Re: [Haskell-cafe] inv f g = f . g . f

19 Aug 2013

      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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Re: [Haskell-cafe] inv f g = f . g . f

Nikita Danilenko