Question

When I write an algorithm I usually write down invariants in comments.

For example, one function might return an ordered list, and the other one expect that a list would be ordered.
I’m aware that theorem provers exists, but I have no experience using them.

I also believe that smart compiler [sic!] can make use of them to optimize the program.
So, is it possible to write down invariants and make compiler check them?

Answer 1

Well, the answer is yes and no. There’s no way to just write an invariant separate from a type and check it. There was an implementation of this in a research fork of Haskell called ESC/Haskell, however: http://lambda-the-ultimate.org/node/1689

You do have various other options. For one, you can use asserts: http://www.haskell.org/ghc/docs/7.0.2/html/users_guide/assertions.html

Then with the appropriate flag, you can turn off these asserts for production.

More generally, you can encode the invariants in your types. I was going to add more here, but dons beat me to the punchlines.

One more example is this very nice encoding of red-black trees: http://www.reddit.com/r/haskell/comments/ti5il/redblack_trees_in_haskell_using_gadts_existential/