
ae4735db | 53 | |
34e49164 C |
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 | |
ae4735db | 58 | |
34e49164 C |
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 | |
5636bb2c | 72 | let or_roots = |
34e49164 C |
73 | List.fold_left |
74 | (function prev -> function cur -> Ast_ctl.Or(prev,cur)) | |
75 | (List.hd match_roots) (List.tl match_roots) in | |
5636bb2c C |
76 | (* no point to search if no path, and the presence of after |
77 | in the AF formula can make things slow *) | |
78 | if List.mem node !roots | |
79 | then acc | |
80 | else | |
81 | (node, | |
82 | Ast_ctl.AF(Ast_ctl.BACKWARD,Ast_ctl.NONSTRICT, | |
83 | Ast_ctl.Or(or_roots,Ast_ctl.Pred(After))), | |
84 | Ast_ctl.And | |
85 | (Ast_ctl.NONSTRICT, | |
86 | Ast_ctl.Not(or_roots), | |
87 | Ast_ctl.EX | |
88 | (Ast_ctl.BACKWARD, | |
89 | Ast_ctl.EU(Ast_ctl.BACKWARD,or_roots,match_node)))) | |
34e49164 C |
90 | (*exef |
91 | (wrap(Ast_ctl.And(Ast_ctl.NONSTRICT,match_node,exef(roots))))*) | |
92 | :: acc) | |
93 | modified [] | |
94 | ||
95 | (* Step 3: check the formula on the control-flow graph *) | |
96 | ||
ae4735db | 97 | module PRED = |
34e49164 C |
98 | struct |
99 | type t = Ograph_extended.nodei nodes | |
100 | let print_predicate = function | |
101 | After -> Format.print_string "after" | |
102 | | Node x -> Format.print_string (string_of_int x) | |
103 | end | |
104 | ||
105 | module ENV = | |
106 | struct | |
107 | type value = unit | |
108 | type mvar = unit | |
109 | let eq_mvar x x' = failwith "should not be invoked" | |
110 | let eq_val v v' = failwith "should not be invoked" | |
111 | let merge_val v v' = failwith "should not be invoked" | |
112 | ||
113 | let print_mvar s = failwith "should not be invoked" | |
114 | let print_value x = failwith "should not be invoked" | |
115 | end | |
116 | ||
117 | ||
ae4735db | 118 | module CFG = |
34e49164 C |
119 | struct |
120 | type node = Ograph_extended.nodei | |
ae4735db C |
121 | type cfg = |
122 | (Control_flow_c.node, Control_flow_c.edge) | |
34e49164 C |
123 | Ograph_extended.ograph_mutable |
124 | let predecessors cfg n = List.map fst ((cfg#predecessors n)#tolist) | |
125 | let successors cfg n = List.map fst ((cfg#successors n)#tolist) | |
126 | let extract_is_loop cfg n = | |
127 | Control_flow_c.extract_is_loop (cfg#nodes#find n) | |
128 | let print_node i = Format.print_string (string_of_int i) | |
129 | let size cfg = cfg#nodes#length | |
485bce71 | 130 | let print_graph cfg label border_nodes fill_nodes filename = () |
34e49164 C |
131 | end |
132 | ||
133 | module ENGINE = Ctl_engine.CTL_ENGINE (ENV) (CFG) (PRED) | |
134 | ||
135 | let test_formula state formula cfg = | |
136 | let label = function | |
137 | Node pred -> [(pred,[],[])] | |
138 | | After -> | |
139 | List.concat | |
140 | (List.map | |
141 | (fun (nodei, node) -> | |
142 | match Control_flow_c.unwrap node with | |
143 | Control_flow_c.AfterNode -> [(nodei,[],[])] | |
144 | | _ -> []) | |
145 | cfg#nodes#tolist) in | |
146 | let verbose = !Flag_ctl.verbose_ctl_engine in | |
147 | let pm = !Flag_ctl.partial_match in | |
485bce71 | 148 | (* let gt = !Flag_ctl.graphical_trace in *) |
34e49164 C |
149 | Flag_ctl.verbose_ctl_engine := false; |
150 | Flag_ctl.partial_match := false; | |
485bce71 C |
151 | Flag_ctl.checking_reachability := true; |
152 | (* Flag_ctl.graphical_trace := ""; *) | |
34e49164 C |
153 | let res = |
154 | ENGINE.sat (cfg,label,List.map fst cfg#nodes#tolist) | |
155 | (CTL.And(CTL.NONSTRICT,CTL.Pred(Node(state)),formula)) | |
156 | [[Node(state)]] in | |
157 | Flag_ctl.verbose_ctl_engine := verbose; | |
158 | Flag_ctl.partial_match := pm; | |
485bce71 C |
159 | Flag_ctl.checking_reachability := false; |
160 | (* Flag_ctl.graphical_trace := gt; *) | |
34e49164 C |
161 | match res with [] -> false | _ -> true |
162 | ||
163 | (* ---------------------------------------------------------------- *) | |
164 | (* Entry point *) | |
165 | ||
166 | (* The argument is a list of triples with a node name, an empty environment | |
167 | and a witness tree *) | |
168 | ||
169 | type witness = | |
170 | (Ograph_extended.nodei, unit, | |
171 | (Ograph_extended.nodei, unit, unit) Ast_ctl.generic_ctl list) | |
172 | Ast_ctl.generic_witnesstree | |
173 | ||
174 | type ('a,'b,'c,'d,'e) triples = | |
175 | (Ograph_extended.nodei * 'a * | |
176 | (Ograph_extended.nodei, | |
177 | ('b, ('c, 'd) Wrapper_ctl.wrapped_binding) CTL.generic_subst list, 'e) | |
178 | CTL.generic_witnesstree list) list | |
179 | ||
180 | let check_reachability triples cfg = | |
181 | Hashtbl.clear modified; | |
182 | List.iter build_modified triples; | |
183 | let formulas = create_formulas() in | |
184 | List.iter | |
185 | (function (node,af_formula,ef_formula) -> | |
186 | if test_formula node af_formula cfg | |
187 | then | |
188 | if test_formula node ef_formula cfg | |
189 | then | |
190 | Printf.printf "warning: node %d may be inconsistently modified\n" | |
191 | node | |
192 | else () | |
193 | else | |
194 | failwith | |
195 | (Printf.sprintf | |
196 | "node %d reachable by inconsistent control-flow paths" node)) | |
197 | formulas |