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Contents

Chapter 1  Introduction

1.1  Batch Mode vs. GUI Mode

The Jessie plug-in allows to perform deductive verification of C programs inside Frama-C. The C file possibly annotated in ACSL is first checked for syntax errors by Frama-C core, before it is translated to various intermediate languages inside the Why Platform embedded in Frama-C, and finally verification conditions (VCs) are generated and a prover is called on these, as sketched in Figure 1.1.

By default, the Jessie plug-in launches in its GUI mode. To invoke this mode on a file ex.c, just type

> frama-c -jessie ex.c

The GUI of the Why Plaform (a.k.a. GWhy) is called. It displays each VC in a row, with available provers arranged as columns.

To invoke Jessie in batch mode, use option -jessie-atp with the prover name as argument, e.g.

> frama-c -jessie -jessie-atp simplify ex.c

runs prover Simplify on generated VCs. Valid identifiers for provers are documented in Why. The list includes alt-ergo, cvc3, yices, z3. See also the prover tricks page http://why.lri.fr/provers.html.

Finally, you can use the generic name goals to just ask for generation of VCs without running any prover.


image
Figure 1.1: Frama-C and the Why Platform

1.2  Basic Use

A program does not need to be complete nor annotated to be analyzed with the Jessie plug-in. As a first example, take program max:

int max(int i, int j) { 
  
return (i < j) ? j : i; 

Calling the Jessie plug-in in batch mode generates the following output:

frama-c -jessie -jessie-atp simplify max.c
Parsing
[preprocessing] running gcc -C -E -I. -include
/usr/local/share/frama-c/jessie/jessie_prolog.h -dD max.c
Cleaning unused parts
Symbolic link
Starting semantical analysis
Starting Jessie translation
Producing Jessie files in subdir max.jessie
File max.jessie/max.jc written.
File max.jessie/max.cloc written.
Calling Jessie tool in subdir max.jessie
Generating Why function f
Calling VCs generator.
why -simplify [...] why/max.why
Running Simplify on proof obligations
(. = valid * = invalid ? = unknown # = timeout ! = failure)
simplify/max_why.sx           :  (0/0/0/0/0)

Simplify is an automatic theorem prover distributed separately from Why and Jessie. Among available automatic provers, it is one that produces good results for software verification. Another automatic prover that produces good results is Alt-Ergo.

The result of calling prover Simplify is succinctly reported as a sequence of symbols ., *, ?, # and ! which denote respectively that the corresponding VC is valid, invalid or unknown, or else that a timeout or a failure occured. By default, timeout is set to 10 s for each VC. This result is summarized as a tuple (v,i,u,t,f) reporting the total number of each outcome.

Here, the summary (0/0/0/0/0) means that there were no VCs to prove (calling Jessie in GUI mode similarly displays no VC to prove). Indeed, function max is safe and we did not ask for the verification of any functional property.

Consider now adding a postcondition to function max:

//@ ensures \result == ((i < j) ? j : i); 
int max(int i, int j) { 
  
return (i < j) ? j : i; 

This ACSL annotation expresses the fact function max returns the maximum of its parameters i and j. Now, running the Jessie plug-in in batch mode outputs:

...
Running Simplify on proof obligations
(. = valid * = invalid ? = unknown # = timeout ! = failure)
simplify/max_why.sx           : .? (1/0/1/0/0)
total   :   2
valid   :   1 ( 50%)
invalid :   0 (  0%)
unknown :   1 ( 50%)
timeout :   0 (  0%)
failure :   0 (  0%)
total wallclock time : 0.19 sec
total CPU time       : 0.16 sec
valid VCs:
    average CPU time : 0.08
    max CPU time     : 0.08
invalid VCs:
    average CPU time : nan
    max CPU time     : 0.00
unknown VCs:
    average CPU time : 0.08
    max CPU time     : 0.08

This means that Simplify could prove one of the two VCs. To see what each VC represents, let us now invoke Jessie in GUI mode. Each VC represents verification of the postcondition in a different context. The first VC represents the context where i < j:

image

The second VC represents the context where i >= j. Context can be seen in the upper right panel of GWhy, expressed in the intermediate language of Why. At this time, GWhy does not assist the user for linking the constructs found in the context to original C expressions or statements, although this can be done by hand for very short functions.

image

Running Simplify inside GWhy shows that the second VC is not proved by Simplify. However, it is proved by prover Alt-Ergo.

