Formal-Methods -

TLA⁺ is more than a DSL for breadth-first search

Posted on September 18, 2024 | Andrew Helwer

Although it isn’t usually taught that way, a lot of TLA⁺ newcomers develop the understanding that TLA⁺ is just a fancy domain-specific language (DSL) for breadth-first search. If you want to model all possible executions of a concurrent system - so the thinking goes - all you have to do is define: The set of variables modeling your system The values of those variables in the initial state(s) Possible actions changing those variables to generate successor states Safety invariants you want to be true in every state The model checker will then use breadth-first search (BFS) to churn through all possible states (& thus execution orders) of your system, validating your invariants. [Read More]

tlaplus formal-methods

TLA⁺ Unicode support

Learning to work with others in open source

Posted on May 28, 2024 | Andrew Helwer

TLA⁺ was developed by Leslie Lamport, originator of \(\LaTeX\), so it’s unsurprising that TLA⁺ syntax looks pretty \(\LaTeX\)-y. It’s a very mathy language, with much use of symbols like (among others) \A,\E, /\, \/, and \in denoting \(\forall\), \(\exists\), \(\land\), \(\lor\), and \(\in\) respectively. The language tools include a tla2tex command to format TLA⁺ specs into \(\LaTeX\) for integration in research papers. However, research papers are not where I spend the most time looking at TLA⁺. [Read More]

tlaplus formal-methods

Wrangling monotonic systems in TLA⁺

Tractable modeling of replicated logs & CRDTs

Posted on November 1, 2023 | Andrew Helwer

TLA⁺ sees a lot of use modeling distributed systems. The ability to explore all possible interleavings of events makes concurrency simple to reason about. For this TLA⁺ uses something called finite model-checking, which is really just a breadth-first search through the entire state space. The key here - and this really must be emphasized - is that the model is finite. There can’t be an infinite number of states, or of course the model checker will run forever. [Read More]

tlaplus distributed-systems formal-methods

Using TLA⁺ at Work

Designing a snapshot coordination system

Posted on April 5, 2023 | Andrew Helwer

Here’s a short report of a time I used TLA⁺ at work, with interesting results. TLA⁺ is a formal specification language that is particularly effective when applied to concurrent & distributed systems. TLA⁺ made it tractable for an ordinary software engineer to reason about a tricky distributed systems problem, and it found a bug introduced by an “optimization” I tried to add (classic). The bug required 12 sequential steps to occur and would not have been uncovered by ordinary testing. [Read More]

tlaplus distributed-systems formal-methods

Pseudocode Showdown

Python vs. PlusCal & TLA⁺

Posted on March 30, 2023 | Andrew Helwer

Last weekend I had a conversation with an undergraduate student new to computer science, who was reading CLRS. “I wish” they said, “that all the pseudocode in my algorithms textbook was just written in Python.” “Ah” I said, “but textbook authors sometimes want their work to endure beyond a decade.” “But Python’s been around for a long time” came the reply, “and it’s very readable, and you can’t execute pseudocode anyway so what’s the harm? [Read More]

formal methods tlaplus

Writing a TLA⁺ tree-sitter grammar

My foray into free software

Posted on January 11, 2023 | Andrew Helwer

2021 saw the completion of my first substantial free software project: a TLA⁺ grammar for tree-sitter, the error-tolerant incremental parser generator. The project stabilized & found users over the course of 2022, then over the holidays I used it to build the TLA⁺ Unicode Converter. The new year is a time to reflect on the past and look to the future, so here in early 2023 seems ideal to publish my experience. [Read More]

formal methods tlaplus

The Missing Prelude to The Little Typer's Trickiest Chapter

Yes, it's the replace function in chapter 9

Posted on October 13, 2022 | Andrew Helwer

It’s hard to find a textbook series garnering more effusive praise than The Little Schemer, The Little Prover, The Little Typer & co. The Little Typer introduces dependent type theory and is the first of the series I’ve read. I quickly grew to appreciate & enjoy its dialogue-based presentation - I’m a real convert! I might release future didactic blog posts as a dialogue rather than straight recitation of material in block paragraphs. [Read More]

formal methods

Regexes in the Z3 Theorem Prover

Analyzing Teleport RBAC

Posted on January 19, 2022 | Andrew Helwer

Republished from Teleport’s official blog (link). I received compensation from Teleport for writing this post. Z3 is a satisfiability modulo theories (SMT) solver developed by Microsoft Research. With a description like that you’d expect it to be restricted to esoteric corners of the computerized mathematics world, but it’s made impressive inroads addressing conventional software engineering needs: analyzing network ACLs and firewalls in Microsoft Azure, for example. Z3 is used to answer otherwise-unanswerable questions like “are these two firewalls equivalent? [Read More]

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How do you reason about a probabilistic distributed system?

Posted on September 11, 2020 | Andrew Helwer

In which I am stunted upon by coin flips Wasn’t too long ago that I felt pretty good about my knowledge of distributed systems. All someone really needed in order to understand them, I thought, was a thorough understanding of the paxos protocol and a willingness to reshape your brain in the image of TLA⁺. Maybe add a dash of conflict-free replicated datatypes, just so you know what “eventual consistency” means. [Read More]

distributed systems formal methods

Doing a math assignment with the Lean theorem prover

Posted on April 5, 2020 | Andrew Helwer

Note: this post was written for Lean 3; the latest version, Lean 4, is a very different language. Turn back the clock to 2009: a confused physics major newly infatuated with math and computer science, I enrolled in MATH 273: Numbers and Proofs at the University of Calgary. This wasn’t my first encounter with mathematical proof; in first-year calculus I’d mastered rote regurgitation of delta-epsilon proofs. Despite writing out several dozen, their meaning never progressed beyond a sort of incantation I can summon to this day (for every \( \epsilon > 0 \) there exists a \( \delta > 0 \) such that…). [Read More]

formal methods