> The reason for using TLA+ is that it isn’t a programming language; it’s mathematics.
I love TLA+, I’ve used it for a decade and reach for it often. I have a huge amount of respect for Leslie Lamport and Chris Newcombe. But I think they’re missing something major here. The sematics of TLA+ are, in my mind, a great set of choices for a whole wide range of systems work. The syntax, on the other hand, is fairly obscure and complex, and makes it harder to learn the language (and, in particular, translate other ways of expressing mathematics into TLA+).
I would love to see somebody who thinks deeply about PL syntax to make another language with the same semantics as TLA+, the same goals of looking like mathematics, but more familiar syntax. I don’t know what that would look like, but I’d love to see it.
It seems like with the right library (see my mathlib point) and syntax, writing a TLA+ program should be no harder than writing a P program for the same behavior, but that’s not where we are right now.
> The errors [types] catch are almost always quickly found by model checking.
This hasn’t been my experience, and in fact a lot of the TLA+ programs I see contain partial implementations of arbitrary type checkers. I don’t think TLA+ needs a type system like Coq’s or Lean’s or Haskell’s, but I do think that some level of type enforcement would help avoid whole classes of common specification bugs (or even auto-generation of a type checking specification, which may be the way to go).
> [A Coq-like type system] would put TLA+ beyond the ability of so many potential users that no proposal to add them should be taken seriously.
I do think this is right, though.
> This may turn out to be unnecessary if provers become smarter, which should be possible with the use of AI.
Almost definitely will. This just seems like a no-brainer to bet on at this stage. See AlphaProof, moogle.ai, and many other similar examples.
> A Unicode representation that can be automatically converted to the ascii version is the best alternative for now.
Yes, please! Lean has a unicode representation, along with a nice UI for adding the Unicode operators in VSCode, and it’s awesome. The ASCII encoding is still something I trip over in TLA+, even after a decade of using it.
Perhaps you would find Quint interesting? https://news.ycombinator.com/item?id=41111790
There's a comment that says Quint uses TLA+ as its base language: https://news.ycombinator.com/item?id=41118162
Disclaimer: I don't know anything about TLA+ or Quint, I just remembered seeing Quint here
Building out any real maths with logic operators yourself is just not feasible in a meaningful timescale.
> The syntax, on the other hand, is fairly obscure and complex, and makes it harder to learn the language
the syntax was very non-standard which was off putting, and the expected dev ux seemed to be of the 'get it right on paper first then just write the text' variety. This was also off putting and I think you're right that there is a space for making a DX focused TLA+ transpiled language
There's another reason to potentially support \EE: it's needed to refine specs with auxiliary variables. Currently, if an abstract spec has `aux_hist` to prove a property or something, you need the refinement to have an `aux_hist` equivalent, even if it doesn't affect the spec behavior at all. But if checkers could handle `\EE` you could instead leave it out of the refinement and check `\EE aux_hist: Abstract(aux_hist)!Spec`.
I think /u/pron once told me that actually checking a property of that form is 2-EXPTIME complete, though. Which is why it's not supported in practice.
Would it be actually possible to write something like an "a la carte temporal logic library" for other proving languages that could get you some of the confidence you can get from TLA+'s modeling?
(Aside: I have a TLA+ book, but it's notably missing really much in terms of exercises or anything. If anyone has any recommendations for a large set of exercises to play around in the space I'd love to hear about it!)
EDIT: turns out just searching for "temporal logic in X language" gets you papers, found this one paper for axiomatizing temporal logic that seems to be a good starting point for anyone looking at this [0]
[0]: https://lim.univ-reunion.fr/staff/fred/Enseignement/Verif-M2...
Temporal logic is just a specific instance of a modal logic, which can be modeled with reasonable ease using a "possible worlds"-based encoding. Note that TLA+ combines temporal logic with non-determinism, which is a different modality.