image

The Jessie plug-in can also be run in batch mode with prover Alt-Ergo instead of Simplify, with option -jessie-atp alt-ergo. This results in the following output:

...
Running Alt-Ergo on proof obligations
(. = valid * = invalid ? = unknown # = timeout ! = failure)
why/max_why.why               : .. (2/0/0/0/0)
total   :   2
valid   :   2 (100%)
invalid :   0 (  0%)
unknown :   0 (  0%)
timeout :   0 (  0%)
failure :   0 (  0%)
total wallclock time : 0.35 sec
total CPU time       : 0.14 sec
valid VCs:
    average CPU time : 0.07
    max CPU time     : 0.08
invalid VCs:
    average CPU time : nan
    max CPU time     : 0.00
unknown VCs:
    average CPU time : nan
    max CPU time     : 0.00

1.3  Safety Checking vs. Functional Verification

In the simple max example, VCs for the postcondition are grouped in the default behavior for function max. In general, VCs for a function are grouped in more than one group:

Here is a more complex variant of function max which takes pointer parameters and returns 0 on success and -1 on failure.

/*@ requires \valid(i) && \valid(j); 
  @ 
requires r == \null || \valid(r); 
  @ 
assigns *r; 
  @ 
behavior zero: 
  @   
assumes r == \null
  @   
assigns \nothing
  @   
ensures \result == 1; 
  @ 
behavior normal: 
  @   
assumes \valid(r); 
  @   
assigns *r; 
  @   
ensures *r == ((*i < *j) ? *j : *i); 
  @   
ensures \result == 0; 
  @*/
 
int max(int *r, int* i, int* j) { 
  
if (!r) return -1; 
  *r = (*i < *j) ? *j : *i; 
  
return 0; 

Notice that the annotations refer to the null pointer using ACSL syntax \null. It would be possible to use also the C macro NULL, but in that case we would have to ask Frama-C preprocessor phase to process the annotations too, since it does not by default. This is done by option -pp-annot of Frama-C. However, this alternative is not recommended since it is depended of the proprecessor in use (see http://bts.frama-c.com/dokuwiki/doku.php?id=mantis:frama-c:start#faq_tips_and_tricks)

Running the Jessie plug-in in GUI mode results in 4 groups of VCs: Safety, Default behavior, Normal behavior ‘normal‘ and Normal behavior ‘zero‘ for the two user-defined behaviors.

image

VCs that are proved in one group can be available to prove VCs in other groups. No circularity paradox is possible here, since the proof of a VC can only rely on other VCs higher in the control-flow graph of the function. We made the following choices:

Next, we detail how to prove each group of VCs.

Chapter 2  Safety Checking

A preliminary to the verification of functional properties using the Jessie plug-in is to verify the safety of functions. Safety has several components: memory safety, integer safety, termination. Memory safety deals with validity of memory accesses to allocated memory. Integer safety deals with absence of integer overflows and validity of operations on integers, such as the absence of division by zero. Termination amounts to check whether loops are always terminating, as well as recursive or mutually recursive functions.

2.1  Memory Safety

Our running example will be the famous binary_search function, which searches for a long in an ordered array of longs. On success, it returns the index at which the element appears in the array. On failure, it returns -1.

#pragma JessieIntegerModel(math) 
#pragma JessieTerminationPolicy(user) 
 
int binary_search(long t[], int n, long v) { 
  int l = 0, u = n
-1; 
  
while (l <= u) { 
    int m = (l + u) / 2; 
    
if (t[m] < v) 
      l = m + 1; 
    
else if (t[m] > v) 
      u = m 
- 1; 
    
else return m;  
  } 
  
return -1; 

To concentrate first on memory safety only, we declare two pragmas as above. The first pragma dictates that integers in C programs behave as infinite-precision mathematical integers, without overflows. The second pragma instructs the plug-in to ignore termination issues.

