inv f g = f . g . f

Christopher Done

17 Aug 2013 17 Aug '13

5:11 a.m.

Anyone ever needed this? Me and John Wiegley were discussing a decent name for it, John suggested inv as in involution. E.g. inv reverse (take 10) inv reverse (dropWhile isDigit) trim = inv reverse (dropWhile isSpace) . dropWhile isSpace That seems to be the only use-case I've ever come across. There's also this one: co f g = f g . g which means you can write trim = co (inv reverse) (dropWhile isSpace) but that's optimizing an ever rarer use-case.

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Ivan Lazar Miljenovic

17 Aug 17 Aug

5:21 a.m.

On 17 August 2013 19:11, Christopher Done wrote:

...

Anyone ever needed this? Me and John Wiegley were discussing a decent name for it, John suggested inv as in involution. E.g.

In terms of a decent name: as soon as I saw the subject, I thought you were somehow inverting a function :/ In terms of how useful it is, I don't think I tend to use such an idiom.

...

inv reverse (take 10) inv reverse (dropWhile isDigit) trim = inv reverse (dropWhile isSpace) . dropWhile isSpace

That seems to be the only use-case I've ever come across.

There's also this one:

co f g = f g . g

which means you can write

trim = co (inv reverse) (dropWhile isSpace)

but that's optimizing an ever rarer use-case.

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-- Ivan Lazar Miljenovic Ivan.Miljenovic@gmail.com http://IvanMiljenovic.wordpress.com

Mateusz Kowalczyk

5:40 a.m.

On 17/08/13 10:11, Christopher Done wrote:

...

Anyone ever needed this? Me and John Wiegley were discussing a decent name for it, John suggested inv as in involution. E.g. First thing I thought was ‘inverse’…

inv reverse (take 10) inv reverse (dropWhile isDigit) trim = inv reverse (dropWhile isSpace) . dropWhile isSpace

That seems to be the only use-case I've ever come across.

I do this a lot as well. Why not skip the ‘g’ all together and have ‘f . reverse . f’ if that's all we're doing? You could even call it fromEnd at that point and we end up with a rather intuitive ‘fromEnd (drop 10)’. Maybe even just have an operator.

...

There's also this one:

co f g = f g . g

which means you can write

trim = co (inv reverse) (dropWhile isSpace)

but that's optimizing an ever rarer use-case.

Is this a proposal for addition to something or is it just general discussion? -- Mateusz K.

Ian Ross

6:02 a.m.

In J (a sort of dialect of APL), there's a thing called "under", written "&.". The expression "(f &. g) x" is equivalent to "(g^:_1) (f (g x))" where "g^:_1" is J's "obverse" of g, which in cases where it exists is usually the inverse of g ( http://www.jsoftware.com/help/dictionary/intro26.htm). Abusing notation with some weird mixture of Haskell and J, this means that "((+) &. log)" multiplies numbers by taking logs, adding and exponentiating. You "inv" is "under" for cases where g == g^-1 (reverse being a good example). In cases where g /= g^-1, it's obviously a useful operation, but the case where g == g^-1 seems a bit specialised. Can you think of any other useful cases than g == reverse? I guess "inv (1/) sum" is the harmonic mean, but that's another special case. On 17 August 2013 11:40, Mateusz Kowalczyk wrote:

...

On 17/08/13 10:11, Christopher Done wrote:

...
Anyone ever needed this? Me and John Wiegley were discussing a decent name for it, John suggested inv as in involution. E.g. First thing I thought was ‘inverse’…

inv reverse (take 10) inv reverse (dropWhile isDigit) trim = inv reverse (dropWhile isSpace) . dropWhile isSpace

That seems to be the only use-case I've ever come across.

I do this a lot as well. Why not skip the ‘g’ all together and have ‘f . reverse . f’ if that's all we're doing? You could even call it fromEnd at that point and we end up with a rather intuitive ‘fromEnd (drop 10)’. Maybe even just have an operator.

...
There's also this one:

co f g = f g . g

which means you can write

trim = co (inv reverse) (dropWhile isSpace)

but that's optimizing an ever rarer use-case.

Is this a proposal for addition to something or is it just general discussion?

-- Mateusz K.

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-- Ian Ross Tel: +43(0)6804451378 ian@skybluetrades.net www.skybluetrades.net

Tom Ellis

9:37 a.m.

On Sat, Aug 17, 2013 at 11:11:07AM +0200, Christopher Done wrote:

...

Anyone ever needed this? Me and John Wiegley were discussing a decent name for it, John suggested inv as in involution. E.g.

inv reverse (take 10) inv reverse (dropWhile isDigit) trim = inv reverse (dropWhile isSpace) . dropWhile isSpace

This sounds like a job for a lens, or similar. Tom

Tobias Dammers

10:52 a.m.

Note that at least for the dropWhile example, there is a specialized function, dropWhileEnd, which is most likely more efficient than reversing the list twice. On Aug 17, 2013 3:35 PM, "Tom Ellis" < tom-lists-haskell-cafe-2013@jaguarpaw.co.uk> wrote:

...

On Sat, Aug 17, 2013 at 11:11:07AM +0200, Christopher Done wrote:

...
Anyone ever needed this? Me and John Wiegley were discussing a decent name for it, John suggested inv as in involution. E.g.

inv reverse (take 10) inv reverse (dropWhile isDigit) trim = inv reverse (dropWhile isSpace) . dropWhile isSpace

This sounds like a job for a lens, or similar.

Tom

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Joachim Breitner

11:11 a.m.

