What are the competitors to this language? Can someone provide a list. I'd like to start learning a provable language, not sure if Dafny is the one I should start with though.
Per this reddit comment [1], the languages supporting some kind of compile-time constraint-checking/proving include Why3, Dafny, Fstar, Coq, Agda, and Idris.
Also, some languages have been extended to support it: LiquidHaskell, Frama-C, and Spark/Ada. I also recall some Java extension but can't find it atm.
Per the Wikipedia page for Whiley[1] the languages akin to Dafny are mentioned when explaining what Whiley is: “The primary purpose of such a tool is to improve software quality by ensuring a program meets a formal specification. In other words, to help identify and eliminate software bug in the programs being developed. Whiley follows many attempts to develop such tools, including notable efforts such as SPARK/Ada, ESC/Java, Spec#, Dafny, Why3 and Frama-C.”
I'm thinking there must be a reason they do not mention F*, Coq, Agda, and Idris, perhaps because they are proof assistants[2] rather than automatic provers of programs with formal specifications. See also Isabelle and others. Regarding Idris (which you mention but is not on that page) and Epigram (which is noteworthy and again not on that page), neither are production ready and the latter is unmaintained.
> I'm thinking there must be a reason they do not mention F* , Coq, Agda, and Idris
The ones they do mention are all imperative languages with added deductive verification in a Hoare calculus style (think loop invariants). The ones you mention are functional languages with a different style of proof (think inductive proofs).
Of course there are overlaps between the two styles (notably in Why3), but there are pronounced differences between them.
Coq is the one I use most. I've heard of lean as well though.
Those are both proof assistants not theorem provers. Dafny uses z3 to attempt to automatically prove theorems about your code. Lean or Coq (for the most part) require that you write the proofs manually in a special language they provide and they will tell you whether or not your proof has errors.
In general these languages lie on a spectrum between more automatic to more manual with the automatic ones taking potentially more time and being more limited but requiring less of you and the manual ones such as lean or coq are more expressive but harder to use because you have to provide all of the proofs.
I should say all this with the caveat that I'm only learning these things now so I've probably said something wrong. Please correct me if that is the case.
It is a gradual range from untyped (assembly) to proof-anything (Isabelle, Coq). The more interesting question is: Where are the sweet spots?
The current mainstream (Java,C++,etc) form a big cluster "sweetrange" of roughly equivalent type safety. Rust with its ownership type system goes one step towards more proofs. ATS is even further. Agda and Idris want to be useable programming languages while providing as much proof as possible. Isabelle can generate code, but is also used as just a theorem prover.
> Rust with its ownership type system goes one step towards more proofs.
Does it really, though? The ownership system only talks about ownership, which you only need to reason about due to the artificial choice of avoiding garbage collection. So yes, you get closer to proofs, but only to proofs of properties that are not necessary to prove for Java, say.
You might use the ownership and lifetime system to derive must-not-alias guarantees that might help with some verification tasks, but I'm not sure how much it would help.
I'd love to see a deductive verification system for Rust, but I wouldn't expect it to be the silver bullet for verification.
Author of that project here, it's the other way around - I'm using the absence oft aliasing to turn mutable Rust code immutable, which I can then embed in Lean. But you're right that ownership (ie, affine types) per se doesn't help.
There's the so-called 'B Method', which seems very similar to this on the programming language side. I haven't checked the proof language so that may be very different.
I've got a two-parter on my blog giving a glimpse of B's programming language[1] and proof language[2].
Perfect Developer [1] is another one not yet mentioned. You write and verify your "specifications" (program-parts to be verified) using a language called "Perfect" and generate C++, C#, or Java from that (SPARK Ada generator in progress).
