This is the Coq development for SeLoC: a relational separation logic for proving non-interference of concurrent stateful programs.

See the paper for more details.

This version is known to compile with:

• Coq 8.12 or later
• Iris developement version 96191ed7ef792478c86890a0ebdbbbea0dc9c9ab
• Equations 1.2.3 or later

If you use opam, then you can install all the dependencies by running the following commands from the root directory:

opam repo add coq-released https://coq.inria.fr/opam/released
opam repo add iris-dev https://gitlab.mpi-sws.org/iris/opam.git
opam update
opam install .

Otherwise you can manually install all the dependencies and run make && make install.

All the Coq modules are in the subfolders of the theories folder:

• program_logic: the definition of double weakest preconditions and the core logic rules, as well as the soundness proof.
• proofmode: tactics that ease symbolic execution proofs.
• logrel: the type system and its interpretation.
• examples: examples studied in the paper.
• heap_lang: operational semantics for HeapLang with deterministic allocation and its adequacy result (see more on that below).

• The set data structure from Section II.A is in examples/set.v. The safe arrays from Section II.B are defined and verified in examples/array.v.
• Rules from Figure 3 are in program_logic/dwp.v, program_logic/lifting.v and program_logic/heap_lang_lifting.v.
• Proposition 4 is proved in examples/rand.v.
• Proposition 6 is proved in examples/value_sensitivity_3.v.
• The types are defined in logrel/types.v, the model for the type system and the compatibility rules are in logrel/interp.v. The typing rules and the fundamental property are in logrel/typing.v.
• Proposition 10 is proved in examples/various.v.
• The modular specifications for dynamically classified references are given in examples/value_dep.v. The example clients that use those specification are in examples/value_sensitivity_2.v and examples/value_sensitivity_4.v.
• The bisimulation is constructed in program_logic/dwp_adequacy.v.

There are some additional examples that did not make the paper. See, in particular, examples/calendar.v for an example of how to handle delimited information release.

There are some differences between the Coq formalization and the presentation in the paper.

First of all, to be compatible with the existing version of HeapLang in Iris, we define double weakest preconditions on top of a language with non-deterministic allocation semantics. However, to have well-defined probabilistic semantics of thread-pools, we require the allocation to be deterministic. We formalize HeapLang with deterministic allocation in heap_lang/lang_det.v (the language is parameterized by an allocation oracle). We prove the following adequacy statement: if we have a double weakest precondition for a program under the standard non-deterministic semantics, we can also have adouble weakest precondition for the same program under the deterministic semantics with an allocator.

Secondly, our type system (and its interpretation) is parameterized by an attacker level ξ, and you can see that throughout the code. In our type system we also have an option type for integers. It is denoted as toption il l where il is the sensitivity label of the underlying integer, and l is the label for the option type (whether it is SOME or NONE); thus it roughly corresponds to option^l (int^il). In the future work we would like to extend the typing rules to arbitrary sum types.

Lastly, In Coq, we do not use the AWP proposition for atomic weakest preconditions we used in the paper. Rather, in the rule dwp-awp (in the formalization: dwp_atomic_lift_wp) we require the expressions e1 and e2 to be atomic and produce no forked off threads. Then, we fall back onto the total weakest precondition from Iris. This allows us to reuse a lot of lemmas and tactics about total weakest preconditions from Iris.