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2020-10-02 15:01:22 <ski> (btw, neither semigroups, monoids, nor groups, need to have a commutative combination/composition operator)
2020-10-02 15:01:40 × caasih quits (sid13241@gateway/web/irccloud.com/x-teuwvboxinwdshpz) (Ping timeout: 244 seconds)
2020-10-02 15:01:46 <Guest18> I see
2020-10-02 15:02:08 <Guest18> Interesting, I wish I remembered more group theory then..
2020-10-02 15:02:20 <Guest18> I need to relearn it
2020-10-02 15:02:30 → cpressey joins (~cpressey@88.144.95.167)
2020-10-02 15:02:38 <ski> well, natural numbers form a rig ("a ring that doen't need to have an additive inverse, negation")
2020-10-02 15:03:25 <ski> (sometimes aka "semiring")
2020-10-02 15:03:29 → caasih joins (sid13241@gateway/web/irccloud.com/x-hlizsalbvmrkznfg)
2020-10-02 15:03:30 → st8less joins (~st8less@2603:a060:11fd:0:f15a:c857:2711:378c)
2020-10-02 15:04:38 × snakemasterflex quits (~snakemast@213.100.206.23) (Ping timeout: 258 seconds)
2020-10-02 15:06:43 × ft quits (~ft@shell.chaostreff-dortmund.de) (Ping timeout: 246 seconds)
2020-10-02 15:06:52 <ski> Guest18 : if you want a quick and short tutorial on monads, i'd suggest "What the hell are Monads?" by Noel Winstanley in 1999 (one of the first monad tutorials) at <http://www-users.mat.uni.torun.pl/~fly/materialy/fp/haskell-doc/Monads.html>
2020-10-02 15:07:14 <ski> Guest18 : it's by no means complete, but could give you an idea of what they're about
2020-10-02 15:07:35 → ft joins (~ft@shell.chaostreff-dortmund.de)
2020-10-02 15:08:28 × Lord_of_Life quits (~Lord@unaffiliated/lord-of-life/x-0885362) (Ping timeout: 258 seconds)
2020-10-02 15:12:46 × FreeBirdLjj quits (~freebirdl@240e:388:4f41:dc00:6980:7e19:3f7b:9844) ()
2020-10-02 15:13:02 → cr3 joins (~cr3@192-222-143-195.qc.cable.ebox.net)
2020-10-02 15:13:41 <dolio> Monads are one of the ways mathematicians talk about algebra, too. And it's actually similar to what Haskell programmers use them for.
2020-10-02 15:14:14 <dolio> There is a monad that characterises the 'extra operations' on top of sets that an algebra (group, ring, etc.) has.
2020-10-02 15:14:39 → spew joins (uid195861@gateway/web/irccloud.com/x-nmkiijbefgbkmaqa)
2020-10-02 15:15:43 × toorevitimirp quits (~tooreviti@117.182.181.38) (Remote host closed the connection)
2020-10-02 15:15:50 <dolio> And Haskell programmers often find it convenient to work in an 'extended language' that has operations (throw/catch, get/put, etc.) that don't exist in the 'pure' language (because it would be confusing for them to exist there).
2020-10-02 15:16:10 ski . o O ( Let's use `do'-notation to talk about algebra. )
2020-10-02 15:18:38 <dolio> You could. There's at least one exact correspondence with monoids.
2020-10-02 15:19:41 <ski> mhm ?
2020-10-02 15:19:53 <Guest18> ski: so.. many.. things.. to bookmark
2020-10-02 15:20:12 × borne quits (~fritjof@200116b86454500007933c164a08810c.dip.versatel-1u1.de) (Ping timeout: 260 seconds)
2020-10-02 15:20:13 <dolio> Although I guess monoids are too plain for traditional algebra. Only category theorists care about those.
2020-10-02 15:20:27 × heatsink quits (~heatsink@107-136-5-69.lightspeed.sntcca.sbcglobal.net) (Remote host closed the connection)
2020-10-02 15:21:24 → solonarv joins (~solonarv@astrasbourg-653-1-252-112.w92-161.abo.wanadoo.fr)
2020-10-02 15:21:41 → yost3d joins (~yost3d@193.56.252.210)
2020-10-02 15:22:04 <dolio> Monoids are what you get by having `zero :: Void` and `bit :: Bool` effects.
