Logs: liberachat/#haskell
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| 2021-07-09 09:08:15 | <tomsmeding> | Does anyone happen to know a class of numerical two-argument functions that 1. are associative, and 2. can be randomly generated? |
| 2021-07-09 09:09:06 | → | trattue joins (~trattue@152.70.182.158) |
| 2021-07-09 09:09:08 | <tomsmeding> | I want to quickcheck a thing that requires a (numerically) differentiable function (a -> a -> a) that is also associative (f(f(x,y),z) == f(x,f(y,z))) |
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| 2021-07-09 09:09:53 | <tomsmeding> | '\x y -> b*x*y + u*x + v*y' is associative for all b and with u in {0,1}, but is there perhaps a larger set? |
| 2021-07-09 09:10:06 | <tomsmeding> | (correction, u and v in {0,1}) |
| 2021-07-09 09:12:45 | <tomsmeding> | (correction, u=v=0 or u=v=1 :p) |
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| 2021-07-09 09:19:56 | <viluon> | surely `\x y -> 3` is also associative? |
| 2021-07-09 09:21:13 | <tomsmeding> | ah, true! |
| 2021-07-09 09:21:48 | <tomsmeding> | maybe this class of things, together with matrix multiplication, is already diverse enough to get some confidence that my function is correct :p |
| 2021-07-09 09:21:56 | <viluon> | could you perhaps arrive at the entire set compositionally? |
| 2021-07-09 09:22:14 | <tomsmeding> | that's what I would be interested in |
| 2021-07-09 09:23:38 | <viluon> | all constant functions are differentiable & associative (so they're in let's say S), multiplications of an f ∈ S by a scalar (αf) are also in S, their additions are also in S, as are their multiplications, where you define + and * on these functions as f + g = \x y -> f x y + g x y (analogically for *) |
| 2021-07-09 09:23:57 | × | eggplantade quits (~Eggplanta@2600:1700:bef1:5e10:44e3:e9f0:ea4d:f039) (Remote host closed the connection) |
| 2021-07-09 09:24:30 | <viluon> | I mean, hopefully right? make sure such + and * makes sense esp. w.r.t. differentiation |
| 2021-07-09 09:24:49 | <tomsmeding> | yeah don't worry about the differentiation :p |
| 2021-07-09 09:25:31 | <viluon> | but that's still all just constant functions if you look closely |
| 2021-07-09 09:25:46 | <tomsmeding> | yeah |
| 2021-07-09 09:25:47 | <viluon> | there's no use of the arguments in the leaves of functions defined as such |
| 2021-07-09 09:26:03 | <tomsmeding> | \x y -> x + y ought to be in S, but \x y -> (x + y) * (x + y) is definitely not in S |
| 2021-07-09 09:26:18 | <viluon> | it'd be great if there were an identity function, but I'm not sure how to do that with two arguments |
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