Abstract

We describe a Coq formalization of a subset of the x86 architecture. One emphasis of the model is brevity: using dependent types, type classes and notation we give the x86 semantics a makeover that counters its reputation for baroqueness. We model bits, bytes, and memory concretely using functions that can be computed inside Coq itself; concrete representations are mapped across to mathematical objects in the SSREFLECT library (naturals, and integers modulo 2 n ) to prove theorems. Finally, we use notation to support conventional assembly code syntax inside Coq, including lexically-scoped labels. Ordinary Coq definitions serve as a powerful “macro” feature for everything from simple conditionals and loops to stack-allocated local variables and procedures with parameters. Assembly code can be assembled within Coq, producing a sequence of hex bytes. The assembler enjoys a correctness theorem relating machine code in memory to a separation-logic formula suitable for program verification.