Armada: Low-Effort Verification of High-Performance Concurrent Programs

-

This paper appeared in PLDI 2020 and is authored by Jacob R. Lorch, Yixuan Chen, Manos Kapritsos, Bryan Parno, Shaz Qadeer, Upamanyu Sharma, James R. Wilcox, and Xueyuan Zhao.

The paper presents the Armada framework for code-level verification of concurrent (multithreaded rather than distributed) programs. Armada is roughly a stepwise-refinement extended version of Dafny. So that is where I will start explaining.


Dafny

Dafny is an open source iterative compiled language for writing verified code. The code is verified with respect to the specifications the developer writes by adding high-level annotations alongside the code, such as ensures P and invariant P. At https://rise4fun.com/Dafny/tutorial you will find an interactive tutorial, that will get you up and running proving programs with Dafny. It is really fun, you should try this out now! 

Dafny leverages Z3 for discharging proof obligations. Ok, so what is Z3?

Z3 is a popular open source Satisfiability modulo theories (SMT) solver. SMT is a decision problem for logical formulas expressed in classical first-order logic with equality (propositional logic+ quantifiers + relations). You can think of Z3 as formalizing constraint programming. Again please give this interactive Z3 tutorial a try at  https://rise4fun.com/z3/tutorial.


*check-sat* determines whether the current formulas on the Z3 stack are satisfiable or not. 

  • If the formulas are satisfiable, Z3 returns *sat*
  • If they are unsatisfiable, Z3 returns *unsat* 
  • Z3 may also return *unknown* when it can't determine whether a formula is satisfiable or not

If you like to use Z3 as part of a higher level language, Z3 bindings are available for Python, C, C++, Java, Rust, etc.




Armada

Armada leverages on Dafny and provides an open source framework for developing verified concurrent systems code via stepwise refinement. It provides 8 verified libraries for performing refinement-based proofs, including region-based pointer reasoning, rely-guarantee, TSO elimination, and reduction.


Armada's goal is to prove that the implementation refines the specification (i.e., all finite behaviors of the implementation simulate the specification). To bridge the semantic gap between the implementation and the specification, the developer writes a series of N Armada programs. 

  • each pair of adjacent levels should be similar enough to facilitate automatic generation of a refinement proof that respects R
  • the developer supplies a short proof recipe that gives Armada enough information to automatically generate such a proof
  • Armada uses Dafny to verify all proof material generated

Here is an example of Armada specification and implementation of Traveling Salesman Problem. 






And here is an example of an intermediate stepwise refinement for TSP.

Armada considers 8 strategies for the refinement framework: Reduction, Rely-guarantee reasoning, TSO elimination, Weakening, Nondeterministic weakening, Combining, Ghost variable introduction, and Variable hiding.

The implementation of Armada consists of

  • a state-machine translator to translate Armada programs to state-machine descriptions (built over Dafny's parser and type inference engine)
  • a framework for proof generation (built over Dafny's abstract syntax tree AST code)
  • a library of lemmas useful for invocation by proofs of refinement (6KLOC Dafny)
  • and an extension of Dafny to translate Armada AST into C compatible with CompCertTSO

The evaluation is performed on four examples: Barrier, Pointers, MCSLock, Lock-free queue from liblfds library. The graph shows that after Armada verification the CompCertTSO verified compilation of the code is as efficient as that of compiling with GCC an unverified compiler, which is as efficient as a hand-written version of liblfds implementation (using modulo rather than bitmask).


Discussion 

Armada is a solid step in the right direction, but it still has several drawbacks. The framework requires a *competent* human in the loop for performing the verification. The human should decide how to divide the refinement steps and work with the framework to show the refinement proofs for each step. My impression is that Armada is still for small programs. Also Armada can only prove safety properties but not liveness, and it cannot verify hyperproperties due to the first order logic requirement imposed by Z3. 

It may be cumbersome trying to feed the proof recipes/hints to the proof system without feedback about why this didn't work. Without feedback from the proof system, how long would a developer be able to continue the process? This is another factor that may make adoption of this difficult by non-expert users.

On the other hand, Armada provides a good option for verifying critical multithreaded programs. Just by using the same language/framework, you can generate provably verified code. It is nice that everything is under the same roof. The trusted code base in this framework is the Armada compiler, Dafny, Z3, Boogie.

