Proposal: Num instance for (a -> b)

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Generalizing some type signatures...

older
Proposal to add mapAccumL function...

Daniel Cartwright

11 Nov 2018 11 Nov '18

4:47 a.m.

relevant reddit comment thread: https://www.reddit.com/r/haskell/comments/9vtis5/the_universe_of_discourse_i... instance Num b => Num (a -> b) where f + g = \x -> f x + g x f * g = \x -> f x * g x f - g = \x -> f x - g x negate f = \x -> negate (f x) abs f = \x -> abs (f x) signum f = \x -> signum (f x) fromInteger i = \x -> fromInteger (f x)

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Henning Thielemann

11 Nov 11 Nov

4:54 a.m.

On Sat, 10 Nov 2018, Daniel Cartwright wrote:

...

relevant reddit comment thread:https://www.reddit.com/r/haskell/comments/9vtis5/the_universe_of_discourse_i... urce=reddit-android

https://wiki.haskell.org/index.php?title=Num_instance_for_functions&oldid=36632 In short: It would make 2(x+y) no longer a type error but equivalent to 2. We would lose a lot of type safety for little syntactic gain.

Henning Thielemann

5 a.m.

On Sun, 11 Nov 2018, Henning Thielemann wrote:

...

On Sat, 10 Nov 2018, Daniel Cartwright wrote:

...
relevant reddit comment thread:https://www.reddit.com/r/haskell/comments/9vtis5/the_universe_of_discourse_i... urce=reddit-android

https://wiki.haskell.org/index.php?title=Num_instance_for_functions&oldid=36632

In short: It would make 2(x+y) no longer a type error but equivalent to 2. We would lose a lot of type safety for little syntactic gain.

Btw. before adding more Wat instances please implement the GHC warning about such instances: https://ghc.haskell.org/trac/ghc/ticket/11796

Dannyu NDos

5:04 a.m.

I suggest adding this as an orphan instance (Like Show (a -> b)) in a seperate module (say, Numeric.Function). 2018년 11월 11일 (일) 14:01에 Henning Thielemann 님이 작성:

...

On Sun, 11 Nov 2018, Henning Thielemann wrote:

...
On Sat, 10 Nov 2018, Daniel Cartwright wrote:

...
relevant reddit comment thread: https://www.reddit.com/r/haskell/comments/9vtis5/the_universe_of_discourse_i... urce=reddit-android

https://wiki.haskell.org/index.php?title=Num_instance_for_functions&oldid=36632

...
In short: It would make 2(x+y) no longer a type error but equivalent to

2. We

...
would lose a lot of type safety for little syntactic gain.

Btw. before adding more Wat instances please implement the GHC warning about such instances: https://ghc.haskell.org/trac/ghc/ticket/11796 _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Henning Thielemann

5:15 a.m.

On Sun, 11 Nov 2018, Dannyu NDos wrote:

...

I suggest adding this as an orphan instance (Like Show (a -> b)) in a seperate module (say, Numeric.Function).

https://hackage.haskell.org/package/NumInstances It would not save much, because in a reasonably big project you will somewhen import a package that transitively depends on the module. E.g. 'diagrams-canvas' depends on NumInstances.

Tom Murphy

5:27 a.m.

On 11/11/18, Henning Thielemann wrote:

...

On Sun, 11 Nov 2018, Henning Thielemann wrote:

...
On Sat, 10 Nov 2018, Daniel Cartwright wrote:

...
relevant reddit comment thread:https://www.reddit.com/r/haskell/comments/9vtis5/the_universe_of_discourse_i... urce=reddit-android

https://wiki.haskell.org/index.php?title=Num_instance_for_functions&oldid=36632

In short: It would make 2(x+y) no longer a type error but equivalent to 2. We would lose a lot of type safety for little syntactic gain.

Btw. before adding more Wat instances please implement the GHC warning about such instances: https://ghc.haskell.org/trac/ghc/ticket/11796

This is my feeling as well. Tom

Dan Burton

6:36 a.m.

-1, per the very confusing errors that would ensue. If this behavior is desired, you can use a newtype wrapper. As it happens, this fits the pattern of ANum http://hackage.haskell.org/package/ANum. (Any Applicative can be made an instance of Num in this way.) -- Dan Burton On Sun, Nov 11, 2018 at 12:28 AM Tom Murphy wrote:

...

