@@ -15,12 +15,22 @@ when analysis is incomplete. The symbolic execution includes constant
1515folding so loops that have a constant number of iterations will be
1616handled completely (assuming the unwinding limit is sufficient).
1717
18- The output of the symbolic execution is a system of equations; an object
19- containing a list of ` symex_target_elements ` , each of which are
20- equalities between ` expr ` expressions. See ` symex_target_equation.h ` .
21- The output is in static, single assignment (SSA) form, which is * not*
22- the case for goto-programs.
18+ The output of symbolic execution is a system of equations; an object
19+ of type ` symex_target_equationt ` , containing a list of
20+ ` symex_target_equationt::SSA_stept ` , each of which are equalities
21+ between ` exprt ` expressions. This list is constructed incrementally as
22+ the symbolic execution engine walks through the goto-program using the
23+ ` symex_targett ` interface. This interface (implemented by
24+ ` symex_target_equationt ` ) exposes functions that append SSA steps into
25+ the aforementioned list while transforming expressions into
26+ Static Single Assignment (SSA) form. For more details on this process
27+ see ` symex_target_equation.h ` , for an overview of SSA see
28+ \ref static-single-assignment.
29+
30+ At a later stage, BMC will convert the generated SSA steps into an
31+ equation that can be passed to the solver.
2332
33+ ---
2434\section symbolic-execution Symbolic Execution
2535
2636In the \ref goto-symex directory.
@@ -95,47 +105,73 @@ execution run does not add any paths to the workqueue but rather merges
95105all the paths together, so the additional path-exploration loop is
96106skipped over.
97107
98- \subsection ssa-renaming SSA renaming levels
99-
100- In goto-programs, variable names get a prefix to indicate their scope
101- (like ` main::1::%foo ` or whatever). At symbolic execution level, variables
102- also get a _ suffix_ because we’re doing single-static assignment. There
103- are three “levels” of renaming. At Level 2, variables are renamed every
104- time they are encountered in a function. At Level 1, variables are
105- renamed every time the functions that contain those variables are
106- called. At Level 0, variables are renamed every time a new thread
107- containing those variables are spawned. We can inspect the renamed
108- variable names with the –show-vcc flag, which prints a string with the
109- following format: ` %%s!%%d@%%d#%%d ` . The string field is the variable name,
110- and the numbers after the !, @, and # are the L0, L1, and L2 suffixes
111- respectively. The following examples illustrate Level 1 and 2 renaming:
108+ ---
109+ \section static-single-assignment Static Single Assignment (SSA) Form
110+
111+ ** Key classes:**
112+ * symex_targett
113+ * symex_target_equationt
114+
115+ * Static Single Assignment (SSA)* form is an intermediate
116+ representation that satisfies the following properties:
117+
118+ 1 . Every variable is * assigned exactly once* .
119+ 2 . Every variable must be * defined* before use.
120+
121+ In-order to convert a goto-program to SSA form all variables are
122+ versioned (renamed) through the addition of a _ suffix_ .
123+
124+ There are three “levels” of versioning:
125+
126+ ** Level 2 (L2):** variables are versioned every time they are encountered
127+ in a function.
128+
129+ ** Level 1 (L1):** variables are versioned every time the functions that
130+ contain those variables are called.
131+
132+ ** Level 0 (L0):** variables are versioned every time a new thread
133+ containing those variables are spawned.
134+
135+ We can inspect the versioned variable names with the ** –show-vcc** flag,
136+ this prints a string with the following format: ` %%s!%%d@%%d#%%d ` .
137+ Where the string field is the variable name, and the numbers after
138+ the !, @, and # are the L0, L1, and L2 suffixes respectively.
139+
140+ \subsection L1-L2 Level 1 and level 2 versioning
141+
142+ The following examples illustrate Level 1 and 2 versioning.
112143
113144 $ cat l1.c
114- int main() {
145+ int main()
146+ {
115147 int x=7;
116148 x=8;
117149 assert(0);
118150 }
151+
119152 $ cbmc --show-vcc l1.c
120153 ...
121154 {-12} x!0@1#2 == 7
122155 {-13} x!0@1#3 == 8
123156
124- That is, the L0 names for both xs are 0; the L1 names for both xs are 1;
125- but each occurrence of x within main() gets a fresh L2 suffix (2 and 3,
126- respectively).
157+ That is, the L0 names for both x's are 0; the L1 names for both x's are
158+ 1; but each occurrence of x within main() gets a fresh L2 suffix (2
159+ and 3, respectively).
127160
128161 $ cat l2.c
129- void foo(){
162+ void foo()
163+ {
130164 int x=7;
131165 x=8;
132166 x=9;
133167 }
134- int main(){
168+ int main()
169+ {
135170 foo();
136171 foo();
137172 assert(0);
138173 }
174+
139175 $ cbmc --show-vcc l2.c
140176 ...
141177 {-12} x!0@1#2 == 7
@@ -150,6 +186,10 @@ incremented (from 1 to 2) and the L0 counter is reset (back to 2, after
150186having been incremented up to 4). The L0 counter then increases every
151187time we access x as we walk through the function.
152188
189+ \subsection L0 Level 0 versioning
190+
191+ TODO
192+
153193---
154194\section counter-example-production Counter Example Production
155195
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