Parametricity @parametricity
Theorems for Free! homepages.inf.ed.ac.uk/wadler/topics/… Parametrikistan Joined January 2015-
Tweets57
-
Followers1K
-
Following0
-
Likes0
I wonder what this function does. flip :: Functor f => f (a -> b) -> a -> f b Wait, no I don't.
f :: Lens a b -> a -> b -> a This does one of two things. ∀ l x y. x /= y => f l x y x /= x Now I know which.
@rightfold is thinking of a function with the type (a -> b) -> a -> b The identity function specialized to functions.
length :: Foldable f => f a -> Int ∴ length (1, '2', "3") must return 1.
Generalize an abstraction because removing nonessential information clarifies its independent meaning. Re-use is accidental. @fronx
a -> (a, a, a, a) I definitely know what this function does. (a, a, a, a) -> a I almost know what this function does.
@catnaroek Fast & Loose Reasoning is Morally Correct.
f :: Monad f=>f T -> f T The result might depend on previous effect values g :: Applicative f=>f T -> f T This definitely doesn't though
Proof `fmap f.fmap g=fmap(f.g)` follows from `fmap id=id` and the free theorem: fpcomplete.com/user/edwardk/s… /cc @BartoszMilewski @parametricity
Using Data.Foldable and parametricity, one can be sure that: foldMap f &&& foldMap g = foldMap (f &&& g)
f :: [a] -> [a] This type tells us some, but not all, things. ∀ x. f [x] = [x] ∀ x y. f (x++y) = f y++f x These tests tell us the rest.
f :: a -> a -> a This function does one of two things. test = f 1 2 == 1 Now it is disambiguated between those two.
Reminder. Fast & Loose Reasoning is Morally Correct.
A csharp<A>(A a) This function returns its argument.
(~.~<.~>\\+.) :: (Profunctor p, Functor f) => (a -> f b) -> p b r -> f (p a r) This operator clearly specifies what it does in the type.
Monad f => f a -> f b -> f b Any (a) values from the effect (f a) are not used.
Correction. Applicative f => f a -> f a This function is implemented with only id, (<*) or (*>). Thanks @dino_joel
Applicative => f a -> f a This function is implemented with only id, (<*) or (*>).
IO Int -> a -> Int This function ignores both arguments.
String -> a -> a This function returns the second argument, ignoring the first.
Bartosz Milewski @BartoszMilewski
35K Followers 34 Following Physicist, programmer, mathematician. Author of Category Theory for Programmers. @[email protected]
Susan Potter @SusanPotter
7K Followers 2K Following Antifascist. Anti-authoritarian. Pro-privacy. Functional programmer. Recovering SRE. Micro-SaaS, real estate & trading. Outsider. Gay af. Genocide is terrible.
deech @deech
5K Followers 1K Following
Matt Parsons @mattoflambda
5K Followers 522 Following Haskell and SQL. Team Lead for Backend Developer UX at @mercury. I wrote @prodhaskell so you can get a Haskell job!
Stephen Diehl @smdiehl
55K Followers 3K Following Left this hellsite for BlueSky. https://t.co/jct5Pfs2NT
vaibhav sagar @vbhvsgr
2K Followers 5K Following future trophy husband; @recursecenter f1'16; 🇦🇺/🇮🇩/🇮🇳; he/him https://t.co/VGk6nI4TOO https://t.co/64Kipz3ghV https://t.co/YetTYcxcvQ on bluesky
KC Sivaramakrishnan @kc_srk
4K Followers 4K Following Profing @iitmadras. CTO @tarides_. Trustee https://t.co/WE1No5QqOA.