Let’s call Frama-C with the Jessie plug-in on this program:

> frama-c -jessie binary-search.c

As seen on Figure 2.1, we get 3 VCs, an obvious one that states the divisor 2 is not null, and two more that state the array access t[m] should be within bounds. This is due to the memory model used, that decomposes any access check into two: one that states the access is above the minimal bound allowed, and one that states the access is below the maximal bound allowed.


image
Figure 2.1: Memory safety with no annotations

The obvious VC is trivially proved by all provers, while the two VCs for memory safety cannot be proved. Indeed, it is false that, in any context, function binary_search is memory safe. To ensure memory safety, binary_search must be called in a context where n is positive and array t is valid between indices 0 and n-1 included. Since function binary_search accesses array t inside a loop, providing a precondition is not enough to make the generated VC provable. One must also provide a loop invariant. A loop invariant is a property that remains true at each iteration of the loop. It is often necessary for the user to provide these properties to help Jessie reason about loops. Assuming that the right property has been provided, Jessie is then left with the easier task of generating and verifying VCs that ensure that the property indeed holds at the beginning of each iteration.

In this example, it is necessary to provide an invariant that states the guarantees provided on the array index, despite its changing value. It states that the value of index l stays within the bounds of the array t.

//@ requires n >= 0 && \valid_range(t,0,n1); 
int binary_search(long t[], int n, long v) { 
  int l = 0, u = n
-1; 
  
//@ loop invariant 0 <= l && u <= n1; 
  
while (l <= u ) { 
    ... 

Seven VCs are now generated: 2 to guarantee the loop invariant is initially established (because the conjunction is split), 2 to guarantee the same loop invariant is preserved throughout the loop, and the 3 VCs seen previously. Not all generated VCs are proved automatically with these annotations. Of the 3 VCs seen previously, the maximal bound check is still not proved. And the preservation of the loop invariant that deals with an upper bound on u is not proved either. It comes from the non-linear expression assigned to min the loop, that is difficult to take into account automatically.

We solve this problem by adding an assertion to help automatic provers, providing some form of hint in the proof. This can be done by inserting assertions in the code, or by adding a globallemma, that should be proved using available axioms, and used as an axiom in proving the VC for safety. This works for our example.

/*@ lemma mean :  
  @   
\forall integer x, y; x <= y ==> x <= (x+y)/2 <= y;  
  @*/
 
 
//@ requires n >= 0 && \valid_range(t,0,n1); 
int binary_search(long t[], int n, long v) { 
  ... 


image
Figure 2.2: Memory safety with precondition and loop invariant

The results are shown on Figure 2.2, where all VCs, are proved by some prover. This guarantees the memory safety of function binary_search. The lemma itself is proved by Alt-Ergo, which has a little knowledge of the division operator. Given the lemma, other VCs are fully proved by Simplify and Z3, and partly by Yices and CVC3.

2.2  Integer Overflow Safety

Let us now consider machine integers instead of idealized mathematical integers. This is obtained by removing the pragma JessieIntegerModel. Without this pragma, integer types are now intepreted as bounded machine integers. However, the default is a defensive interpretation, which forbids the arithmetic operations to overflow.1


image
Figure 2.3: Memory safety + integer overflow safety

The result can be seen in Figure 2.3. There are ten more VCs to check that integer operations return a result within bounds, only one of which is not proved. With this exception, the results are nearly the same as with exact integers (proving the lemma takes more time, due to the additional encoding for bounded integers).

The only unproved VC expresses that l+u does not overflow. Nothing prevents this from happening with our current precondition for function binary_search [7]. There are two possibilities here. The easiest is to strengthen the precondition by requiring that n is no more than half the maximal signed integer INT_MAX. The best way is to change the source of binary_search to prevent overflows even in presence of large integers. It consists in changing the buggy line

    int m = (l + u) / 2;

into

    int m = l + (u - l) / 2;

This is our choice here. As shown in Figure 2.4, all VCs are now proved automatically.


image
Figure 2.4: Safety for patched program

2.3  Checking Termination

The last kind of safety property we want is termination. To check it, we first remove the pragma JessieTerminationPolicy. If we run the VC generation again, we get an additional VC that requires to prove the property 0 > 0. This VC is false, so our first step should be to help Jessie generate a more provable VC. The VC 0 > 0 is generated because we did not provide any loop variant for the while loop. A loop variant is a quantity which must decrease strictly at each loop iteration, while provably remaining non-negative for as long as the loop runs. In this example, a proper variant is ul. So our annotated program now looks as follows:

/*@ lemma mean :  
  @   
\forall integer x, y; x <= y ==> x <= (x+y)/2 <= y;  
  @*/
 
 
//@ requires n >= 0 && \valid_range(t,0,n1); 
int binary_search(long t[], int n, long v) { 
  int l = 0, u = n
-1; 
  
/*@ loop invariant 0 <= l && u <= n1; 
    @ 
loop variant ul; 
    @*/
 
  
while (l <= u) { 
    int m = l+(u
-l) / 2; 
    
if (t[m] < v) 
      l = m + 1; 
    
else if (t[m] > v) 
      u = m 
- 1; 
    
else return m; 
  } 
  
return -1; 

The additional VC is now proved.