TLA+ isn't taught in most universities and while I've read about so many interesting applications, I'm yet to convince myself that someone would hire me for knowing it rather than just teaching it to me on the job. Any tips to get started would also be appreciated!
If nothing else, spending a few days playing with it will give you an idea of what it's good for and if you want to continue, or it'll make it stick in your mind so you can come back to it if you ever need it.
I guess this must be true on places like SF since I see this so often on HN, but almost every single job listing I've seen strictly requires knowledge of a specific tech stack, with the exception of a few internship programs.
I did not find it straight forwardly grokkable, which makes me sad. Maybe it needs a library of axioms? I feel there's probably a very nice way to work through it without ingesting effectively a graduate school course in proving software.
It really is just math and proofs, it shouldn't be so hard... to start.
Well, that's my take. Could be wrong. Might just need to hit the books.
That said, since non-deterministic choices are equi-probable in P, failure conditions are triggered at much higher frequencies than in a conventional testing scenario.
Then I look through some of the specs I've written with clients and find the one absolutely insane thing I did in TLA+ that would be impossible in that replacement.
Shoutout to operator labels.
- It cannot compile to working code
- Steep learning curve
Opportunities for TLA+
- Helps you understand complex abstractions & systems clearly.
- It's extremely effective at communicating the components that make up a system with others.
Let get give you a real practical example.
In the AI models there is this component called a "Transformer". It under pins ChatGPT (the "T" in ChatGPT).
If you are to read the 2018 Transfomer paper "Attention is all you need".
They use human language, diagrams, and mathematics to describe their idea.
However if your try to build you own "Transformer" using that paper as your only resource your going to struggle interpreting what they are saying to get working code.
Even if you get the code working, how sure are you that what you have created is EXACTLY what the authors are talking about?
English is too verbose, diagrams are open to interpretation & mathematics is too ambiguous/abstract. And already written code is too dense.
TLA+ is a notation that tends to be used to "specify systems".
In TLA+ everything is a defined in terms of a state machine. Hardware, software algorithms, consensus algorithms (paxos, raft etc).
So why TLA+?
If something is "specified" in TLA+;
- You know exactly what it is — just by interpreting the TLA+ spec
- If you have an idea to communicate. TLA+ literate people can understand exactly what your talking about.
- You can find bugs in an algorithms, hardware, proceseses just by modeling them in TLA+. So before building Hardware or software you can check it's validity & fix flaws in its design before committing expensive resources only to subsequently find issues in production.
The issue of TLA+ is that it doesn’t come from the right side of the field. Most formal specifications tools were born out of necessity from the engineering fields requiring them. TLA+ is a computer science tool. It sometimes shows in the vocabulary used and in the way it is structured.
I bet you a million dollars [0] that Mr. Lamport absolutely is the sole author of this sentence.
[0] which I don't have. You may resume reading.
Is TLA+ simple? I find this hard to accept.
> TLA+ isn’t a programming language; it’s mathematics.
Mathematics is not executable, though, whereas TLA+ is.
> TLA+ [is better] for its purpose than a programming language.
"TLA+ is a formal specification language designed by Leslie Lamport for the specification of system behavior."
"specification of system behavior" sounds like a programming language to me. A systems programming language, even.
All this is to say that it seems TLA+ really has no future. If there was a future, like a goal or a roadmap or something, it would be outlined in this document a lot more clearly - whereas, instead, it is more like "nope, everything's good, no changes needed", even as the language appears nowhere on the TIOBE rankings.
It seems to me that TLA+ is executable in the sense that a difference equation can be run forward in time. Plenty of mathematics is executable in that sense.
Specification is not the same thing as implementation. A specification language does not tell a machine what operations to perform, a programming language does.
System behavior and systems programming are entirely different uses of the word system.
> A specification language does not tell a machine what operations to perform, a programming language does.
