Proposal: add `on` to the Prelude

[David Feuer]

I agree with your general conservatism, but I think some of these things
are not like the others. I like `on` for the Prelude because, despite its
size, it carries with it the idea of carrying a relationship between two
values through a function. Notably, for *any* function f,

    eq `on` f defines a decidable equivalence relation if eq does.
    cmp `on` f defines a decidable partial order if cmp does.
    d `on` f is a pseudometric if d is.

What a beautiful and useful concept! I find it much harder to get excited
about the idea of flipping function application.

On Tue, Sep 10, 2019, 9:50 PM Elliot Cameron <eacameron at gmail.com> wrote:

> Part of me would too...but I just don't know when this line of reasoning
> stops. Do we add (>>>) and (<<<) from Category too? Then (&&&)? Of course
> then we might want first, second... Oh and (<$) isn't exported but ($>) is?
> Fix that too. Then come join, fix, void, when, unless, bool, fromMaybe.....
> I've come to the conclusion that Prelude should err on the side of very
> small because Haskell is just too diverse a place to expect everyone to
> agree on all these little things. We should all be making project-specific
> Preludes instead IMO.
>
> On Tue, Sep 10, 2019 at 9:41 PM chessai . <chessai1996 at gmail.com> wrote:
>
>> I would also prefer if (&) and `for` were exported from the Prelude.
>>
>> On Tue, Sep 10, 2019, 9:33 PM Elliot Cameron <eacameron at gmail.com> wrote:
>>
>>> Hilariously, I'm mild -1 on this. Haskell is an extremely import-heavy
>>> language. Anyone who isn't willing to just write their own mini-Prelude
>>> should be ready to import things like `on`. Why isn't `for` exported in
>>> Prelude? What about `&`? Both of these are extremely useful and common,
>>> even moreso than *on*! And their implementation is *even shorter*. It's a
>>> slippery slope.
>>>
>>> On Tue, Sep 10, 2019 at 6:59 PM David Feuer <david.feuer at gmail.com>
>>> wrote:
>>>
>>>> Indeed, there are a lot more conflicts than I'd have expected. Ignoring
>>>> functions with the same type, Hoogle shows this name in the below packages.
>>>> I have no sense of the overall significance of the specific packages or
>>>> (equally importantly) of the `on` function within each.
>>>>
>>>> haskell-gi-base:
>>>> on :: forall object info m . (GObject object, MonadIO m, SignalInfo
>>>> info) => object -> SignalProxy object info -> HaskellCallbackType info -> m
>>>> SignalHandlerId
>>>>
>>>> brick:
>>>> on :: Color -> Color -> Attr
>>>>
>>>> esqueletto:
>>>> on :: SqlExpr (Value Bool) -> SqlQuery ()
>>>>
>>>> relational-query (both):
>>>> on :: MonadQuery m => Predicate Flat -> m ()
>>>> on :: MonadQuery m => QueryA m (Predicate Flat) ()
>>>>
>>>> threepenny-gui:
>>>> on :: (element -> Event a) -> element -> (a -> UI void) -> UI ()
>>>>
>>>> miso:
>>>> on :: MisoString -> Decoder r -> (r -> action) -> Attribute action
>>>>
>>>> wild-bind:
>>>> on :: i -> v -> Binder i v ()
>>>>
>>>> massiv-io:
>>>> on :: Pixel X Bit
>>>>
>>>> selda-postgresql:
>>>> on :: Text -> Text -> PGConnectInfo
>>>>
>>>>
>>>> On Tue, Sep 10, 2019, 6:42 PM Ryan Trinkle <ryan.trinkle at gmail.com>
>>>> wrote:
>>>>
>>>>> One note: this does conflict with some other libraries, for instance
>>>>> GTK2HS
>>>>>
>>>>> On Tue, Sep 10, 2019 at 6:26 PM chessai . <chessai1996 at gmail.com>
>>>>> wrote:
>>>>>
>>>>>> +1
>>>>>>
>>>>>> On Tue, Sep 10, 2019, 5:53 PM David Feuer <david.feuer at gmail.com>
>>>>>> wrote:
>>>>>>
>>>>>>> Every time I reach for Data.Function.on, I feel like a total dolt
>>>>>>> for having to import a module to get a function whose implementation is
>>>>>>> barely longer than the import. And it's a really good function too! Can we
>>>>>>> please add it to the Prelude?
>>>>>>>
>>>>>>>   on :: (b -> b -> c) -> (a -> b) -> a -> a -> c
>>>>>>>   (.*.) `on` f = \x y -> f x .*. f y
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