On 11/11/18, Henning Thielemann wrote:

...
On Sun, 11 Nov 2018, Henning Thielemann wrote:

...
On Sat, 10 Nov 2018, Daniel Cartwright wrote:

...
relevant reddit comment thread:

...
...
...
urce=reddit-android

https://wiki.haskell.org/index.php?title=Num_instance_for_functions&oldid=36632

...
In short: It would make 2(x+y) no longer a type error but equivalent to

https://www.reddit.com/r/haskell/comments/9vtis5/the_universe_of_discourse_i... 2.

...
...
We would lose a lot of type safety for little syntactic gain.

Btw. before adding more Wat instances please implement the GHC warning about such instances: https://ghc.haskell.org/trac/ghc/ticket/11796

This is my feeling as well.

Tom _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Daniel Cartwright

9:44 p.m.

ANum seems to be just Data.Monoid.Ap. Also, I can see not wanting to worsen the error messages, though it is worth pointing out that we already have a Monoid instance with the same semantics, and a similar potential for confusing error messages. On Sun, Nov 11, 2018, 1:36 AM Dan Burton

...

-1, per the very confusing errors that would ensue.

If this behavior is desired, you can use a newtype wrapper. As it happens, this fits the pattern of ANum http://hackage.haskell.org/package/ANum. (Any Applicative can be made an instance of Num in this way.)

-- Dan Burton

On Sun, Nov 11, 2018 at 12:28 AM Tom Murphy wrote:

...
On 11/11/18, Henning Thielemann wrote:

...
On Sun, 11 Nov 2018, Henning Thielemann wrote:

...
On Sat, 10 Nov 2018, Daniel Cartwright wrote:

...
relevant reddit comment thread:

https://www.reddit.com/r/haskell/comments/9vtis5/the_universe_of_discourse_i...

...
...
...
urce=reddit-android

https://wiki.haskell.org/index.php?title=Num_instance_for_functions&oldid=36632

...
In short: It would make 2(x+y) no longer a type error but equivalent

to 2.

...
We would lose a lot of type safety for little syntactic gain.

Btw. before adding more Wat instances please implement the GHC warning about such instances: https://ghc.haskell.org/trac/ghc/ticket/11796

This is my feeling as well.

Tom _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Oleg Grenrus

10:10 p.m.

Monoid doesn't have fromInteger -like function. For example, we don't have FromString b => FromString (a -> b) instance. Unfortunately fromInteger is part of Num, so comparison with Monoid is unjust. Sent from my iPhone

...

On 11 Nov 2018, at 23.44, Daniel Cartwright wrote:

ANum seems to be just Data.Monoid.Ap. Also, I can see not wanting to worsen the error messages, though it is worth pointing out that we already have a Monoid instance with the same semantics, and a similar potential for confusing error messages.

...
On Sun, Nov 11, 2018, 1:36 AM Dan Burton
If this behavior is desired, you can use a newtype wrapper. As it happens, this fits the pattern of ANum. (Any Applicative can be made an instance of Num in this way.)

-- Dan Burton

...
On Sun, Nov 11, 2018 at 12:28 AM Tom Murphy wrote: On 11/11/18, Henning Thielemann wrote:

...
On Sun, 11 Nov 2018, Henning Thielemann wrote:

...
On Sat, 10 Nov 2018, Daniel Cartwright wrote:

...
relevant reddit comment thread:https://www.reddit.com/r/haskell/comments/9vtis5/the_universe_of_discourse_i... urce=reddit-android

https://wiki.haskell.org/index.php?title=Num_instance_for_functions&oldid=36632

In short: It would make 2(x+y) no longer a type error but equivalent to 2. We would lose a lot of type safety for little syntactic gain.

Btw. before adding more Wat instances please implement the GHC warning about such instances: https://ghc.haskell.org/trac/ghc/ticket/11796

This is my feeling as well.

Tom _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Daniel Cartwright

10:30 p.m.

I'm not quite sure the comparison is unjust - i was referring to +,-,* giving strange error messages, not necessarily fromInteger. Recall that the instance is Monoid b => Monoid (a -> b). An example is a user might mistakenly type `mempty "text"`, which is just `const mempty`, though this might not be what they mean (GHC 8.6 will give the hole in `f :: Text -> Text; f x = _ x;` a suggestion of `mempty`, which might certainly be confusing to a beginner). Similarly `2 4` might parse 2 as being applied to 4, if (a -> b) had a Num instance (correct me if i'm wrong in saying thats how such a string might be parsed). On Sun, Nov 11, 2018, 5:10 PM Oleg Grenrus

...

Monoid doesn't have fromInteger -like function. For example, we don't have FromString b => FromString (a -> b) instance.

