Formal Validation of Pattern Matching code

Abstract

When addressing the formal validation of generated software, two main
alternatives consist either to prove the correctness of compilers or
to directly validate the generated code.  Here, we focus on directly
proving the correctness of compiled code issued from powerful
pattern matching constructions typical of ML like languages or
rewrite based languages such as ELAN, MAUDE or Tom.

In this context, our first contribution is to define a general
framework for anchoring algebraic pattern-matching capabilities
in existing languages like C, Java or ML. Then, using a just enough
powerful intermediate language, we formalize the behavior of compiled
code and define the correctness of compiled code with respect to
pattern-matching behavior.  This allows us to prove the equivalence of
compiled code correctness with a generic first-order proposition whose
proof could be achieved via a proof assistant or an automated theorem
prover. We then extend these results to the multi-match situation
characteristic of the ML like languages.

The whole approach has been implemented on top of the Tom compiler
and used to validate the syntactic matching code of the Tom compiler
itself.