sclv @sclv
2K Followers 3K Following "more important than being able to do mathematics is to be sure the applications are meaningful." - e. bishop • https://t.co/45nJUN3IqD
Senior Oops Engineer @ReinH
20K Followers 2K Following doin capitalism a frighten, https://t.co/mROKLREFXT deleted my bsky account because of the racism don't ask me to come back
Jakub Kozłowski @kubukoz
5K Followers 297 Following Functional Scala developer, small-time content creator, brainrot enjoyer. https://t.co/i99bvhwYNi he/him
Kostas @kos446
35 Followers 90 Following
refiammingo @refiammingo
389 Followers 6K Following non sequitur // λ // 🇮🇹 - randomly replying to your posts.
Vladimir Logachev @logachev_dev
23 Followers 252 Following
Saeid Akbari @saeidscorp
6 Followers 20 Following
Andrew Zhuang @andrew_zhuang
58 Followers 542 Following
Bilder 🍑 @BilderRyuu
66 Followers 1K Following Across the Great Fire Wall, we can reach every corner in the world. I intend to practice English, Japanese and sightsee on Twitter. よろしくお願いします。
Praise Dare @PraiseDare2
36 Followers 231 Following
Rekwass @Moinard_Nicolas
3 Followers 36 Following
OlaoluwaM @OlaoluMustapha
173 Followers 1K Following Software Engineer (@learnfreckle) 'Surpass your limits right here right now' ~ Yami Sukehiro
Sa @Genius__pg
76 Followers 3K Following
Conor Keville @KevilleConor
132 Followers 1K Following Senior Content Strategy Manager at Blockdaemon
Linkstation @_Linkstation
1 Followers 46 Following LinkStation - internet link global aggregator and link bookmark manager https://t.co/UqOv47oq2l
Mike @Mike33910119
18 Followers 1K Following
Functional Maths @FunctionalM4ths
0 Followers 5 Following
Nuxituchka2 @nuxituchka2
6 Followers 83 Following
Iván Portilla @ivportilla27
343 Followers 3K Following Software Developer. Decentralization will change the world as we know it.
shzmwfgwzf @asnawysl
120 Followers 4K Following Charity Volunteer, Buddhist Believer, Help those who are struggling in life and God will bless you
roadside_picnic @poadside_ricnic
12 Followers 2K Following
Bart van Pelt @bart_pelt
5 Followers 60 Following
Liang Dai @LiangDai3
11 Followers 30 Following
90 @a9032676
16 Followers 64 Following Coding (Kotlin, Scala, Agda, Haskell, Lean) | Osu! player | Maths studying
Chris Clark @cfclrk
6 Followers 45 Following
loddity @loddity
134 Followers 962 Following A complete non sequitur being. F#, C#, Scala Senior Developer with a fascination for emptiness.
方讫 @UnderlingOfNPU
31 Followers 536 Following
Yevhen Susidka @Yevhen_Susidka
936 Followers 5K Following
Long Tran @LongTran02
1K Followers 1K Following researcher @usmc, national guard mechanic, physics student
Even Brenden 🇺🇦 @evenbrenden
35 Followers 308 Following I like Haskell, Nix and 1987-2005 Star Trek series.
kuroky @johann_coconut
11 Followers 250 Following
Your Nightmare @hwmaniac
5 Followers 272 Following Konzervativec 🏛️, vývojář HW, zastánce open-source přístupu, absolutní svobody slova a svobody internetu. 🗽 Ve volném čase uvažuji. Zájmena: já/veliký 😎
Titus Pinta @PintaTitus
9 Followers 141 Following Maths PhD student @ Göttingen Asking Gauss' ghost for inspiration on a daily basis. I have not yet figured out what I am doing (he/him)
Félix Sanhueza @felixsanhueza
159 Followers 371 Following
rottensunday @Arnachim
56 Followers 1K Following
蜘蛛在一個東歐... @fortranie
13 Followers 514 Following arcane bit magic | linguistics | potentials and molecules | Linux | anime/manga
Polarlog @polarlog
11 Followers 37 Following
JB @JBezivin
4K Followers 3K Following Observing the world from Brittany. “Let's cultivate our garden.” Voltaire, Candide JBezivin @jbezivin.bsky.social on bsky @[email protected] on Mastodon
John Corley @eulerBall
144 Followers 2K Following Data Scientist. Programmer. Lover of Games. Honest. Relentless... .. . .. ... .. . .. ...
Rex McArthur @drexmcarthur
334 Followers 1K Following AI research @youdotcom Technical Advisor at @us_abstract formerly led AI @heyjasperai @Apple Maps, Lyft.
Anton Harniakou @tryzniak
54 Followers 824 FollowingTrends for United States
You might like