Termination of recursive functions can be dealt with similarly by adding a decreases clause to the function’s contract. It is also possible to prove termination by using variants over any datatype d equipped with a well-founded relation. See the ACSL documentation for details.


1
In a context where it is intended for the operations to overflows, and thus operations are intentionnally done modulo, the same pragma should be set to the value modulo, see Jessie manual.

Chapter 3  Functional Verification

3.1  Behaviors

3.1.1  Simple functional property

Now that the safety of function binary_search has been established, one can attempt the verification of functional properties, like the input-output behavior of function binary_search. At the simplest, one can add a postcondition that binary_search should respect upon returning to its caller. Here, we add bounds on the value returned by binary_search. To prove this postcondition, strengthening the loop invariant is necessary.

/*@ lemma mean : \forall integer x, y; x <= y ==> x <= (x+y)/2 <= y; */ 
 
/*@ requires n >= 0 && \valid_range(t,0,n1); 
  @ 
ensures 1 <= \result <= n1; 
  @*/
 
int binary_search(int* t, int n, int v) { 
  int l = 0, u = n
-1; 
  
/*@ loop invariant 0 <= l && u <= n1; 
    @ 
loop variant ul; 
    @*/
 
  
while (l <= u) { 
    int m = l + (u 
- l) / 2; 
    
if (t[m] < v) 
      l = m + 1; 
    
else if (t[m] > v) 
      u = m 
- 1; 
    
else return m; 
  } 
  
return -1; 

As shown in Figure 3.1, all VCs are proved automatically here.


image
Figure 3.1: General postcondition

3.1.2  More advanced functional properties

One can be more precise and separate the postcondition according to different behaviors. The assumes clause of a behavior gives precisely the context in which a behavior applies. Here, we state that function binary_search has two modes: a success mode and a failure mode. This directly relies on array t to be sorted, thus we add this as a general requirement. The success mode states that whenever the calling context is such that value v is in the range of t searched, then the value returned is a valid index. The failure mode states that whenever the calling context is such that value v is not in the range of t searched, then function binary_search returns -1. Again, it is necessary to strengthen the loop invariant to prove the VC generated.

 
//@ lemma mean : \forall integer x, y; x <= y ==> x <= (x+y)/2 <= y;  
 
/*@ requires n >= 0 && \valid_range(t,0,n1); 
  @ 
behavior success: 
  @   
assumes // array t is sorted in increasing order 
  @     
\forall integer k1, k2; 0 <= k1 <= k2 <= n1 ==> t[k1] <= t[k2]; 
  @   
assumes // v appears somewhere in the array t 
  @     
\exists integer k; 0 <= k <= n1 && t[k] == v; 
  @   
ensures 0 <= \result <= n1; 
  @ 
behavior failure: 
  @   
assumes // v does not appear anywhere in the array t 
  @     
\forall integer k; 0 <= k <= n1 ==> t[k] != v; 
  @   
ensures \result == 1; 
  @*/
 
int binary_search(long t[], int n, long v) { 
  int l = 0, u = n
-1; 
  
/*@ loop invariant 0 <= l && u <= n1; 
    @ 
for success: 
    @   
loop invariant  
    @     
\forall integer k; 0 <= k < n && t[k] == v ==> l <= k <= u; 
    @ 
loop variant ul; 
    @*/
 
  
while (l <= u) { 
    int m = l + (u 
- l) / 2; 
    
if (t[m] < v) 
      l = m + 1; 
    
else if (t[m] > v) 
      u = m 
- 1; 
    
else return m; 
  } 
  
return -1; 

Figure 3.2 summarizes the results obtained in that case, for each behavior.


image
Figure 3.2: Postconditions in behaviors

3.2  Advanced Algebraic Modeling

The following example introduces use of algebraic specification. The goal is the verify a simple sorting algorithm (by extraction of the minimum).