Hi, Am Samstag, den 17.08.2013, 11:11 +0200 schrieb Christopher Done:

...

inv reverse (take 10)

if you want that fast and lazy, check out http://www.joachim-breitner.de/blog/archives/600-On-taking-the-last-n-elemen... Greetings, Joachim -- Joachim “nomeata” Breitner mail@joachim-breitner.de • http://www.joachim-breitner.de/ Jabber: nomeata@joachim-breitner.de • GPG-Key: 0x4743206C Debian Developer: nomeata@debian.org

Anton Nikishaev

1:20 p.m.

Christopher Done writes:

...

Anyone ever needed this? Me and John Wiegley were discussing a decent name for it, John suggested inv as in involution. E.g.

inv reverse (take 10) inv reverse (dropWhile isDigit) trim = inv reverse (dropWhile isSpace) . dropWhile isSpace

That seems to be the only use-case I've ever come across.

And it's here only because reverse^-1 ≡ reverse, is not it? I only can see how f ∘ g ∘ f^-1 can be a pattern.

...

There's also this one:

co f g = f g . g

which means you can write

trim = co (inv reverse) (dropWhile isSpace)

but that's optimizing an ever rarer use-case.

-- lelf

Dan Burton

4:43 p.m.

This is indeed a job for lens, particularly, the Iso type, and the "under" function. Lens conveniently comes with a typeclassed isomorphism called "reversed", which of course has a list instance.

...

...
...
under reversed (take 10) ['a'.. 'z'] "qrstuvwxyz"

-- Dan Burton On Aug 17, 2013 10:23 AM, "Anton Nikishaev" wrote:

...

Christopher Done writes:

...
Anyone ever needed this? Me and John Wiegley were discussing a decent name for it, John suggested inv as in involution. E.g.

inv reverse (take 10) inv reverse (dropWhile isDigit) trim = inv reverse (dropWhile isSpace) . dropWhile isSpace

That seems to be the only use-case I've ever come across.

And it's here only because reverse^-1 ≡ reverse, is not it? I only can see how f ∘ g ∘ f^-1 can be a pattern.

...
There's also this one:

co f g = f g . g

which means you can write

trim = co (inv reverse) (dropWhile isSpace)

but that's optimizing an ever rarer use-case.

-- lelf

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Dan Burton

4:57 p.m.

The lens docs even have an example of another helper function, "involuted" for functions which are their own inverse.

...

...
...
"live" & involuted reverse %~ ('d':) "lived"

inv f g = involuted f %~ g http://hackage.haskell.org/packages/archive/lens/3.9.0.2/doc/html/Control-Le... -- Dan Burton On Sat, Aug 17, 2013 at 1:43 PM, Dan Burton wrote:

...

This is indeed a job for lens, particularly, the Iso type, and the "under" function. Lens conveniently comes with a typeclassed isomorphism called "reversed", which of course has a list instance.

...
...
...
under reversed (take 10) ['a'.. 'z'] "qrstuvwxyz"

-- Dan Burton On Aug 17, 2013 10:23 AM, "Anton Nikishaev" wrote:

...
Christopher Done writes:

...
Anyone ever needed this? Me and John Wiegley were discussing a decent name for it, John suggested inv as in involution. E.g.

inv reverse (take 10) inv reverse (dropWhile isDigit) trim = inv reverse (dropWhile isSpace) . dropWhile isSpace

That seems to be the only use-case I've ever come across.

And it's here only because reverse^-1 ≡ reverse, is not it? I only can see how f ∘ g ∘ f^-1 can be a pattern.

...
There's also this one:

co f g = f g . g

which means you can write

trim = co (inv reverse) (dropWhile isSpace)

but that's optimizing an ever rarer use-case.

-- lelf

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Nikita Danilenko

19 Aug 19 Aug

4:01 a.m.

Hi, as for the nomenclature - mathematically the pattern f^{-1} . g . f is sometimes called "conjugation" [1]. One (trivial) type of occurrence is data Foo a = Foo { unFoo :: a } deriving Show instance Functor Foo where fmap f = Foo . f . unFoo The under function from the lens library [2] allows expressing this as follows: instance Functor Foo where fmap = under (iso Foo unFoo) which is a very elegant way of capturing the essence of the pattern. Best regards, Nikita [1] http://en.wikipedia.org/wiki/Conjugacy_class [2] http://hackage.haskell.org/packages/archive/lens/3.9.0.2/doc/html/Control-Le... On 17/08/13 22:57, Dan Burton wrote:

...

The lens docs even have an example of another helper function, "involuted" for functions which are their own inverse.

...
...
...
"live" & involuted reverse %~ ('d':) "lived"

inv f g = involuted f %~ g

http://hackage.haskell.org/packages/archive/lens/3.9.0.2/doc/html/Control-Le...

-- Dan Burton

On Sat, Aug 17, 2013 at 1:43 PM, Dan Burton mailto:danburton.email@gmail.com> wrote:

This is indeed a job for lens, particularly, the Iso type, and the "under" function. Lens conveniently comes with a typeclassed isomorphism called "reversed", which of course has a list instance.

>>> under reversed (take 10) ['a'.. 'z'] "qrstuvwxyz"

-- Dan Burton

On Aug 17, 2013 10:23 AM, "Anton Nikishaev" mailto:me@lelf.lu> wrote:

Christopher Done mailto:chrisdone@gmail.com> writes:

> Anyone ever needed this? Me and John Wiegley were discussing a decent > name for it, John suggested inv as in involution. E.g. > > inv reverse (take 10) > inv reverse (dropWhile isDigit) > trim = inv reverse (dropWhile isSpace) . dropWhile isSpace > > That seems to be the only use-case I've ever come across.

And it's here only because reverse^-1 ≡ reverse, is not it? I only can see how f ∘ g ∘ f^-1 can be a pattern.

> There's also this one: > > co f g = f g . g > > which means you can write > > trim = co (inv reverse) (dropWhile isSpace) > > but that's optimizing an ever rarer use-case.

-- lelf

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