Efficiency of telescopes about sml-telescopes

[favonia]

@jonsterling It seems no one except the library itself uses SnocView. We can probably drop it or make it super expensive. Also I only found two usage of cons in sequent.sml. It is probably not that difficult to implement output-restricted deques either. Maybe just a pair of lists is sufficient.

[favonia]

@jonsterling on the second thought the polymorphic recursion is not so hard to deal with. I paused the working because telescopes also support lots of other operations, like splice, where I wonder if there is a better data structure.

[favonia]

Closed as the current implementation seems fine.

[jonsterling]

@favonia At one time I had tried to do finger trees, but it was just too painful to code in SML sadly, so I would lean towards one of the other two options. Do you have any recommendations?

[favonia]

@jonsterling I think I need to know where and how SnocView and ConsView are used in practice.

[jonsterling]

@favonia My guess is that the thing is used most heavily is ConsView, as in: https://github.com/RedPRL/sml-dependent-lcf/blob/master/src/dependent_lcf/lcf.fun#L35

In general, we tend to traverse a telescope from the left (in "cons" style), but we usually append to a telescope from the right (in "snoc" style).

[favonia]

Hmm a queue would be much simpler. Do you think we really need both views?

[jonsterling]

@favonia That's a great point; somehow in the beginning, I expected that both views would be used equally often, but it seems like in practice that is not the case. I like your proposal...

[favonia]

@jonsterling Thanks. To decide between the amortized and worst-case analysis, is it common to share the same telescope everywhere? The worst case is that we share the telescope right before the data structure would start to adjust itself, where it will have to do the same adjustment many times.