The first step is to introduce logical predicates to define the meanings for an array to be sorted in increasing order, to be a permutation of another. This is done as follows, in a separate file say sorting.h

 
 
/*@ predicate Swap{L1,L2}(int *a, integer i, integer j) = 
  @   
\at(a[i],L1) == \at(a[j],L2) && 
  @   
\at(a[j],L1) == \at(a[i],L2) && 
  @   
\forall integer k; k != i && k != j 
  @       ==> 
\at(a[k],L1) == \at(a[k],L2); 
  @*/
 
 
/*@ inductive Permut{L1,L2}(int *a, integer l, integer h) { 
  @  
case Permut_refl{L}: 
  @   
\forall int *a, integer l, h; Permut{L,L}(a, l, h) ; 
  @  
case Permut_sym{L1,L2}: 
  @    
\forall int *a, integer l, h; 
  @      Permut{L1,L2}(a, l, h) ==> Permut{L2,L1}(a, l, h) ; 
  @  
case Permut_trans{L1,L2,L3}: 
  @    
\forall int *a, integer l, h; 
  @      Permut{L1,L2}(a, l, h) && Permut{L2,L3}(a, l, h) ==> 
  @        Permut{L1,L3}(a, l, h) ; 
  @  
case Permut_swap{L1,L2}: 
  @    
\forall int *a, integer l, h, i, j; 
  @       l <= i <= h && l <= j <= h && Swap{L1,L2}(a, i, j) ==> 
  @     Permut{L1,L2}(a, l, h) ; 
  @ } 
  @*/
 
 
/*@ predicate Sorted{L}(int *a, integer l, integer h) = 
  @   
\forall integer i; l <= i < h ==> a[i] <= a[i+1] ; 
  @*/
 

The code is then annotated using these predicates as follows

#pragma JessieIntegerModel(math) 
 
#include "sorting.h" 
 
/*@ requires \valid(t+i) && \valid(t+j); 
  @ 
assigns t[i],t[j]; 
  @ 
ensures Swap{Old,Here}(t,i,j); 
  @*/
 
void swap(int t[], int i, int j) { 
  int tmp = t[i]; 
  t[i] = t[j]; 
  t[j] = tmp; 

     
/*@ requires \valid_range(t,0,n1); 
  @ 
behavior sorted: 
  @   
ensures Sorted(t,0,n1); 
  @ 
behavior permutation: 
  @   
ensures Permut{Old,Here}(t,0,n1); 
  @*/
 
void min_sort(int t[], int n) { 
  int i,j; 
  int mi,mv; 
  
if (n <= 0) return
  
/*@ loop invariant 0 <= i < n; 
    @ 
for sorted:  
    @  
loop invariant  
    @   Sorted(t,0,i) &&  
    @   (
\forall integer k1, k2 ;  
    @      0 <= k1 < i <= k2 < n ==> t[k1] <= t[k2]) ; 
    @ 
for permutation: 
    @  
loop invariant Permut{Pre,Here}(t,0,n1); 
    @ 
loop variant ni; 
    @*/
 
  
for (i=0; i<n-1; i++) { 
    
// look for minimum value among t[i..n1] 
    mv = t[i]; mi = i; 
    
/*@ loop invariant i < j && i <= mi < n; 
      @ 
for sorted:  
      @  
loop invariant 
      @    mv == t[mi] && 
      @    (
\forall integer k; i <= k < j ==> t[k] >= mv); 
      @ 
for permutation: 
      @  
loop invariant 
      @   Permut{Pre,Here}(t,0,n
1); 
      @ 
loop variant nj; 
      @*/
 
    
for (j=i+1; j < n; j++) { 
      
if (t[j] < mv) {  
        mi = j ; mv = t[j];  
      } 
    } 
    swap(t,i,mi); 
  } 

 

Each VC is proved by at least one prover. Figure 3.3 displays the results in GWhy, with emphasis on the VC for preservation of the loop invariant for permutation behavior, the most difficult one, only proved by Alt-Ergo.


image
Figure 3.3: VCs for minimum sort

Chapter 4  Inference of Annotations

Inference of annotations is an experimental feature of the Jessie plug-in, whose theoretical bases are described in [5, 6].