Unfortunately fromInteger is part of Num, so comparison with Monoid is unjust.

Sent from my iPhone

On 11 Nov 2018, at 23.44, Daniel Cartwright wrote:

ANum seems to be just Data.Monoid.Ap. Also, I can see not wanting to worsen the error messages, though it is worth pointing out that we already have a Monoid instance with the same semantics, and a similar potential for confusing error messages.

On Sun, Nov 11, 2018, 1:36 AM Dan Burton
...
-1, per the very confusing errors that would ensue.

If this behavior is desired, you can use a newtype wrapper. As it happens, this fits the pattern of ANum http://hackage.haskell.org/package/ANum. (Any Applicative can be made an instance of Num in this way.)

-- Dan Burton

On Sun, Nov 11, 2018 at 12:28 AM Tom Murphy wrote:

...
On 11/11/18, Henning Thielemann wrote:

...
On Sun, 11 Nov 2018, Henning Thielemann wrote:

...
On Sat, 10 Nov 2018, Daniel Cartwright wrote:

...
relevant reddit comment thread:

https://www.reddit.com/r/haskell/comments/9vtis5/the_universe_of_discourse_i...

...
...
...
urce=reddit-android

https://wiki.haskell.org/index.php?title=Num_instance_for_functions&oldid=36632

...
In short: It would make 2(x+y) no longer a type error but equivalent

to 2.

...
We would lose a lot of type safety for little syntactic gain.

Btw. before adding more Wat instances please implement the GHC warning about such instances: https://ghc.haskell.org/trac/ghc/ticket/11796

This is my feeling as well.

Tom _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Daniel Cartwright

10:42 p.m.

Sorry, the parsing is tied to fromInteger. So i see what you mean about the poor errors not being as comparable. Henning and another brought up a good point, that either users ought to be warned or it would go in its own module ala Text.Show.Function. On Sun, Nov 11, 2018, 5:30 PM Daniel Cartwright

...

I'm not quite sure the comparison is unjust - i was referring to +,-,* giving strange error messages, not necessarily fromInteger. Recall that the instance is Monoid b => Monoid (a -> b).

An example is a user might mistakenly type `mempty "text"`, which is just `const mempty`, though this might not be what they mean (GHC 8.6 will give the hole in `f :: Text -> Text; f x = _ x;` a suggestion of `mempty`, which might certainly be confusing to a beginner). Similarly `2 4` might parse 2 as being applied to 4, if (a -> b) had a Num instance (correct me if i'm wrong in saying thats how such a string might be parsed).

On Sun, Nov 11, 2018, 5:10 PM Oleg Grenrus
...
Monoid doesn't have fromInteger -like function. For example, we don't have FromString b => FromString (a -> b) instance.

Unfortunately fromInteger is part of Num, so comparison with Monoid is unjust.

Sent from my iPhone

On 11 Nov 2018, at 23.44, Daniel Cartwright wrote:

ANum seems to be just Data.Monoid.Ap. Also, I can see not wanting to worsen the error messages, though it is worth pointing out that we already have a Monoid instance with the same semantics, and a similar potential for confusing error messages.

On Sun, Nov 11, 2018, 1:36 AM Dan Burton
...
-1, per the very confusing errors that would ensue.

If this behavior is desired, you can use a newtype wrapper. As it happens, this fits the pattern of ANum http://hackage.haskell.org/package/ANum. (Any Applicative can be made an instance of Num in this way.)

-- Dan Burton

On Sun, Nov 11, 2018 at 12:28 AM Tom Murphy wrote:

...
On 11/11/18, Henning Thielemann wrote:

...
On Sun, 11 Nov 2018, Henning Thielemann wrote:

...
On Sat, 10 Nov 2018, Daniel Cartwright wrote:

> relevant reddit comment > thread:

https://www.reddit.com/r/haskell/comments/9vtis5/the_universe_of_discourse_i...

...
...
> urce=reddit-android

https://wiki.haskell.org/index.php?title=Num_instance_for_functions&oldid=36632

...
In short: It would make 2(x+y) no longer a type error but equivalent

to 2.

...
We would lose a lot of type safety for little syntactic gain.

Btw. before adding more Wat instances please implement the GHC warning about such instances: https://ghc.haskell.org/trac/ghc/ticket/11796

This is my feeling as well.

Tom _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Daniel Cartwright

10:46 p.m.

It would be nice if the Semiring/Ring[1] parts of Num were pulled into its own class. The overloading of integer literals to functions does seem disruptive. [1]: http://hackage.haskell.org/package/semirings-0.2.1.1/docs/Data-Semiring.html On Sun, Nov 11, 2018, 5:42 PM Daniel Cartwright

...

