Am Donnerstag, den 07.09.2017, 04:54 +0300 schrieb Wolfgang Jeltsch:
Am Samstag, den 02.09.2017, 14:08 -0500 schrieb Jonathan S:
I think that in addition to nesting and sliding, we should have the following law:
ffix (\x -> fmap (f x) g) = fmap (\y -> fix (\x -> f x y)) g
I guess I'd call this the "pure left shrinking" law because it is the composition of left shrinking and purity:
I wonder whether “pure left shrinking” is an appropriate name for this. The shrinking is on the left, but the purity is on the right. Note that in “pure right shrinking”, a derived property discussed in Erkok’s thesis, both the shrinking and the purity are on the right.
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