Concurrent Permission Machine for modular proofs of optimizing compilers with shared memory concurrency
Optimizing compilers change a program based on a formal analysis of its code, and
modern processors further rearrange the program order. It is hard to reason about
such transformations, which makes them a source of bugs, particularly for concurrent shared-memory programs where the order of execution is critical. On the other
hand, programmers should reason about their program in the source language, which
abstracts such low level details.
We present the Concurrent Permission Machine (CPM), a semantic model for
shared-memory concurrent programs, which is: (1) sound for higerh-order Concurrent Separation Logic, (2) convenient to reason about compiler correctness, and (3)
useful for proving reduction theorems on weak memory models. The key feature of
the CPM is that it exploits the fact that correct shared-memory programs are permission coherent: threads have (at any given time) noncompeting permission to access
memory, and their load/store operations respect those permissions.
Compilers are often written with sequential code in mind, and proving the correctness of those compilers is hard enough without concurrency. Indeed, the machinechecked proof of correctness for the CompCert C compiler was a major advance in the
field. Using the CPM to conveniently distinguish sequential execution from concurrent interactions, I show how to reuse the (sequential) CompCert proof, without major
changes, to guarantee a stronger concurrent-permission-aware notion of correctness.