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2026-06-24 00:57:46 +0000vanishingideal(~vanishing@user/vanishingideal) vanishingideal
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2026-06-24 01:08:21 +0000 <monochrom> My answer to "why you accept static and strong typing but not totality, it sounds inconsistent" is that trade-offs and cost-vs-benefit considerations are consistent. Strong static typing gives me a lot of benefits with very little cost and/or inconvenience. Totality is a lot of cost for what it's worth.
2026-06-24 01:09:49 +0000 <monochrom> IMO totality is never going to be worthwhile because, for the same price, you should go for big-Theta complexity instead. I.e., don't bother proving termination; if anything, go straight for proving linear time or log time or whatever. Who cares about termination if it ends up being triple-expoenential time.
2026-06-24 01:09:55 +0000ski(~ski@90-224-14-130-no600.tbcn.telia.com) (Ping timeout: 264 seconds)
2026-06-24 01:11:42 +0000 <monochrom> Almost every termination proof hides a time bound so it is counterproductive to throw the time bound away.
2026-06-24 01:12:13 +0000 <monochrom> (It is not like you have a non-constructive proof of termination using the axiom of choice, is it? >:) )
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2026-06-24 01:17:55 +0000 <jreicher> A type system that checked complexity would be really interesting.
2026-06-24 01:20:33 +0000ski(~ski@90-224-14-130-no600.tbcn.telia.com) ski
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2026-06-24 01:42:41 +0000 <EvanR> monochrom, to solve for totality first solve for complexity then set n = finite
2026-06-24 01:43:15 +0000 <EvanR> monochrom, ~~axiom of choice~~ markov's principle
2026-06-24 01:43:44 +0000 <EvanR> if you base the argument on that, it might actually be convincing
2026-06-24 01:44:12 +0000 <monochrom> Err sorry, what is markov's principle again?
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2026-06-24 01:46:38 +0000 <EvanR> for any function on naturals f, if there not existing an n such that f(n)=0 would be a contradiction, then there's some n where f(n) = 0
2026-06-24 01:46:55 +0000 <jreicher> EvanR: I don't think anybody said "solve for complexity" in the general case
2026-06-24 01:47:20 +0000 <EvanR> that was a joke in analogy to solve the problem for all n then set n = 2
2026-06-24 01:48:16 +0000 <monochrom> Yeah how to visualize 6 dimensions? Visualize n dimensions, then set n=6. >:)
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2026-06-24 01:52:24 +0000 <jreicher> :)
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2026-06-24 02:27:44 +0000 <EvanR> *decidable f
2026-06-24 02:28:12 +0000 <EvanR> proposition on naturals
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2026-06-24 02:32:24 +0000EvanR(~EvanR@user/evanr) EvanR
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2026-06-24 02:44:28 +0000poscat0x04(~poscat@user/poscat) poscat
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2026-06-24 02:52:06 +0000Katarushisu69Katarushisu6
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2026-06-24 02:59:54 +0000 <monochrom> Oh, decidable f makes the principle much less powerful. I mean much more realistic and closer to being constructive!
2026-06-24 03:01:25 +0000 <EvanR> yes the realization of this principle is... the purported n can't not exist, so just start looping through them all in order until you find it
2026-06-24 03:02:00 +0000 <EvanR> as you sit there waiting for the search to terminate, you might start to feel like you're looking at the "proof" that the turing machine is infinite
2026-06-24 03:02:11 +0000 <monochrom> Yeah.
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2026-06-24 05:32:24 +0000 <dolio> Markov's principle says that semi-decidable propositions are ¬¬-stable.
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