[pron]

> But does it happen because it is the only option or the best option?

I don't understand the difference. Model-checking scales better than deductive proofs and is far cheaper. If you have less than 5 years to write a 10 KLOC program or your program is larger, then deductive proofs won't work. Does that mean it's better or that it's the only choice?

> Also, encoding semantics specs is hard, so proper verification of algorithmic side is usually not an option anyway.

This is true for all formal methods, but here, too, most of them beat deductive proofs. With deductive proofs you have to annotate every unit (or work much harder). Model-checking (and concolic tests) can handle partial specifications. This is yet another reason why formal methods research is not focusing its efforts on deductive proofs.

> Again, I don't need separate model checker here, moderately advance GHC type system works just fine.

It doesn't, though. Memory safety is a compositional property, as is every kind of property that can be easily checked by deductive proofs (or almost compositional, requiring one or two inferences). Most correctness properties are not compositional. That deductive proofs (of propositions that aren't compositional) don't scale is not some hypothesis of mine. They've been tried for years, and they just don't. The biggest programs ever verified with them are ~10KLOC and they took years of expert work.

> Wiki disagrees with you. Oh, well.

No, it doesn't. But if you think it does, it means you don't yet know what signatures, theories, structures, interpretations and models are -- the very basics of all formal logics -- so explaining that might take a while (in short, if propositions and functions are part of the structure, of course FOL can quantify over them; if it couldn't, it wouldn't have been the lingua franca of mathematics and the crowning achievement of formal logic). You can read my very short introduction to formal logic here: https://pron.github.io/posts/tlaplus_part2#what-is-a-logic . It's relevant to any formal logic you may want to learn at some point, as they're all more similar to one another than differen, but it may be too terse if you don't have any prior background.

> As I said, at best I might be interested in HOL Isabelle. And even that is doubtful, so far Agda and Coq appear more useful for what I'm interested in.

Sure. In general, Lean/Coq/HOL are more geared toward research -- inventing new logics, formalizing "high" mathematics -- and TLA+ is more geared toward industry use and verification of software and hardware, and because that's what I need, that's the one I use most. But it really doesn't matter which you learn -- they're all much more similar to one another than different. Their most important differences are in user-friendliness and their tooling. I would recommend Lean over Coq and Agda, though; I think it subsumes both, and its documentation and tutorials are better, so it's easier to learn. I enjoyed TLA+ and Lean more than Coq and HOL, and I haven't tried Agda. But this could be a matter of personal preference. Again, they're all more similar than different.

[permeakra]

>It doesn't, though.

read this: https://serokell.io/blog/dimensions-and-haskell-introduction , then look into the referenced libraries.

Have fun arguing with objective reality.

As for resource safety, Haskell is yet to follow Rust and introduce linear types, but many cases are covered by bracket pattern https://wiki.haskell.org/Bracket_pattern which can be enforced on type level using some tricks with ST monad. BTW, it is very similar to RAI discipline suggested by many C++ guidelines, but here it can be enforced.

Again, have fun arguing with objective reality.

>This is true for all formal methods, but here, too, most of them beat deductive proofs.

Sure, feel free to feel superior about that. The problem is, again, type system can be embedded into programming language and allow for quite a bit of guarantees even without full blown dependent types. Java has static typing for a reason.

Sure, to enforce some properties using type system we need an uncomfortably deep delve into type theory or use awkwardly polymorphic code. However, a lot of properties can be enforced with relatively low cost, and Haskell is a long-running research project on what properties are practical to enforce this way.

So, why I need to use proof assistants for properties that can be enforced via practical type system? I really don't see a reason.

[pron]

> read this: https://serokell.io/blog/dimensions-and-haskell-introduction , then look into the referenced libraries.

