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Distributed Separation Logic: a framework for compositional verification of distributed protocols and their implementations in Coq


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Disel: Distributed Separation Logic

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Disel is a framework for implementation and compositional verification of distributed systems and their clients in Coq. In Disel, users implement distributed systems using a domain specific language shallowly embedded in Coq which provides both high-level programming constructs as well as low-level communication primitives. Components of composite systems are specified in Disel as protocols, which capture system-specific logic and disentangle system definitions from implementation details.


Building and installation instructions

The easiest way to install the latest released version of Disel: Distributed Separation Logic is via OPAM:

opam repo add coq-released
opam install coq-disel

To instead build and install manually, do:

git clone
cd disel
make   # or make -j <number-of-cores-on-your-machine> 
make install

Project Structure

  • theories/Core -- Disel Coq implementation, metatheory and inference rules;
  • theories/Examples -- Case studies implemented in Disel using Coq
    • Calculator -- the calculator system;
    • Greeter -- a toy "Hello World"-like protocol, where participants can only exchange greetings with each other;
    • TwoPhaseCommit -- Two Phase Commit protocol implementation;
    • Query -- querying protocol and its composition with Two Phase Commit via hooks;
  • shims -- DiSeL runtime system in OCaml

VM Instructions

Please download the virtual machine, import it into VirtualBox, and boot the machine. This VM image has been tested with VirtualBox versions 5.1.24 and 5.1.28 with Oracle VM VirtualBox Extension Pack. Versions 4.X are known not to work with this image.

If prompted for login information, both the username and password are "popl" (without quotes).

For your convenience, all necessary software, including Coq 8.6 and ssreflect have been installed, and a checkout of Disel is present in ~/disel. Additionally, emacs and Proof General are installed so that you can browse the sources.

We recommend checking the proofs using the provided Makefile and running the two extracted applications. Additionally, you might be interested to compare the definitions and theorems from some parts of the paper to their formalizations in Coq.

Checking the proofs can be accomplished by opening a terminal and running

cd ~/disel
make clean; make -j 4

You may see lots of warnings about notations and "nothing to inject"; these are expected. Success is indicated by the build terminating without printing "error".

Extracting and running the example applications is described below.

Code corresponding to the paper

The following describes how the paper corresponds to the code:

  • The Calculator (Section 2)
    • The directory Examples/Calculator contains the relevant files.
    • The protocol is defined in CalculatorProtocol.v, including the state space, coherence predicate, and four transitions described in Figure 2. Note that the coherence predicate is stronger than the one given in the paper: it incorporates Inv_1 from Section 2.3. This is discussed further below.
    • The program that implements blocking receive of server requests from Section 2.2 is defined in CalculatorServerLib.v, as blocking_receive_req.
    • The simple server from Section 2.3, as well as the batching and memoizing servers from Figure 3 are implemented in SimpleCalculatorServers.v. They are all implemented in terms of the higher-order server_loop function. The invariant Inv1 from Section 2.3 is incorporated into the protocol itself, as part of the coherence predicate.
    • The simple client from Section 2.4 is implemented in CalculatorClientLib.v. The invariant Inv2 is proved as a separate inductive invariant using the WithInv rule in CalculatorInvariant.v. It is used to prove the clients satisfy their specifications.
    • The delegating server is in DelegatingCalculatorServer.v. It again uses the invariant Inv2.
    • A runnable example using extraction to OCaml is given in SimpleCalculatorApp.v. It consists of one client and two servers, one of which delegates to the other. Instructions for how to run the example are given below under "Extracting and Running Disel Programs".
  • The Logic and its Soundness (Section 3)
    • The definitions from Figure 6 in Section 3.1 are given in Core/State.v Core/Protocols.v, and Core/Worlds.v.
    • The primitives of Disel language is defined in Core/Actions.v (defines send/receive wrappers as in Definitions 3.2 and 3.3).
    • Core/Process.v, Core/Always.v and Core/HoareTriples.v define traces, modal predicates (always is the formalization of post-safety from Definition 3.6). Definition 3.7 from the paper corresponds to has_spec from Core/HoareTriples.v. The Theorem 3.8 follows from the soundness of the shallow embedding into Coq: any well-typed program has a specification ascribed to it.
    • Inference rules are represented by lemmas named *_rule in Core/InferenceRules.v. For example, bind_rule is an implementation of Bind from Figure 8.
  • Two-Phase Commit and Querying (Section 4)
    • The relevant directory is Examples/TwoPhaseCommit.
    • The protocol as described in Section 4.1 is implemented in TwoPhaseProtocol.v.
    • The implementations of the coordinator (described in 4.2) and the participant are in TwoPhaseCoordinator.v and TwoPhaseParticipant.v.
    • The strengthened invariant from 4.3 is stated in TwoPhaseInductiveInv.v and proved to be preserved by all transitions in TwoPhaseInductiveProof.v.
    • A runnable example is in SimpleTPCApp.v. Instructions for how to run it are given below under "Extracting and Running Disel Programs".
    • The querying protocol from Section 4.4 is implemented in the directory Examples/Querying.

