I was initially excited about this; a prover with a logic like Coq (dependent types!) but with awesome extensions (effects!) and with the automation of Z3 seems pretty neat. I decided to test-drive it with the first few chapters of the Software Foundations book (https://www.cis.upenn.edu/~bcpierce/sf/current/index.html).
Unfortunately, proving in F* turned out to be a pain. The basic problem is that during proving you have no idea at all about the state of the proof; the only way I could get anything done when automation failed (and that was more often than I had hoped) was by working out, in comments, a very detailed proof, and then applying appropriate lemmas. If you know Coq, think of it as writing down tactics without seeing the proof state in the side pane, and having to get it complete before you get a simple yes/no answer telling you whether what you did was good enough to make the entire proof go through. But in fact, it it is even more painful than that: In Coq, you can apply/rewrite with lemmas just by naming them, but in F* you need to instantiate all arguments. So a proof step for one of the lemmas in the second document above, which would be rewrite -> plus_swap in Coq, in F* must be written plus_swap n m' (mult (S n) m') although Z3 could easily find the correct arguments itself. But leaving arguments off is simply not possible in a system of this kind based on the notion that a "proof" is written a well-typed program.
Oh well. Back to Isabelle/HOL for my regular theorem proving needs, although its logic is really weird and I wish there was some system combining the automation of Isabelle with the Calculus of Constructions.
Now, I must admit, I'm a lot less excited :-( You can see my results for (almost all of) the first two chapters here: http://pastebin.com/5bL7Wugq http://pastebin.com/GRFLCF8Z
Unfortunately, proving in F* turned out to be a pain. The basic problem is that during proving you have no idea at all about the state of the proof; the only way I could get anything done when automation failed (and that was more often than I had hoped) was by working out, in comments, a very detailed proof, and then applying appropriate lemmas. If you know Coq, think of it as writing down tactics without seeing the proof state in the side pane, and having to get it complete before you get a simple yes/no answer telling you whether what you did was good enough to make the entire proof go through. But in fact, it it is even more painful than that: In Coq, you can apply/rewrite with lemmas just by naming them, but in F* you need to instantiate all arguments. So a proof step for one of the lemmas in the second document above, which would be rewrite -> plus_swap in Coq, in F* must be written plus_swap n m' (mult (S n) m') although Z3 could easily find the correct arguments itself. But leaving arguments off is simply not possible in a system of this kind based on the notion that a "proof" is written a well-typed program.
Oh well. Back to Isabelle/HOL for my regular theorem proving needs, although its logic is really weird and I wish there was some system combining the automation of Isabelle with the Calculus of Constructions.