[Haskell-beginners] Re: Enforcing Monad Laws

[Jorden M]

On Sun, Jul 4, 2010 at 11:16 AM, Daniel Fischer
<daniel.is.fischer at web.de> wrote:
> On Sunday 04 July 2010 16:05:48, Jorden M wrote:
>> > Now that I've had a really short look at Axioms, I think the Haskell
>> > equivalent would be QuickCheck properties. After all, Axioms are not
>> > enforced by the compiler, their only effect is documentation. Granted,
>> > they
>>
>> Really? I thought they were.
>>
>
> I think that's not even possible in general.

It would equate to solving the Halting Problem, I suppose. The point
of axioms for compiler use must then have been to say, `All right,
assume this is true and make optimizations if possible.'

A bit fast and loose in the presence of careless programmers, no? At
least calling them axioms makes more sense.

> Generally, you can't decide the equality of functions [okay, we're dealing
> with finite domains in a computer, so in principle one could check all
> possible inputs, but even for a small type like uint64_t, that's
> impractical].
>
>> > are part of the source code, but frankly, I don't see how this has
>> > more effect than stating invariants as QuickCheck properties or
>> > writing them down in a comment.
>>
>> Would it make sense to try to formalize things like the monad laws
>> using QuickCheck?.
>
> To a certain extent. You'd have a good chance to catch gross violations of
> the monad laws with QuickCheck. But for subtle violations, the odds are
> minuscule.
>

I wonder if the effort to do so would be useful.