Comments

Post a Comment

Popular posts from this blog

Hints for Distributed Systems Design

-
This is with apologies to Butler Lampson, who published the " Hints for computer system design " paper 40 years ago in SOSP'83. I don't claim to match that work of course. I just thought I could draft this post to organize my thinking about designing distributed systems and get feedback from others. I start with the same  disclaimer Lampson gave. These hints are not novel, not foolproof recipes, not laws of design, not precisely formulated, and not always appropriate. They are just hints.  They are context dependent, and some of them may be controversial. That being said, I have seen these hints successfully applied in distributed systems design throughout my 25 years in the field, starting from the theory of distributed systems (98-01), immersing into the practice of wireless sensor networks (01-11), and working on cloud computing systems both in the academia and industry ever since. These heuristic principles have been applied knowingly or unknowingly and has proven...
Read more >>

Learning about distributed systems: where to start?

-
This is definitely not a "learn distributed systems in 21 days" post. I recommend a principled, from the foundations-up, studying of distributed systems, which will take a good three months in the first pass, and many more months to build competence after that. If you are practical and coding oriented you may not like my advice much. You may object saying, "Shouldn't I learn distributed systems with coding and hands on? Why can I not get started by deploying a Hadoop cluster, or studying the Raft code." I think that is the wrong way to go about learning distributed systems, because seeing similar code and programming language constructs will make you think this is familiar territory, and will give you a false sense of security. But, nothing can be further from the truth. Distributed systems need radically different software than centralized systems do.  --A. Tannenbaum This quotation is literally the first sentence in my distributed systems syllabus. Inst...
Read more >>

Making database systems usable

-
Image
C. J. Date's Sigmod 1983 keynote, "Database Usability", was prescient. Usability is the most important thing to the customers. They care less about impressive benchmarks or clever algorithms, and more about whether they can operate and use a database efficiently to query, update, analyze, and persist their data with minimal headache. (BTW, does anyone have a link to the contents of this Sigmod'83 talk? There is no transcript around, except for this short abstract .) The paper we cover today is from Sigmod 2007. It takes on the database usability problem raised in that 1983 keynote head-on, and calls out that the king is still naked.  Let's give some context for the year 2007. Yes, XML format was still popular then. The use-case in the paper is XQuery. The paper does not contain any  reference to json. MongoDB would be released in 2009 with the document model; and that seems to be great timing for some of the usability pains mentioned in the paper! Web 2.0 was in ...
Read more >>

Looming Liability Machines (LLMs)

-
As part of our zoom reading group ( wow, 4.5 years old now ), we discussed a paper that uses LLMs for automatic root cause analysis (RCA) for cloud incidents. This was a pretty straightforward application of LLMs. The proposed system employs an LLM to match incoming incidents to incident handlers based on their alert types, predicts the incident's root cause category, and provides an explanatory narrative. The only customization is through prompt-engineering. Since this is a custom domain, I think a more principled and custom-designed  machine learning system would be more appropriate rather than adopting LLMs. Anyways, the use of LLMs for RCAs spooked me vicerally. I couldn't find the exact words during the paper discussion, but I can articulate this better now. Let me explain. RCA is serious business Root cause analysis (RCA) is the process of identifying the underlying causes of a problem/incident, rather than just addressing its symptoms. One RCA heuristic is asking 5 Why...
Read more >>

Foundational distributed systems papers

-
I talked about the importance of reading foundational papers last week. To followup, here is my compilation of foundational papers in the distributed systems area. (I focused on the core distributed systems area, and did not cover networking, security, distributed ledgers, verification work etc. I even left out distributed transactions, I hope to cover them at a later date.)  I classified the papers by subject, and listed them in chronological order. I also listed expository papers and blog posts at the end of each section. Time and State in Distributed Systems Time, Clocks, and the Ordering of Events in a Distributed System. Leslie Lamport, Commn. of the ACM,  1978. Distributed Snapshots: Determining Global States of a Distributed System. K. Mani Chandy Leslie Lamport, ACM Transactions on Computer Systems, 1985. Virtual Time and Global States of Distributed Systems.  Mattern, F. 1988. Practical uses of synchronized clocks in distributed systems. B. Liskov, 1991. Exp...
Read more >>

