Thoughts on scala.Zero, and algebraic structures in the scala library

[Matthew Willson-3]

Spotted this in the recent scala additions:

http://lampsvn.epfl.ch/trac/scala/changeset/19291/scala/trunk/src/library/scala/Zero.scala

My thoughts:

- To call something a 'Zero' on a particular type, doesn't make much  
sense (and isn't much use) without the context of a (typically  
associative) binary operation on that set which it's a zero of
- 'Identity' is a better term than 'zero' in this general context, in  
particular it may be a left identity or a right identity or both
- There's a name for sets with an identity and an associative binary  
operation - a Monoid
- Monoids would actually be pretty useful to have in the library, and  
I think each of these implicit Zero instances should rather be a  
Monoid instance, supplying the binary operation as well as its identity

Found an example of a monoid class (and implicit monoids) mentioned  
here: http://www.scala-lang.org/node/114

So yeah, just wondering what the rationale here was, and more  
generally, what the philosophy is about modelling algebraic structures  
in the scala library.

Personally I'd love to see a really well-engineered set of classes for  
algebraic structures made available, and it pains me a bit to see odds  
and ends of mathematical structure done in the library in a rather ad-
hoc way which could be quite hard to make really consistent / coherent  
further down the road once everyone's relying on them. This is what  
happened with haskell, which is rather a sad tale. There are a few  
alternative Preludes available for haskell now which 'do it right',  
but at the cost of replacing the core of the standard library everyone  
else is using.

Happy to help out here if anyone feels code would speak louder than  
words :)

-Matt

[Paul Phillips-3]

On Wed, Nov 04, 2009 at 01:58:05AM +0000, Matthew Willson wrote:
> Spotted this in the recent scala additions:

You'll be happy to know that as is the rule more than the exception with
me lately, I'll be reverting it in the near future.

--
Paul Phillips      | These are the climbs that apply men's soles.
Everyman           |
Empiricist         |
pp: i haul pills   |----------* http://www.improving.org/paulp/ *----------

[Ben Hutchison-3]

On Wed, Nov 4, 2009 at 12:58 PM, Matthew Willson
<matthew.willson@...> wrote:
> So yeah, just wondering what the rationale here was, and more generally,
> what the philosophy is about modelling algebraic structures in the scala
> library.
>
> Personally I'd love to see a really well-engineered set of classes for
> algebraic structures made available, and it pains me a bit to see odds and
> ends of mathematical structure done in the library in a rather ad-hoc way
> which could be quite hard to make really consistent / coherent further down
> the road once everyone's relying on them.

I agree with the above.

I'd like to see the Scala library design ruthlessly mine Haskell for
its ideas and wisdom, especially with respect to algebraic structures.

For an example of Haskell Wisdom, see the Typeclassopedia in:
http://www.haskell.org/sitewiki/images/8/85/TMR-Issue13.pdf

-Ben

[Eastsun]

Scala 2.8 has some other Type relate to algebraic structures in my opinion, e.g. Fractional, Integral, Numeric ,(Addable ?)..

Matthew Willson-3 wrote:

Spotted this in the recent scala additions:

http://lampsvn.epfl.ch/trac/scala/changeset/19291/scala/trunk/src/library/scala/Zero.scala

My thoughts:

- To call something a 'Zero' on a particular type, doesn't make much  
sense (and isn't much use) without the context of a (typically  
associative) binary operation on that set which it's a zero of
- 'Identity' is a better term than 'zero' in this general context, in  
particular it may be a left identity or a right identity or both
- There's a name for sets with an identity and an associative binary  
operation - a Monoid
- Monoids would actually be pretty useful to have in the library, and  
I think each of these implicit Zero instances should rather be a  
Monoid instance, supplying the binary operation as well as its identity

Found an example of a monoid class (and implicit monoids) mentioned  
here: http://www.scala-lang.org/node/114

So yeah, just wondering what the rationale here was, and more  
generally, what the philosophy is about modelling algebraic structures  
in the scala library.

Personally I'd love to see a really well-engineered set of classes for  
algebraic structures made available, and it pains me a bit to see odds  
and ends of mathematical structure done in the library in a rather ad-
hoc way which could be quite hard to make really consistent / coherent  
further down the road once everyone's relying on them. This is what  
happened with haskell, which is rather a sad tale. There are a few  
alternative Preludes available for haskell now which 'do it right',  
but at the cost of replacing the core of the standard library everyone  
else is using.

