Towards the formalization of SPARK 2014 semantics with explicit run-time checks using coq

Abstract

We present the first steps of a broad effort to develop a formal representation of SPARK 2014 suitable for supporting machine-verified static analyses and translations. In our initial work, we have developed technology for translating the GNAT compiler's abstract syntax trees into the Coq proof assistant, and we have formalized in Coq the dynamic semantics for a toy subset of the SPARK 2014 language. SPARK 2014 programs must ensure the absence of certain run-time errors (for example, those arising while performing division by zero, accessing non existing array cells, overflow on integer computation). The main novelty in our semantics is the encoding of (a small part of) the run-time checks performed by the compiler to ensure that any well-formed terminating SPARK programs do not lead to erroneous execution. This and other results are mechanically proved using the Coq proof assistant. The modeling of on-the-fly run-time checks within the semantics lays the foundation for future work on mechanical reasoning about SPARK 2014 program correctness (in the particular area of robustness) and for studying the correctness of compiler optimizations concerning run-time checks, among others.