Exploring further

We encourage you to explore Disel further by extending one of the examples or trying your own. For example, you could build an application that uses the calculator to evaluate arithmetic expressions and prove its correctness. As a more involved example, you could define a new protocol for leader election in a ring and prove that at most one node becomes leader. To get started, we recommend following the Calculator example and modifying it as necessary.

Extracting and Running Disel Programs

As described in Section 5.1, Disel programs can be extracted to OCaml and run. You can build the two examples as follows.

  • From ~/disel, run make CalculatorMain.d.byte to build the calculator application. The extracted code will be placed in extraction/calculator. (Note that all the proofs will be checked as well.) Then run ~/disel/scripts/ to execute the system in three processes locally. The system will make several requests to a delegating calculator to add up some numbers. (See the definition of client_input in Examples/Calculator/SimpleCalculatorApp.v.) A log of messages from the client perspective is printed to the console. Logs of the servers are available in the files server1.log (the delegating server) and server3.log (the server that actually computes).

    Each log contains a debugging info about the state of each node and the messages it sends and receives. For example, the first message sent by the client is logged as

sending msg in protocol 1 with tag = 0, contents = [1; 2] to 1

Tag 0 indicates a request in the Calculator protocol. Contents 1; 2 indicate the arguments to the function being calculated (in this case, addition). The message is sent to node 1, which is the delegating server.

The client then receives a response logged as

got msg in protocol 1 with tag = 1, contents = [3; 1; 2] from 1

Tag 1 indicates a response. The contents mean that the answer to 1 + 2 is 3.

Several more rounds of messages are exchanged. The final line summarizes the entire execution.

client got result list [([1; 2], 3); ([3; 4], 7); ([5; 6], 11); ([7; 8], 15); ([9; 10], 19)]
  • Run make TPCMain.d.byte from the root folder to build the Two-Phase Commit application. Then run ./scripts/ to execute the system in four processes on the local machine. The system will achieve consensus on several values. (See the definition of data_seq in Examples/TwoPhaseCommit/SimpleTPCApp.v.) Each participant votes on whether to commit the value or abort it. (See the definitions of choice_seq1, choice_seq2, and choice_seq3.) A log of messages from the coordinator's point of view is printed to the console. Participant logs are available in participant1.log, participant2.log, and participant3.log.

    The protocol executes a sequence of four rounds, since there are four elements in data_seq. Each round consists of two phases. The first messages sent by the coordinator are prepare messages which request votes about the first data item. They are logged as

sending msg in protocol 0 with tag = 0, contents = [0; 1; 2] to 1
sending msg in protocol 0 with tag = 0, contents = [0; 1; 2] to 2
sending msg in protocol 0 with tag = 0, contents = [0; 1; 2] to 3

Tag 0 indicates a prepare message. The contents indicate the index of the current request (0, since this is the first data item) and the actual data to commit (in this case, [1; 2], as specified in data_seq). A separate prepare message is sent to each participant.

The participants respond with votes, which are logged as follows

got msg in protocol 0 with tag = 1, contents = [0] from 1
got msg in protocol 0 with tag = 1, contents = [0] from 3
got msg in protocol 0 with tag = 1, contents = [0] from 2

Tag 1 indicates a Yes vote. The messages are ordered nondeterministically based on the operating system's and network's scheduling decisions.

Since all participants voted yes, the coordinator proceeds to commit the data by sending Commit messages (tag 3) to all participants.

sending msg in protocol 0 with tag = 3, contents = [0] to 1
sending msg in protocol 0 with tag = 3, contents = [0] to 2
sending msg in protocol 0 with tag = 3, contents = [0] to 3

Participants acknowledge the commit with AckCommit messages (tag 5)

got msg in protocol 0 with tag = 5, contents = [0] from 3
got msg in protocol 0 with tag = 5, contents = [0] from 1
got msg in protocol 0 with tag = 5, contents = [0] from 2

This completes the first round. The remaining three rounds execute similarly, based on the decisions from the choice sequences. When any participant votes no (tag 2), the coordinator instead aborts the transaction by sending Abort messages (tag 4). In that case, participants respond with AckAbort messages (tag 6). Once all four rounds are over, all nodes exit.

Proof Size Statistics

Section 5.2 and Table 1 describe the size of our development. Those were obtained by using the coqwc tool on manually dissected files, according to our vision of what should count as a program, spec, or a proof. These numbers might slightly differ from reported in the paper due to the evolution of the project since the submission.