VMCAI'22: research paper

Lightweight Shape Analysis based on Physical Types

General topic

type safety; formal methods; cod analysis;

Memory errors are the source of the most pervasive and critical security vulnerabilities. Programs written in low-level systems languages, like C/C++ and assembly, perform low-level pointer and memory operations and are particularly subject to these kind of errors.

In this paper, we are interested in memory abstractions expressive enough to verify type safety, i.e. the preservation of structural invariants expressed by types, in non-trivial linked data-structure manipulations in both high- and low-level code (such as assembly or low-level C). This type safety entails spatial memory safety, namely that each memory access is done on an address that was previously allocated (and thus that null or out-of-bound pointer dereferences are impossible). We also seek for a high level of automation (i.e., by avoiding the requirement of complex handwritten program annotations) and of efficiency.

Many verification techniques aimed at verifying the correctness of memory manipulating programs have been developed. On one end of the precision spectrum, pointer analyses infer basic conservative relations between pointer values and can tackle basic memory errors. However, they are limited in that, unlike our analysis technique, they cannot establish safety when doing so requires reasoning over the structure of data.

Consider for example the following function, manipulating a disjoint-set data structure:

typedef struct uf {
  struct uf* parent;
} uf;

uf *uf_find(uf *x) {
  while(x->parent != 0) {
    uf *parent = x->parent;
    if(parent->parent == 0)
      return parent;
    x->parent = parent->parent;
    x = parent->parent;
  return x;

The correctness of this code requires some non-nullness analysis, as well as hypotheses on the structure of the memory pointed by the function argument x. Such reasoning goes beyond usual pointer analyses, while our analysis successfully validates this function.

On the other hand, shape analyses based on three-valued logics like TVLA or on separation logics attempt to establish precise structural invariants, such as the existence of some list or tree data-structures. Such analyses can cope with the verification of memory safety in presence of sophisticated structures, yet they are typically less scalable than basic pointer analyses and also less resilient to a local precision loss in the sense that losing precision over a fragment of the memory often entails no information can be recovered about that region. Another limitation is that such analyses are difficult to apply to low-level code, like low-level C or binary code. On the contrary, our technique scales less due to being mostly a storeless abstraction, and was made to handle the low-level type-punning code patterns typical of low-level systems programs.


To achieve this, we propose:

  • A novel memory abstraction that is inspired by the classical notion of types, but applies to the physical representation of data-structures. The analysis effectively performs a type inference of a dependent type system using abstract interpretation.
  • Two independent extensions of the domain to track “retained” and “staged” points-to predicates to improve the precision of the analysis by representing memory updates in a flow-sensitive way.
  • An experimental evaluation on a set of challenging benchmarks, showing that the combination naturally deals with both C and binary code manipulating dynamic data structures.

Further information