Re: FunctorFix

I see that a general right shrinking axiom would be a bad idea as it would rule out many sensible instances of MonadFix. However, I think that it is very reasonable to have the following restricted right shrinking axiom:     mfix (\ ~(x, _) -> liftM2 (,) (f x) g) = liftM2 (,) (mfix f) g The important difference compared to general right shrinking is that the shape (or effect) of g does not depend on the output of f x. Does this restricted right shrinking follow from the current MonadFix axioms? At the moment, it does not look to me that it would. An interesting fact about this restricted right shrinking is that it makes sense not only for all monads, but for all applicative functors. All the best, Wolfgang Am Donnerstag, den 07.09.2017, 10:11 -0500 schrieb Jonathan S:

Your right shrinking law is almost exactly the (impure) right shrinking law specified in Erkok's thesis on page 22, equation 2.22. The problem with this law, as shown on page 56, is that most of the MonadFix instances we care about do not follow the right shrinking law. In general (see Proposition 3.1.6 on page 27), if (>>=) is strict in its left argument then either the monad is trivial or right shrinking is not satisfied.

On Wed, Sep 6, 2017 at 9:21 PM, David Feuer wrote:

...

I think you'll at least have to specify that g is lazy, because f may let its argument "leak" arbitrarily into the return value of the action it produces. But I don't have a clear sense of whether this is a good law otherwise.

On Sep 6, 2017 10:04 PM, Wolfgang Jeltsch wrote:

While we are at pure right shrinking, let me bring up another question: Why is there no general right shrinking axiom for MonadFix? Something like the following:

Right Shrinking:

    mfix (\ ~(x, _) -> f x >>= \ y -> g y >>= \z -> return (y, z)) >>= return . snd     =     mfix f >>= g

Can this be derived from the MonadFix axioms? Or are there reasonable MonadFix instances for which it does not hold?

All the best, Wolfgang