Book of Abstracts - IRIT

Effective Types for C formalized in Coq
Robbert Krebbers
The main novelty of our model is that the memory, although being fairly abstract, still
supports low level operations; in particular byte-wise copying of objects. The model includes
three layers: (a.) values with machine integers and pointers as leafs, (b.) memory values with
arrays of bytes as leafs, and (c.) arrays of bytes. As in CompCert [4], bytes corresponding
to uninitialized memory and fragments of pointers are symbolic. The following figure displays
these three layers for the object struct { short x, *p; } s = { 33; &s.x }.
(a)
33 •
of val
to val
0x00 0x21 • • • •
(b)
to bytes of bytes
(c)
0x00 0x21 • • • •
When copying an object by assignment, it is converted to an actual value when loaded (using
to val) and converted back when stored (using of val). The conversion back yields a set of
possible representations. When copying an object byte-wise (using to bytes and of bytes),
information about the variants of contained unions may be lost (as that cannot be stored in
bytes). We define a partial order ⊆ to capture that information about the variants of unions
may have gotten lost, and that uninitialized memory may have become initialized.
Theorem 2.1. For each memory value v and type τ with v : τ, there exists a memory value w
such that: (a.) w ∈ of val (to val v), and (b.) w ⊆ of bytes τ (to bytes v).
A consequence of the previous theorem is that a copy by assignment can be transformed
into a byte-wise copy. If a copy of v by assignment has defined behavior, then it does not go
wrong for each representation obtained by conversion to a value and back. As for one of these
representations w we have w ⊆ of bytes τ (to bytes v) by the theorem, and the fact that all
operations on the memory respect ⊆, we obtain soundness of this transformation.
3 Future work
The eventual goal of this work is to develop a semantics for a large part of the C11 programming
language. In previous work [3] we developed a concise operational and axiomatic semantics for
non local control flow (goto and return statements). Recently, we have extended this operational
and axiomatic semantics with sequence points and non-deterministic expressions with sideeffects.
The next step is to create a fully fledged memory model on top of the abstract version
introduced here, and to integrate it into our formalization [2]. Another direction for future
research is to prove a correspondence with the CompCert memory model [4].
References
[1] Chucky Ellison and Grigore Rosu. An executable formal semantics of C with applications. In
POPL, pages 533–544, 2012.
[2] Robbert Krebbers. The CH 2O formalization, 2013. http://robbertkrebbers.nl/research/ch2o/.
[3] Robbert Krebbers and Freek Wiedijk. Separation Logic for Non-local Control Flow and Block Scope
Variables. In FoSSaCS, volume 7794 of LNCS, pages 257–272, 2013.
[4] Xavier Leroy, Andrew W. Appel, Sandrine Blazy, and Gordon Stewart. The CompCert Memory
Model, Version 2. Research report RR-7987, INRIA, 2012.
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