Can Haskell functions be proved/model-checked/verified with correctness properties?

Question

Continuing on from ideas in: Are there any provable real-world languages?

I don\'t know about you, but I\'m sick of writing code that I can\'t guarantee.

Answer 1

Your seemingly simple example, add(a,b), is actually difficult to verify - floating point, overflow, underflow, interrupts, is the compiler verified, is the hardware verified, etc.

Habit is a simplified dialect of Haskell that allows for proving program properties.

Hume is a language with 5 levels, each more limitedand therefore easier to verify:

Full Hume
  Full recursion
PR−Hume
  Primitive Recursive functions
Template−Hume
  Predefined higher−order functions
  Inductive data structures
  Inductive  Non−recursive first−order functions
FSM−Hume
  Non−recursive data structures
HW−Hume
  No functions
  Non−recursive data structures

Of course, the most popular method today for proving program properties is unit testing, which provides strong theorems, but these theorems are overly specific. "Types Considered Harmful", Pierce, slide 66

Answer 2

It's certainly possible to prove some properties of Haskell programs formally. I've had to do so at my FP exam: given two expressions, prove that they denote the same function. It's not possible to do this in general since Haskell is Turing-complete, so any mechanical prover would either have to be a proof assistant (semi-automatic with user guidance) or a model checker.

There have been attempts in this direction, see e.g. P-logic: property verification for Haskell programs or Proving the correctness of functional programs using Mizar. Both are academic papers describing methods more than implementations.

Answer 3

Have you had a look at quickcheck? It may offer some of the things you need.

http://www.haskell.org/haskellwiki/Introduction_to_QuickCheck

Answer 4

The tool AProVE is (at least) able to prove termination of Haskell programs, which is part of proving correctness. More information can be found in this paper (shorter version).

Apart from that, you might be interested in Dependent Types. Here, the type system is extended and used to make wrong programs impossible.

Answer 5

Some very recent effort by MSR Cambridge: http://research.microsoft.com/en-us/um/people/simonpj/papers/verify/hcc-popl.pdf

Answer 6

Sounds like you want ESC/Haskell: http://research.microsoft.com/en-us/um/people/simonpj/papers/verify/index.htm

Oh, and Agda now does have a web framework (proof of concept, at least): http://www.reddit.com/r/haskell/comments/d8dck/lemmachine_a_web_framework_in_agda/