Separation Logic for Small-step Cminor (extended version)

Cminor is a mid-level imperative programming language (just below C), and there exist proved-correct optimizing compilers from C to Cminor and from Cminor to machine language. We have redesigned Cminor so that it is suitable for Hoare Logic reasoning, we have designed a Separation Logic for Cminor, we have given a small-step operational semantics so that extensions to concurrent Cminor will be possible, and we have a machine-checked proof of soundness of our Separation Logic. This is the first large-scale machine-checked proof of a Separation Logic w.r.t. a small-step semantics, or for a language with nontrivial reducible control-flow constructs. Our sequential soundness proof of the sequential Separation Logic for the sequential language features will be reusable change within a soundness proof of Concurrent Separation Logic w.r.t. Concurrent Cminor. In addition, we have a machine-checked proof of the relation between our small-step semantics and Leroy's original big-step semantics; thus sequential programs can be compiled by Leroy's compiler with formal end-to-end correctness guarantees