2020-10-02 15:22:21 × cheater quits (~user@unaffiliated/cheater) (Quit: BitchX Official WWW Site -- http://www.bitchx.org/)
2020-10-02 15:22:30 <TMA> I remember from my algebra course that monoids were glossed over in one of the lectures. They are merely a stepping stone to groups from that vantage point
2020-10-02 15:22:47 → cheater joins (~user@unaffiliated/cheater)
2020-10-02 15:23:40 → constR joins (uid58205@gateway/web/irccloud.com/x-ljcnzijchvmxodjj)
2020-10-02 15:23:49 <ski> dolio : <https://en.wikipedia.org/wiki/Associative_algebra> ?
2020-10-02 15:24:29 <dolio> Oh yeah, they need to satisfy some equations, of course.
2020-10-02 15:24:44 → Tuplanolla joins (~Tuplanoll@91-159-68-239.elisa-laajakaista.fi)
2020-10-02 15:25:48 <ski> these are just monoid objects in the monoidal category of vector spaces (with tensor), aiui
2020-10-02 15:26:13 → p-core joins (~Thunderbi@2001:718:1e03:5128:2ab7:7f35:48a1:8515)
2020-10-02 15:26:25 × justanotheruser quits (~justanoth@unaffiliated/justanotheruser) (Ping timeout: 240 seconds)
2020-10-02 15:26:38 <dolio> Well, there's probably a lot of examples like that.
2020-10-02 15:26:50 <dolio> I meant specifically monoids in Set.
2020-10-02 15:27:32 <ski> TMA : endomorphisms over a structure naturally form a monoid, i suppose. for an abelian group, you even get a ring
2020-10-02 15:27:37 <ski> ok
2020-10-02 15:27:52 → fresheyeball joins (~isaac@c-71-237-105-37.hsd1.co.comcast.net)
2020-10-02 15:29:22 <dolio> I think traditional algebraists thought that monoids in set were too boring to be studied, but there are actually interesting things to say about them.
2020-10-02 15:29:54 × Franciman quits (~francesco@host-212-171-42-250.retail.telecomitalia.it) (Quit: Leaving)
2020-10-02 15:29:59 <ski> what about more restricted classes, that might not be as wild ?
2020-10-02 15:30:21 <ski> like cancellative monoids, idempotent monoids, ..
2020-10-02 15:30:24 → heatsink joins (~heatsink@107-136-5-69.lightspeed.sntcca.sbcglobal.net)
2020-10-02 15:30:40 <dolio> But, like, rings are monoid objects in Ab. And I think abelian groups are monoid objects in Grp.
2020-10-02 15:30:58 → snakemasterflex joins (~snakemast@213.100.206.23)
2020-10-02 15:31:22 × Saukk quits (~Saukk@2001:998:f1:3966:96a6:dee2:2e9:fdf3) (Remote host closed the connection)
2020-10-02 15:32:23 → bitmapper joins (uid464869@gateway/web/irccloud.com/x-tarhbdjsvwboswmi)
2020-10-02 15:32:38 × madjestic quits (~madjestic@86-88-72-244.fixed.kpn.net) (Ping timeout: 256 seconds)
2020-10-02 15:33:03 <dolio> Oh, maybe it needs to be a group object for the latter.
2020-10-02 15:33:26 ← coot parts (~coot@37.30.49.34.nat.umts.dynamic.t-mobile.pl) ()
2020-10-02 15:33:27 <ski> hm, perhaps it had something to do with the Erlangen program focusing on automorphisms and isomorphisms, rather than on more general endomorphisms and homomorphisms ?
2020-10-02 15:34:15 <dolio> I'm not clear on the details. I just know there's someone on the category zulip whose work is about monoids.
2020-10-02 15:34:35 × heatsink quits (~heatsink@107-136-5-69.lightspeed.sntcca.sbcglobal.net) (Ping timeout: 240 seconds)
2020-10-02 15:35:18 <dolio> I think at least some of that is that monoids are a special case of categories, so a lot of things you can do with categories have special properties when you look at just doing them with monoids.