Sorry, the parsing is tied to fromInteger. So i see what you mean about the poor errors not being as comparable. Henning and another brought up a good point, that either users ought to be warned or it would go in its own module ala Text.Show.Function.

On Sun, Nov 11, 2018, 5:30 PM Daniel Cartwright
...
I'm not quite sure the comparison is unjust - i was referring to +,-,* giving strange error messages, not necessarily fromInteger. Recall that the instance is Monoid b => Monoid (a -> b).

An example is a user might mistakenly type `mempty "text"`, which is just `const mempty`, though this might not be what they mean (GHC 8.6 will give the hole in `f :: Text -> Text; f x = _ x;` a suggestion of `mempty`, which might certainly be confusing to a beginner). Similarly `2 4` might parse 2 as being applied to 4, if (a -> b) had a Num instance (correct me if i'm wrong in saying thats how such a string might be parsed).

On Sun, Nov 11, 2018, 5:10 PM Oleg Grenrus
...
Monoid doesn't have fromInteger -like function. For example, we don't have FromString b => FromString (a -> b) instance.

Unfortunately fromInteger is part of Num, so comparison with Monoid is unjust.

Sent from my iPhone

On 11 Nov 2018, at 23.44, Daniel Cartwright wrote:

ANum seems to be just Data.Monoid.Ap. Also, I can see not wanting to worsen the error messages, though it is worth pointing out that we already have a Monoid instance with the same semantics, and a similar potential for confusing error messages.

On Sun, Nov 11, 2018, 1:36 AM Dan Burton
...
-1, per the very confusing errors that would ensue.

If this behavior is desired, you can use a newtype wrapper. As it happens, this fits the pattern of ANum http://hackage.haskell.org/package/ANum. (Any Applicative can be made an instance of Num in this way.)

-- Dan Burton

On Sun, Nov 11, 2018 at 12:28 AM Tom Murphy wrote:

...
On 11/11/18, Henning Thielemann wrote:

...
On Sun, 11 Nov 2018, Henning Thielemann wrote:

> On Sat, 10 Nov 2018, Daniel Cartwright wrote: > >> relevant reddit comment >> thread:

https://www.reddit.com/r/haskell/comments/9vtis5/the_universe_of_discourse_i...

...
>> urce=reddit-android > > https://wiki.haskell.org/index.php?title=Num_instance_for_functions&oldid=36632 > > In short: It would make 2(x+y) no longer a type error but equivalent to 2. > We > would lose a lot of type safety for little syntactic gain.

Btw. before adding more Wat instances please implement the GHC warning about such instances: https://ghc.haskell.org/trac/ghc/ticket/11796

This is my feeling as well.

Tom _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Dan Burton

12 Nov 12 Nov

3:38 a.m.

...

The overloading of integer literals to functions does seem disruptive.

Most, if not all, of my objection has to do with the concern that integer literals (and floating point literals, if functions also got a comparable Floating instance) could be accidentally used as functions. Everything else about these potential instances seems benign. -- Dan Burton On Sun, Nov 11, 2018 at 5:46 PM Daniel Cartwright wrote:

...

It would be nice if the Semiring/Ring[1] parts of Num were pulled into its own class. The overloading of integer literals to functions does seem disruptive.

[1]: http://hackage.haskell.org/package/semirings-0.2.1.1/docs/Data-Semiring.html

On Sun, Nov 11, 2018, 5:42 PM Daniel Cartwright
...
Sorry, the parsing is tied to fromInteger. So i see what you mean about the poor errors not being as comparable. Henning and another brought up a good point, that either users ought to be warned or it would go in its own module ala Text.Show.Function.

On Sun, Nov 11, 2018, 5:30 PM Daniel Cartwright
...
I'm not quite sure the comparison is unjust - i was referring to +,-,* giving strange error messages, not necessarily fromInteger. Recall that the instance is Monoid b => Monoid (a -> b).

An example is a user might mistakenly type `mempty "text"`, which is just `const mempty`, though this might not be what they mean (GHC 8.6 will give the hole in `f :: Text -> Text; f x = _ x;` a suggestion of `mempty`, which might certainly be confusing to a beginner). Similarly `2 4` might parse 2 as being applied to 4, if (a -> b) had a Num instance (correct me if i'm wrong in saying thats how such a string might be parsed).

On Sun, Nov 11, 2018, 5:10 PM Oleg Grenrus
...
Monoid doesn't have fromInteger -like function. For example, we don't have FromString b => FromString (a -> b) instance.

