The proper type for callCC would be rank-3. The current form is an
under-approximation that only allows you to choose to use the continuation
at one type.
Going higher rank (usefully) is still pretty straight-forward. There is the
Mendler-style encoding of functors that gets used every once in a while in
recursion-schemes work. It adds a rank to get rid of a Functor constraint.
This is basically replacing a functor f with (forall b. (a -> b) -> f b),
which is the same as the Yoneda f a newtype.
For more information, see some of the lovely examples in
https://www.ioc.ee/~tarmo/papers/msfp08.pdf like
update :: (forall c’. (forall y’. (y’ -> c’) -> (y’ -> Mu f) -> f y’ -> c’)
-> y -> c’) -> (Mu f -> c) -> (forall c’. (forall y’. (y’ -> c) -> (y’ ->
c’) -> f y’ -> c’) -> y -> c’)
-Edward
On Mon, Apr 2, 2018 at 11:36 PM, Timotej Tomandl
Hello,
So we need rank-2 type in runST :: (forall s. ST https://hackage.haskell.org/package/base-4.11.0.0/docs/Control-Monad-ST.html... s a) -> a, to prevent s from appearing in a.
I have been thinking about this for a bit, but I failed to come up with a practical situation, where rank-3 types are necessary for safety of some abstraction.
The rank-3 example in here and any other I found, look very synthetic, i.e. limiting computation to id: https://ocharles.org.uk/blog/guest-posts/2014-12-18-rank-n-types.html and compared to the runST example of limiting a scope of a type variable for purposes of safety looks unnatural. Could anyone please point me to a practical example of rank-3 polymorphism, where it is necessary for safety of an abstraction, if it exists?
I suspect there is a situation, where rank-3 is necessary for maintaining abstration exists, but I can't think of any. Any ideas about such situations and even better situations where this is used on hackage?
Timotej Tomandl
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