4.1  Postconditions and Loop Invariants

To alleviate the annotation burden, it is possible to ask the Jessie plug-in to infer some of them, through a combination of abstract interpretation and weakest preconditions. This requires that APRON library for abstract interpretation is installed and Frama-C configuration recognized it. Then, one can call

 > framac -jessie -jessie-atp=simplify -jessie-infer-annot inv max.c

to perform abstract interpretation on program max.c, which computes necessary loop invariants and postconditions (meaning an overapproximation of the real ones).

int max(int *r, int* i, int* j) { 
  
if (!r) return -1; 
  *r = (*i < *j) ? *j : *i; 
  
return 0; 

On our unannotated max.c program, this produces postcondition true for the first return and \valid(r) && \valid(i) && \valid(j) for the second return.

Various domains from APRON library are available with option -jessie-abstract-domain:

4.2  Preconditions and Loop Invariants

Preconditions can also be computed by calling

> framac -jessie -jessie-atp=simplify -jessie-infer-annot pre max.c

which attempts to compute a sufficient precondition to guard against safety violations and prove functional properties. In case it computes false as sufficient precondition, which occurs e.g. each time the property is beyond the capabilities of our method, it simply ignores it. Still, our method can compute a stronger precondition than necessary. E.g., on function max, it computes precondition \valid(r) && \valid(i) && \valid(j), while a more precise precondition would allow r to be null. Still, the generated precondition is indeed sufficient to prove the safety of function max:

 Running Simplify on proof obligations
 (. = valid * = invalid ? = unknown # = timeout ! = failure)
 simplify/max_why.sx           : ......... (9/0/0/0/0)

To improve on the precision of the generated precondition, various methods have been implemented:

Chapter 5  Separation of Memory Regions

By default, the Jessie plug-in assumes different pointers point into different memory regions. E.g., the following postcondition can be proved on function max, because parameters r, i and j are assumed to point into different regions.

/*@ requires \valid(i) && \valid(j); 
  @ 
requires r == \null || \valid(r); 
  @ 
ensures *i == \old(*i) && *j == \old(*j); 
  @*/
 
int max(int *r, int* i, int* j) { 
  
if (!r) return -1; 
  *r = (*i < *j) ? *j : *i; 
  
return 0; 

To change this default behavior, add the following line at the top of the file:

# pragma SeparationPolicy(none)

In this setting, the postcondition cannot be proved:

Running Simplify on proof obligations
(. = valid * = invalid ? = unknown # = timeout ! = failure)
simplify/max_why.sx           : ?..?........ (10/0/2/0/0)

Now, function max should only be called in a context where parameters r, i and j indeed point into different regions, like the following:

int main(int a, int b) { 
  int c; 
  max(&c,&a,&b); 
  
return c; 

In this context, all VCs are proved.

In fact, regions that are only read, like the regions pointed to by i and j, need not be disjoint. Since nothing is written in these regions, it is still correct to prove their contract in a context where they are assumed disjoint, whereas they may not be disjoint in reality. It is the case in the following context:

int main(int a, int b) { 
  int c; 
  max(&c,&a,&a); 
  
return c; 

In this context too, all VCs are proved.

Finally, let’s consider the following case of a context in which a region that is read and a function that is written are not disjoint:

int main(int a, int b) { 
  int c; 
  max(&a,&a,&b); 
  
return c; 

The proof that regions are indeed disjoint boils down to proving that set of pointers {&a} and {&a} are disjoint (because function max only writes and reads *r and *i), which is obviously false.

image

Chapter 6  Treatment of Unions and Casts

Unions without pointer fields are translated to bitvectors, so that access in these unions are translated to low-level accesses. Thus, the following code can be analyzed, but we do not yet provide a way to prove the resulting assertions, by asserting that any subset of bits from the bitvector representation of 0 is 0:

union U { 
  int i; 
  
struct { short s1; short s2; } s; 
}; 
 
//@ requires \valid(x); 
void zero(
union U* x) { 
  x
->i = 0; 
  
//@ assert x>s.s1 == 0; 
  
//@ assert x>s.s2 == 0; 

Unions with pointer fields (either direct fields or sub-fields of structure fields) are translated differently, because we treat pointers differently than other types, to allow an automatic analysis of separation of memory blocks. Thus, we treat unions with pointer fields as discriminated unions, so that writing in a field erases all information on other fields. This allows to verify the following program:

union U { 
  int i; 
  int* p; 
}; 
 
//@ requires \valid(x); 
void zero(
union U* x) { 
  x
->i = 0; 
  
//@ assert x>i == 0; 
  x
->p = (int*)malloc(sizeof(int)); 
  *x
->p = 1; 
  
//@ assert *x>p == 1; 

Finally, casts between pointer types are allowed, with the corresponding accesses to memory treated as low-level accesses to some bitvector. This allows to verify the safety of the following program:

//@ requires \valid(x); 
void zero(int* x) { 
  char *c = (char*)x; 
  *c = 0; 
  c++; 
  *c = 0; 
  c++; 
  *c = 0; 
  c++; 
  *c = 0; 

Notice that unions are allowed in logical annotations, but pointer casts aren’t yet.

