## Abstract

The Verified Software Toolchain builds foundational machine-checked proofs of the functional correctness of C programs. Its program logic, Verifiable C, is a shallowly embedded higher-order separation Hoare logic which is proved sound in Coq with respect to the operational semantics of CompCert Clight. This paper introduces VST-Floyd, a verification assistant which offers a set of semiautomatic tactics helping users build functional correctness proofs for C programs using Verifiable C.

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## Notes

- 1.
The “heap” in Verifiable C is actually a step indexed model of CompCert’s memories, following Hobor et al. [17].

- 2.
Readers can understand the type of

*P*as \(\text {stack} \rightarrow \text {heap} \rightarrow \text {Prop}\). But actually, this predicate must be monotonic w.r.t. the step indexing, i.e. we define it Coq as a dependent pair of a predicate and a proof of monotonicity [3, Part V]. - 3.
This specification of is not strong enough, because it does not say whether the values of \(\llbracket \texttt {x} \rrbracket \) and \(\llbracket \texttt {y} \rrbracket \) change or not after running the function. In actual verification, we will use:

$$\begin{aligned} \texttt {swapint(x, y)}: \{\llbracket \texttt {x} \rrbracket = p \wedge \llbracket \texttt {y} \rrbracket = q \wedge p \mapsto a * q \mapsto b\} \{p \mapsto b * q \mapsto a\} \end{aligned}$$ - 4.
In actual Coq code, Clight uses identifiers to represent C variable names and C function names. So, when we write , the real Coq code is “\(\mathsf {\_swapint}\)” which is an identifier, i.e. a positive number, in Coq. Similarly, the real Coq code for is “\(\mathsf {tint}\)” whose type is \(\mathsf {Clight.type}\), a Coq inductive type representing the syntax tree of C types.

- 5.
Our \(\mapsto \) and \(\mathsf {data\_at}\) predicates take another argument that we omit in this article: a permission-share indicating read-only, read-write, or various other levels of access to the data.

- 6.
In CompCert 2.4 and earlier versions, the Clight type definition is a Coq inductive type. However, from CompCert 2.5, and types are represented by name instead of by structure. Specifically, every Clight program is associated with a \(\mathsf {composite\_env}\). A \(\mathsf {composite\_env}\) is a dictionary mapping every / name to a list of all its fields. The meaning of a or a needs to be interpreted by looking it up in the dictionary. From then on, \(\mathsf {reptype}\) and \(\mathsf {data\_at\_rec}\) are no longer Coq functions recursive on Coq inductive structure. The CompCert developers accepted our suggestion that every type should be tagged with a rank, which is a natural number. The ranking system ensures that the rank of a struct type is the max rank of its fields plus one; the rank of a union type is the max rank of its fields plus one; the rank of an array type is the rank of its element type plus one. The rank of elementary types (including pointers) is zero. Our current definition of \(\mathsf {reptype}\) and \(\mathsf {data\_at\_rec}\) are recursive functions on this rank.

- 7.
In the Coq development, we use the name for what we call “stack” in the paper.

- 8.
In our Coq development, we actually turn the symbolic clauses into binary trees first. Then we look up in these trees during symbolic evaluation. We omit the technical details here.

- 9.
All the load and store rules of this section also need typechecking side conditions, i.e., \(\mathsf {tc\_expr}(\varDelta ,e)\) for each involved C expression

*e*. We omit them for brevity. - 10.
One might wonder why the expression evaluation function does not directly return a field address. For and fields, this could work, but for array indices, it wouldn’t, because the field-address operator is only well-defined if the array index is within the array bounds, but adding an integer to a pointer is always defined in CompCert Clight, even if dereferencing it might be undefined. So the evaluation function could only use the field-address operator if the array index is within bounds, but it cannot know whether this is the case, because it does not have access to the array size.

- 11.
The kind of hints we are talking about here are

*not*related to Coq’s hint databases.

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## Acknowledgements

This work was supported in part by NSF grant CCF-1521602 and by DARPA grant FA8750-12-2-0293.

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Cao, Q., Beringer, L., Gruetter, S. *et al.* VST-Floyd: A Separation Logic Tool to Verify Correctness of C Programs.
*J Autom Reasoning* **61, **367–422 (2018). https://doi.org/10.1007/s10817-018-9457-5

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### Keywords

- Separation logic
- Symbolic execution
- Program verification
- Proof automation