Advice to the young

-
Image
I notice I haven't written any advice posts recently. Here is a collection of my advice posts pre 2020. I've been feeling all this elderly wisdom pent up in me, ready to pour at any moment. So here it goes. Get ready to quench your thirst from my fount of wisdom. No man, think for yourself, only get what works for you. It is called foundations, not theory Foundations of computer science (or rather any field of study) are the most important topics you can learn. These lay down the frame of thinking/perspective for that area of study. Yet, I am saddened to hear these called as "theory", and labeled as "unpractical". This couldn't be farther from the truth. Take a look at how I recommend studying distributed systems . Don't you dare call this "theory" and "unpractical". This lays the bedrock that you build your practice on. Don't skimp on the foundations. Don't build your home on quicksand. Keep your hands dirty, your mind cl...
Read more >>

Linearizability: A Correctness Condition for Concurrent Objects

-
Image
This paper is from Herlihy and Wing appeared in ACM Transactions on Programming Languages and Systems 1990. This is the canonical reference for the linearizability definition. I had not read this paper in detail before, so I thought it would be good to go to the source to see if there are additional delightful surprises in the original text. Hence, this post. I will dive into a technical analysis of the paper first, and then discuss some of my takes toward the end. I had written an accessible explanation of linearizability earlier; you may want to read that first. I will assume an understanding of linearizability to keep this review at reasonable length. Introduction I love how the old papers just barge in with the model, without bothered by pleasantries such as motivation of the problem. These are the first two sentences of the introduction. "A concurrent system consists of a collection of sequential processes that communicate through shared typed objects . This model encompass...
Read more >>

Understanding the Performance Implications of Storage-Disaggregated Databases

-
Image
Storage-compute disaggregation in databases has emerged as a pivotal architecture in cloud environments, as evidenced by Amazon ( Aurora ), Microsoft ( Socrates ), Google (AlloyDB), Alibaba ( PolarDB ), and Huawei (Taurus). This approach decouples compute from storage, allowing for independent and elastic scaling of compute and storage resources. It provides fault-tolerance at the storage level. You can then share the storage for other services, such as adding read-only replicas for the databases. You can even use the storage level for easier sharding of your database. Finally, you can also use this for exporting a changelog asynchronously to feed into peripheral cloud services, such as analytics. Disaggregated architecture was the topic of Sigmod 23 panel . I think this quote summarizes the industry's thinking on the topic. "Disaggregated architecture is here, and is not going anywhere. In a disaggregated architecture, storage is fungible, and computing scales independently. ...
Read more >>

Scalable OLTP in the Cloud: What’s the BIG DEAL?

-
Image
This paper is from Pat Helland, the apostate philosopher of database systems, overall a superb person, and a good friend of mine. The paper appeared this week at CIDR'24. (Check out the program for other interesting papers). The motivating question behind this work is: " What are the asymptotic limits to scale for cloud OLTP (OnLine Transaction Processing) systems? " Pat says that the CIDR 2023 paper "Is Scalable OLTP in the Cloud a Solved Problem?" prompted this question.  The answer to the question? Pat says that the answer lies in the joint responsibility of database and the application. If you know of Pat's work, which I have summarized several in this blog , you would know that Pat has been advocating along these lines before. But this paper provides a very crisp, specific, concrete answer. Read on for my summary of the paper. Disclaimer: This is a wisdom and technical information/detail packed 13-page paper, so I will try my best to summarize the sa...
Read more >>

Designing Data Intensive Applications (DDIA) Book

-
Image
We started reading this book as part of Alex Petrov's book club . We just got started, so you can join us, by joining the discord channel above. We meet Wednesday's 11am Eastern Time.  Previously we had read transaction processing book by Grey and Reuters. This page links to my summaries of that book. Chp 1. Reliable, Scalable, and Maintainable Applications I love the diagrams opening each chapter. Beautiful! The first chapter consists of warm up stuff. It talks about the definitions of reliabilty, scalability, and maintainability. It is still engaging, because  it is written with an educator and technical blogger voice, rather than a dry academic voice. This book came out on 2017. Martin is working on the new version. So if you have comments for things to focus on for the new version, it would be helpful to collect them in a document and email it to Martin. For example, I am curious about how the below paragraph from the Preface will get revised with 8 more years of hindsight...
Read more >>