Dude, I actually work with dependent type proof assistants (Lean), with a HOL proof assistants (Why3), and FOL/ZFC proof assistant (TLA+'s TLAPS), as well as with a model checker for TLA+ (TLC); I've also worked with a model checker for Java in the past. I have read several books on the subject, and have written two (both available online: https://pron.github.io/tlaplus, and https://pron.github.io/computation-logic-algebra). I've also trained engineers in formal methods.

> Have fun arguing with objective reality.

You've read a few blog posts on one aspect of one formal method, and seem to have not even heard of the majority of software correctness research. You certainly don't seem to have practiced formal methods in industry even using one method, let alone more than one. You don't even seem to know what first-order logic is, what higher-order logic is, and I'm sure that if I asked you the difference between HOL and Martin-Löf type theory, or between classical and constructive mathematics you won't even know what I'm talking about; ditto if I asked you what it means for a type theory to have a set-theoretical interpretation (as Lean's, and maybe Agda's -- I don't know -- type theories do). You've read a few blog posts about a small part of one of the most complex, refractory topics in all of computer science and software engineering. You don't know what the objective reality is.

That you can prove some stuff with dependent types has been true for at least 30 years now. That other approaches, of which you seem to know nothing, scale much better in practice to the point that industry rarely uses deductive proof for anything but small, niche problems and uses model checkers all the time to verify some of the software your life depends on is just a fact. If you don't know what the alternatives are, how can you argue with what I'm saying?

> Sure, feel free to feel superior about that.

I don't feel superior. It seems that, unlike you, I actually use deductive proofs for verification, as well as model checkers, because, unlike you, I actually practice formal verification. But, knowing the tools, I know what works and when. I'm not researching one approach or another; I use which one currently works best, and the reality is pretty clear.

> The problem is, again, type system can be embedded into programming language

Contract systems are also embedded into programming languages. You seem to know one thing (know of, seems more accurate) and argue it's the best, when you have no idea what other things are out there.

> and allow for quite a bit of guarantees even without full blown dependent types. Java has static typing for a reason.

Sure, that because static types are awesome! There are some things -- simple, compositional properties -- for which nothing else works better. Type systems beat the alternatives for these simple properties and, at least currently, lose to the alternatives when deeper properties are involved. Correctness is complicated, and different properties require different tools. That is why, when deep properties are involved, I prefer separating the specification method from the verifiation method. Contract systems are embedded into programming languages and work alongside simple types. They then allow you to choose the best verification tool for the job: you can use deductive proofs, like depdendent types do, and other verification methods when those work better (which is the majority of cases). Dependent types tie you down to the verification method that is the most restrictive and least scalable.

> So, why I need to use proof assistants for properties that can be enforced via practical type system? I really don't see a reason.

You don't. The two are equivalent. I.e., they are equally the least scalable verification method we know. But contract systems, unlike depdent types, allow you to choose: you can use deductive proofs or other, cheaper, more scalable approaches. You need them because deductive proofs -- the only verification approach that dependent types give you -- just don't scale. But I don't need to convince you. I encourage you to learn Idris/HOL/Lean/TLA+/Coq -- whichever one you like (better yet, learn more than one) -- and try writing deductive proofs for large programs. Try different kinds of programs, too: sequential, interactive, concurrent and distributed. Knock yourself out. Perhaps when you speak from experience you'll have a better grasp of what objective reality is. In the process, you will learn a lot, so I truly wish you the best of luck!

But take one piece of advice: don't become dogmatic about something until you've actually looked around. If you argue that X is better than Y and Z because X is all you know, you just sound like a cultist. Learn first, argue later.

[permeakra]

>If you argue that X is better than Y and Z because X is all you know, you just sound like a cultist. Learn first, argue later.

Apparently, you didn't look in the mirror. Oh, well. Thank you for proving my prejudices right with this post =).

[pron]

I've tried all the methods discussed, and my point-of-view is based on my personal experience and years of involvement with formal methods. You've tried none, and your point-of-view is based on... a couple of blog posts you've read?