Chapter 7  Reference Manual

7.1  General usage

The Jessie plug-in is activated by passing option -jessie to frama-c. Running the Jessie plug-in on a file f.jc produces the following files:

The plug-in will then automatically call the Jessie tool of the Why platform to analyze the generated file f.jc above. By default, VCs are generated and displayed in the GWhy interface. The -jessie-atp=<p> option allows to run VCs in batch, using the given theorem prover <p>.

7.2  Unsupported features

7.2.1  Unsupported C features

Arbitrary gotos
 
only forward gotos, not jumping into nested blocks, are allowed. There is no plan to support arbitrary gotos in a near future.
Function pointers
 
There is no plan to support them in a near future. In some cases, Frama-C’s specialization plug-in can be used to remove function pointers.
Arbitrary cast
 
  • from integers to pointers, from pointer to integers: no support
  • between pointers: experimental support, only for casts in code, not logic
Note: casts between integer types are supported
Union types
 
experimental support, both in code and annotations
Variadic C functions
 
unsupported
volatile declaration modifier
 
not supported
const declaration modifier
 
accepted but not taken into account, that is treated as non-const.

7.2.2  partially supported ACSL features

Inductive predicates
 
supported, but must follow the positive Horn clauses style presented in the ACSL documentation.
Axiomatic declarations
 
supported (experimental)

7.2.3  Unsupported ACSL features

Logic language
 
  • direct equality on structures is not supported. Equality of each field should be used instead (e.g. by introducing an adequate predicate). Similarly, direct equality of arrays is not supported, and equality of each cells should be used instead.
  • array and structure field functional modifiers are not supported
  • higher-order constructs \lambda, \sum, \prod, etc. are not supported
Logic specifications
 
  • model variables and fields
  • global invariants and type invariants
  • volatile declarations
  • \initialized and \specified predicates
Contract clauses
 
  • terminates clause
  • abrupt termination clauses
  • general code invariants (only loop invariants are supported)
Ghost code
 
  • it is not checked whether ghost code does not interfere with program code.
  • ghost structure fields are not supported

7.3  Command-line options

-jessie
activates the plug-in, to perform C to Jessie translation
-jessie-project-name=<s>
specify project name for Jessie analysis
-jessie-atp=<s>
do not launch the GUI but run specified automated theorem prover in batch (among alt-ergo, cvc3, simplify, yices, z3), or just generate the verification conditions (goals)
-jessie-cpu-limit=<i>
set the time limit in sec. for proving each VC. Only works when -jessie-atp is set.
-jessie-behavior=<s>
restrict verification to the given behavior (safety, default or a user-defined behavior)
-jessie-std-stubs
(obsolete) use annotated standard headers
-jessie-hint-level=<i>
level of hints, i.e. assertions to help the proof (e.g. for string usage)
-jessie-infer-annot=<s>
infer function annotations (inv, pre, spre, wpre)
-jessie-abstract-domain=<s>
use specified abstract domain (box, oct or poly)
-jessie-jc-opt=<s>
give an option to the jessie tool (e.g., -trust-ai)
-jessie-why-opt=<s>
give an option to Why (e.g., -fast-wp)

7.4  Pragmas

Integer model
 
# pragma JessieIntegerModel(value)

Possible values: math, defensive, modulo.

Default value: defensive

  • math: all int types are modeled by mathematical, unbounded integers ;
  • defensive: int types are modeled by integers with appropriate bounds, and for each arithmetic operations, it is mandatory to show that no overflow occur ;
  • modulo: models exactly machine integer arithmetics, allowing overflow, that is results must be taken modulo 2n for the appropriate n for each type.
Floating point model
 
# pragma JessieFloatModel(value)

Possible values: math, defensive, full, multirounding.

Default value: defensive.