2020-10-02 15:35:24 → coot joins (~coot@37.30.49.34.nat.umts.dynamic.t-mobile.pl)
2020-10-02 15:35:40 × GyroW quits (~GyroW@unaffiliated/gyrow) (Quit: Someone ate my pie)
2020-10-02 15:35:41 × wroathe quits (~wroathe@c-68-54-25-135.hsd1.mn.comcast.net) (Ping timeout: 258 seconds)
2020-10-02 15:36:02 <dolio> Like, "what special properties do presheaves on monoids have"?
2020-10-02 15:36:25 <ski> hm, `mempty = case zero of' and `x <> y = if bit then y else x' ?
2020-10-02 15:36:36 × dhil quits (~dhil@11.29.39.217.dyn.plus.net) (Ping timeout: 256 seconds)
2020-10-02 15:36:42 <dolio> Right.
2020-10-02 15:36:48 → GyroW joins (~GyroW@d54c03e98.access.telenet.be)
2020-10-02 15:36:48 × GyroW quits (~GyroW@d54c03e98.access.telenet.be) (Changing host)
2020-10-02 15:36:48 → GyroW joins (~GyroW@unaffiliated/gyrow)
2020-10-02 15:36:59 × mananamenos quits (~mananamen@84.122.202.215.dyn.user.ono.com) (Read error: Connection reset by peer)
2020-10-02 15:37:59 → madjestic joins (~madjestic@86-88-72-244.fixed.kpn.net)
2020-10-02 15:38:09 → heatsink joins (~heatsink@107-136-5-69.lightspeed.sntcca.sbcglobal.net)
2020-10-02 15:38:32 <ski> and then `x = if bit then case zero of else x',`if bit then x else case zero of = x',`if bit then if bit then x else y else z = if bit then x else if bit then y else z'
2020-10-02 15:38:33 <dolio> MonadPlus is basically the theory of monoids.
2020-10-02 15:38:55 <ski> "theory", in a Lawvere sense ?
2020-10-02 15:39:45 <dolio> Yeah. Probably only if you pick the right choice of the laws people have for it.
2020-10-02 15:39:56 × chappi quits (~swaroop@157.45.23.171) (Ping timeout: 256 seconds)
2020-10-02 15:40:32 <dolio> Like left/right cancellation.
2020-10-02 15:40:42 <Guest18> Say I want to make a safeDiv function that returns a string if the divider is 0, the result otherwise. Is this the way to do it? safeDiv :: (Num a, Fractional a, Eq a) => a -> a -> Either a String
2020-10-02 15:40:42 <Guest18> safeDiv _ 0 = Right "Ooops!"
2020-10-02 15:40:43 <Guest18> safeDiv x y = Left $ x/y
2020-10-02 15:40:50 <Guest18> Like, is there a better way here?
2020-10-02 15:40:57 → dan64- joins (~dan64@dannyadam.com)
2020-10-02 15:41:17 <Guest18> I don't want to use Maybe, but I want to learn how Either functions
2020-10-02 15:41:28 <ski> i'd flip the order of the alternatives (and not use `$')
2020-10-02 15:42:03 <ski> also .. `"Ooops!"' is not a that informative failure condition
2020-10-02 15:42:09 <Guest18> Why flip the order?
2020-10-02 15:42:28 <ski> because then one can use `fmap' (from `Functor') on the `a' in the result (if present)
2020-10-02 15:42:41 <Guest18> I know it isn't, just wrote it as an exercise, and wanted it to be a string
2020-10-02 15:42:45 × dan64 quits (~dan64@dannyadam.com) (Ping timeout: 240 seconds)
2020-10-02 15:42:51 <cpressey> Guest18: by convention, Left contains an error value and Right contains the "right answer".
2020-10-02 15:42:54 <ski> @quote stark
2020-10-02 15:42:54 <lambdabot> AlanPerlis says: The string is a stark data structure and everywhere it is passed there is much duplication of process. It is a perfect vehicle for hiding information.
2020-10-02 15:43:19 <cpressey> (when Either is used this way)
2020-10-02 15:43:46 <ski> (i'd generally try to avoid using `String's to represent failure conditions)
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