A verified compiler for Handel-C

The recent popularity of Field Programmable Gate Array (FPGA) technology has made the synthesis of Hardware Description Language (HDL) programs into FPGAs a very attractive topic for research. In particular, the correctness in the synthesis of an FPGA programming file from a source HDL program has gained significant relevance in the context of safety or mission-critical systems. The results presented here are part of a research project aiming at producing a verified compiler for the Handel-C language. Handel-C is a high level HDL based on the syntax of the C language extended with constructs to deal with parallel behaviour and process communications based on CSP. Given the complexity of designing a provably correct compiler for a language like Handel-C, we have adopted the algebraic approach to compilation as it offers an elegant solution to this problem. The idea behind algebraic compilation is to create a sound reasoning framework in which the a formal model of the source Handel-C program can be embedded and refined into a formal abstraction of the target hardware. As the algebraic rules used to compile the program are proven to preserve the semantics, the correctness of the entire compilation process (i.e., semantic equivalence between source and target programs) can be argued by construction, considering each programming construct in isolation, rather than trying to assert the correctness of the compilation in a single step. Regarding hardware synthesis, the algebraic approach has already been applied to subsets of Occam and Verilog. Our work builds on some ideas from these works but focuses on the more complex timing model imposed by Handel-C. Moreover, our work covers features like shared variables, multi-way communications and priorities which, to our knowledge, have never been addressed within the framework of algebraic compilation. Finally, one characteristic of the algebraic approach is that the basic reduction laws in the reasoning framework are postulated as axioms. As an invalid axiom would allow us to prove invalid results (up to the extent of being able to prove a false theorem) we are also concerned about the consistency of the basic postulates in our theory. We addressed this by providing denotational semantics for Handel-C and its reasoning extensions in the context of the Unifying Theories of Programming (UTP). Our UTP denotational semantics not only provided a model for our theory (hence, proving its consistency) but also allowed us to prove all the axioms in the compilation framework.