Unfortunately fromInteger is part of Num, so comparison with Monoid is unjust.

Sent from my iPhone

On 11 Nov 2018, at 23.44, Daniel Cartwright wrote:

ANum seems to be just Data.Monoid.Ap. Also, I can see not wanting to worsen the error messages, though it is worth pointing out that we already have a Monoid instance with the same semantics, and a similar potential for confusing error messages.

On Sun, Nov 11, 2018, 1:36 AM Dan Burton
...
-1, per the very confusing errors that would ensue.

If this behavior is desired, you can use a newtype wrapper. As it happens, this fits the pattern of ANum http://hackage.haskell.org/package/ANum. (Any Applicative can be made an instance of Num in this way.)

-- Dan Burton

On Sun, Nov 11, 2018 at 12:28 AM Tom Murphy wrote:

...
On 11/11/18, Henning Thielemann wrote: > > On Sun, 11 Nov 2018, Henning Thielemann wrote: > >> On Sat, 10 Nov 2018, Daniel Cartwright wrote: >> >>> relevant reddit comment >>> thread: https://www.reddit.com/r/haskell/comments/9vtis5/the_universe_of_discourse_i... >>> urce=reddit-android >> >> https://wiki.haskell.org/index.php?title=Num_instance_for_functions&oldid=36632 >> >> In short: It would make 2(x+y) no longer a type error but equivalent to 2. >> We >> would lose a lot of type safety for little syntactic gain. > > Btw. before adding more Wat instances please implement the GHC warning > about such instances: > https://ghc.haskell.org/trac/ghc/ticket/11796

This is my feeling as well.

Tom _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Bertram Felgenhauer

10:07 a.m.

Oleg Grenrus wrote:

...

Monoid doesn't have fromInteger -like function. For example, we don't have FromString b => FromString (a -> b) instance.

Monoid does have `mempty` though, with the unfortunate property that mempty [1,2] /= mempty `mappend` [1,2] But I'm less worried about this than in the case of Num; I occasionally copy formulas from a CAS into Haskell code and then add the missing * operations manually; I estimate that about half of the time I miss one instance and am rescued by the type checker. So to me, `2 (x + y)` no longer being a type error would have practical implications. -1 on the proposal from me. Cheers, Bertram

Jon Fairbairn

10:16 a.m.

Daniel Cartwright writes:

...

ANum seems to be just Data.Monoid.Ap. Also, I can see not wanting to worsen the error messages, though it is worth pointing out that we already have a Monoid instance with the same semantics, and a similar potential for confusing error messages.

The existence of a previous bad decision doesn’t seem to me to be a good reason to make another one. -- Jón Fairbairn Jon.Fairbairn@cl.cam.ac.uk http://www.chaos.org.uk/~jf/Stuff-I-dont-want.html (updated 2014-04-05)

Daniel Cartwright

1:14 p.m.

I'm not sure I would label it a bad decision, but the concerns here make sense. On Mon, Nov 12, 2018, 5:16 AM Jon Fairbairn

...

Daniel Cartwright writes:

...
ANum seems to be just Data.Monoid.Ap. Also, I can see not wanting to worsen the error messages, though it is worth pointing out that we already have a Monoid instance with the same semantics, and a similar potential for confusing error messages.

The existence of a previous bad decision doesn’t seem to me to be a good reason to make another one.

-- Jón Fairbairn Jon.Fairbairn@cl.cam.ac.uk http://www.chaos.org.uk/~jf/Stuff-I-dont-want.html (updated 2014-04-05)

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Dannyu NDos

11 Nov 11 Nov

4:55 a.m.

I'm +1 on this, since it is conventional to write addition (and others) over function as such in most math textbooks. 2018년 11월 11일 (일) 13:48에 Daniel Cartwright 님이 작성:

...

relevant reddit comment thread: https://www.reddit.com/r/haskell/comments/9vtis5/the_universe_of_discourse_i...

instance Num b => Num (a -> b) where f + g = \x -> f x + g x f * g = \x -> f x * g x f - g = \x -> f x - g x negate f = \x -> negate (f x) abs f = \x -> abs (f x) signum f = \x -> signum (f x) fromInteger i = \x -> fromInteger (f x) _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

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participants (8)

Bertram Felgenhauer
Dan Burton
Daniel Cartwright
Dannyu NDos
Henning Thielemann
Jon Fairbairn
Oleg Grenrus
Tom Murphy

Proposal: Num instance for (a -> b)

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