There is a style of programming (usually functional or relational programming) that does not bother itself with operations, and which aims to merely describe a result. Specifications are still different from implementations written in such a style of programming.
And I would agree, TLA+ as a specification is different from TLA+ as an implementation. I generally disregard specs, I was talking about TLA+ the implementation when I said it had no future. It seems it will be in perpetual maintenance mode with barely any new features.
Regarding simple vs. easy, I challenge you to argue that temporal logic is "simple" in any sense of the word.
Specification languages are explicitly not programming languages, for the core reason that programming languages dictate only what must occur; whereas specification languages can dictate what must not occur. It's not possible with a "specification" written using a programming language to determine what of a program is actually the specification, vs. what is an accident of the implementation.
More relevant today, you can execute other "specification" languages like Coq and Idris because they support things outside the narrow feature set of specification usecases.
TLA+ isn't executable and doesn't look like an imperative language because the authors don't want it to be, not because there's some universal line dividing specification languages from programming languages. It's also one of the biggest hurdles to TLA+ usage.
Lamport has directly and repeatedly addressed the differences between what's desirable in a specification language versus what's desirable in a programming language. Understanding the difference is vital to writing specifications.
It is very, very simple, and I would say easier to learn than Python, as long as you remember that it is not programming but maths. For example, suppose you specify this function on the integers:
f ≜ CHOOSE f ∈ [Int → Int] :
∀ x ∈ Int : f[x] = -f[x]
f :: Integer -> Integer
f x = -(f x)
It is definitely not executable (i.e. not any more than mathematics is; you can specify executable things in maths and therefore in TLA+, but not everything you specify is executable). You can specify non-computable things (e.g. it is trivial to specify a halting oracle) as well as things involving real numbers. Moreover, when you check a TLA+ specification with a model-checker like TLC, it doesn't actually execute the specification, as it can check a specification of uncountable many executions, each of infinite length in a second.
However, you can certainly write formulas specifying the behaviour of an executable program and simulate it with TLC. But this is because you can use mathematics to describe physical systems, but not everything you can describe in mathematics can have a physical representation.
> "specification of system behavior" sounds like a programming language to me. A systems programming language, even.
A program is, indeed, one way of specifying a system, and TLA+ does allow you to specify an algorithm in this way (because maths allows you to specify programs), but it also allows you to specify systems in very useful ways that are very much not programs. For example, you can specify a component that sorts things without ever writing an algorithm for sorting, which is useful when the details of the sorting algorithm are irrelevant to the questions you want to answer. It's like how you can write a formula that treats planets as point-masses if you're interested in orbital mechanics, yet specify the earth in a much more detailed way if you're interested in predicting the weather.
> even as the language appears nowhere on the TIOBE rankings.
It is not a programming language. While it is true that far more people write programs than use mathematics to reason about physics, biology, or the way software systems behave (especially complicated interactive and distributed systems, which is where TLA+ excels), that doesn't mean such disciplines have no future.
> f ≜ CHOOSE f ∈ [Int → Int] : > ∀ x ∈ Int : f[x] = -f[x]
> What function is it? Clearly, it's the zero function
Did you mean your example is the constant function [1], rather than a zero function [2] (where c = 0)?
def f(x):
return -xBy "specification language" Lamport means one capable of verification via model checking.
In contrast, "programming languages" are not capable of such verification.
TIOBE rankings are widely considered to be useless by those who care about programming languages, but even aside from that your dismissal on those grounds is absurd given that you had just barely criticized TLA+ for trying to duck the label of "programming language" at all. You can't criticize it for trying not to be a programming language and then turn around and criticize it for not showing up on a ranking of programming languages.
It's excluded from the TIOBE index in the same way that HTML, CSS, or Markdown are excluded, and that's by choice.
Where is the outline for English? French has a more structured oversight with organizations and goals, so it will beat English?
Even the most popular languages such as Python have just a few viable implementations.
Roadmap/focus is useful in a collaboration.