Analyzing Array Manipulating Programs by Program Transformation

Abstract

We explore a transformational approach to the problem of verifying simple array-manipulating programs. Traditionally, verification of such programs requires intricate analysis machinery to reason with universally quantified statements about symbolic array segments, such as “every data item stored in the segment A[i] to A[j] is equal to the corresponding item stored in the segment B[i] to B[j].” We define a simple abstract machine which allows for set-valued variables and we show how to translate programs with array operations to array-free code for this machine. For the purpose of program analysis, the translated program remains faithful to the semantics of array manipulation. Based on our implementation in LLVM, we evaluate the approach with respect to its ability to extract useful invariants and the cost in terms of code size.

A Array Operations with Non-segment Variables

Figure 6(a) assumes that the index variable of every read or write is included in the set of segment bounds. Figure 14 gives a revised version of transform_body which handles writes to indices that are not included in the set of segment bounds. When we transform a write to an index in the set of segment bounds (determined by the predicate is_idx), the transformation is as usual. Otherwise, we emit code to walk through the current set of segments, and apply the write operation to the appropriate one. The dispatch process is similar to the operation of split_transform, except that all leaves jump back to the continuation of the basic block after the write, rather than continuing under the modified ordering.

Fig. 14.

Revised pseudo-code for transforming array writes, allowing for omitted indices. Array reads are transformed similarly.