  • math: all float types are modeled by mathematical unbounded real numbers
  • defensive: float types are modeled by real numbers with appropriate bounds and roundings, and for each floating-point arithmetic operations, it is mandatory to show that no overflow occur. This model follows the IEEE-754 standard, under its strict form, as explained in [1, 2].
  • full: models the full IEEE-754 standard, including infinite values and NaNs. This model is the full model discussed in [1, 2].
  • multirounding: models floating-point arithmetics so as to support combinations of compilerd and architectures that do not strictly follows IEEE-754 standard (e.g. double roundings, 80-bits extended formats, compilation usinf fused-multiply-add instructions). This is based on paper [3, 4].
Floating point rounding mode
 
# pragma JessieFloatRoundingMode(value)

Possible values: nearesteven, down, up, tozero, nearestaway.

Default value: nearesteven.

Separation policy
 
# pragma SeparationPolicy(value)

Possible values: none, regions

Invariant policy
 
# pragma InvariantPolicy(value)

Possible values: none, arguments, ownership

Termination policy
 
# pragma JessieTerminationPolicy(value)

Possible values: always, never, user

Default: always

  • always means that every loop and every recursive function should be proved terminating. If they are not annotated by variants, then an unprovable VC (0<0) is generated.
  • user means that VCs for termination are generated for each case where a loop or function variant is given. Otherwise no VC is generated.
  • never means no VC for termination are ever generated, even for annotated loop or recursive function.

7.5  Troubleshooting

Here is a set of common error messages and possible fix or workaround.

unsupported "cannot handle this lvalue"
this message may appear in the following situations:
  • use an array as a parameter of a logic function. You should use a pointer instead.
unsupported "this kind of memory access is not currently supported"
this message may appear in the following situations:
  • equality on structures in the logic. The workaround is to check equality field by field. Tip: define field-by-field equality as a logic predicate.
unsupported "Jessie plugin does not support struct or union as parameter to logic functions."
This is already quite explicit: jessie does not support structures or unions as a parameter of logic functions or predicates. You can circumvent this limitation by using an indirection via a pointer.
unsupported "cannot take address of a function"
The jessie plugin does not support functions as parameters to other functions. There is no simple workaround. One thing you can try is to remove the function parameter and use a fixed abstract function (i.e. with a contract but no body), and then prove that all the functions that might be passed as parameters respect this contract.
unsupported "Type builtin_va_list not allowed"
Jessie does not handle varyadic functions. The same trick as above could be attempted.
unsupported "Casting from type <..> to type <..> not allowed"
Jessie does not support this cast, typically between pointer and integer. There is no simple workaround. One way of proving such kind of code is to replace the casts by an abstract function, whose post-condition explicitly explains how the conversion is made.
failure: cannot interpreted this lvalue
This may happen if
  • using a structure in an assigns clause. You need to expand ans say which field are assigned.

References

[1]
Ali Ayad and Claude Marché. Behavioral properties of floating-point programs. Hisseo publications, 2009. http://hisseo.saclay.inria.fr/ayad09.pdf.
[2]
Ali Ayad and Claude Marché. Multi-prover verification of floating-point programs. In Jürgen Giesl and Reiner Hähnle, editors, Fifth International Joint Conference on Automated Reasoning, Lecture Notes in Artificial Intelligence, Edinburgh, Scotland, July 2010. Springer.
[3]
Sylvie Boldo and Thi Minh Tuyen Nguyen. Hardware-independent proofs of numerical programs. Hisseo publications, 2009. http://hisseo.saclay.inria.fr/tuyen09.pdf.
[4]
Sylvie Boldo and Thi Minh Tuyen Nguyen. Hardware-independent proofs of numerical programs. In César Mu noz, editor, Proceedings of the Second NASA Formal Methods Symposium, NASA Conference Publication, pages 14–23, Washington D.C., USA, April 2010.
[5]
Yannick Moy. Automatic Modular Static Safety Checking for C Programs. PhD thesis, Université Paris-Sud, January 2009.
[6]
Yannick Moy and Claude Marché. Modular inference of subprogram contracts for safety checking. Journal of Symbolic Computation, 2010. to appear.
[7]
Harvey Tuch, Gerwin Klein, and Michael Norrish. Types, bytes, and separation logic. In Martin Hofmann and Matthias Felleisen, editors, Proc. 34th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL’07), pages 97–108, Nice, France, January 2007.

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