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@_chenson__@krismicinski@aramh well, and maybe i'm also disagreeing with something you *didn't* say that "you need substitution to do more than intrinsic typing"
Respectfully disagree with @_chenson__ here, but agreed that existing categorical approaches add way too much abstract machinery without worrying about implementation.
one can model syntax combinatorially and still have dependent-flavoured types without substitution! https://t.co/LElQCDGJ8J
Substitution is a mistake, it's not a fundamental operation. Not only that this has been shown by interaction nets, but no real language on any real computer uses it. Rather, β-reduction is implemented using some form of forwarding.
In fact, in the process interpretation of linear logic forwarding becomes explicit.
Substitution is problematic in λ-calculus, but explicit substitution calculi are even worse, a step in the wrong direction entirely. We need a more principled notion of a scope. De Bruijn indices are but a feeble attempt at this, solving half the problem while fixing the representation.
ah I actually don't agree! i think a lot of it can be explained purely in terms of datastructures without caring about theory (not that this explanation has *been* done tho)
i only started doing category theory because I had been badly reinventing some datastructure that arises naturally from symmetric monoidal categories
@krismicinski@aramh i honestly don't think it's THAT hard, just massively underexplored relative to the majority of literature
doin' my best to fix it though.
Dana Scott basically complained about this in the 70s too, wish I could remember which paper it was though
If you could watch yourself do things for a whole day, how many inefficiencies would you spot and be able to improve?
Now; notice that you can in fact actually record yourself and watch the playback
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