Happy to help out here if anyone feels code would speak louder than  
words :)

-Matt

[_retronym]

The good news is that you can layer these on top of Scala with the Scalaz library. Runar and Tony describe the relationship here, in response to an earlier message from Ben: http://groups.google.com/group/scalaz/browse_thread/thread/b686d161d9e5cd78/35ecff815569a2a1?hl=en&lnk=gst&q=implicit#35ecff815569a2a1

The limited resources of the core team may be better applied to the compiler rather than the contentious task of 'haskell-ification' of the standard lib.

-jason

On Wed, Nov 4, 2009 at 4:04 AM, Ben Hutchison <brhutchison@...> wrote:

I'd like to see the Scala library design ruthlessly mine Haskell for
its ideas and wisdom, especially with respect to algebraic structures.

For an example of Haskell Wisdom, see the Typeclassopedia in:
http://www.haskell.org/sitewiki/images/8/85/TMR-Issue13.pdf

-Ben

[Viktor Klang]

This is all fine and dandy, but how about Money?

On Wed, Nov 4, 2009 at 8:11 AM, Jason Zaugg <jzaugg@...> wrote:

The good news is that you can layer these on top of Scala with the Scalaz library. Runar and Tony describe the relationship here, in response to an earlier message from Ben: http://groups.google.com/group/scalaz/browse_thread/thread/b686d161d9e5cd78/35ecff815569a2a1?hl=en&lnk=gst&q=implicit#35ecff815569a2a1

The limited resources of the core team may be better applied to the compiler rather than the contentious task of 'haskell-ification' of the standard lib.

-jason

On Wed, Nov 4, 2009 at 4:04 AM, Ben Hutchison <brhutchison@...> wrote:

I'd like to see the Scala library design ruthlessly mine Haskell for
its ideas and wisdom, especially with respect to algebraic structures.

For an example of Haskell Wisdom, see the Typeclassopedia in:
http://www.haskell.org/sitewiki/images/8/85/TMR-Issue13.pdf

-Ben

--
Viktor Klang
| "A complex system that works is invariably
| found to have evolved from a simple system
| that worked." - John Gall

Blog: klangism.blogspot.com
Twttr: viktorklang
Code: github.com/viktorklang

[Daniel Sobral]

If you think Paul was in any way pursuing a "haskell-ification" of anything, I have some bottom land you might be interested in...

AFAIK, the whole purpose of his Zero was being able to generalize the implementation of certain parameterized classes.

On Wed, Nov 4, 2009 at 5:11 AM, Jason Zaugg <jzaugg@...> wrote:

The good news is that you can layer these on top of Scala with the Scalaz library. Runar and Tony describe the relationship here, in response to an earlier message from Ben: http://groups.google.com/group/scalaz/browse_thread/thread/b686d161d9e5cd78/35ecff815569a2a1?hl=en&lnk=gst&q=implicit#35ecff815569a2a1

The limited resources of the core team may be better applied to the compiler rather than the contentious task of 'haskell-ification' of the standard lib.

-jason

On Wed, Nov 4, 2009 at 4:04 AM, Ben Hutchison <brhutchison@...> wrote:

I'd like to see the Scala library design ruthlessly mine Haskell for
its ideas and wisdom, especially with respect to algebraic structures.

For an example of Haskell Wisdom, see the Typeclassopedia in:
http://www.haskell.org/sitewiki/images/8/85/TMR-Issue13.pdf

-Ben

--
Daniel C. Sobral

Veni, vidi, veterni.

[_retronym]

For the record, I used the term "haskell-ification" in reference to Ben's suggested direction, not in specific reference to the all-to-brief appearance of Zero, of which I was rather fond. :)

-jason

On Wed, Nov 4, 2009 at 11:59 AM, Daniel Sobral <dcsobral@...> wrote:

If you think Paul was in any way pursuing a "haskell-ification" of anything, I have some bottom land you might be interested in...

AFAIK, the whole purpose of his Zero was being able to generalize the implementation of certain parameterized classes.

[Matthew Willson-3]

> AFAIK, the whole purpose of his Zero was being able to generalize  
> the implementation of certain parameterized classes.

Perhaps something like scala.Monoid could fill the same role? a  
generalised zero is a whole lot more useful if there's a generalised  
'plus' to use with it... although:

> The limited resources of the core team may be better applied to the  
> compiler rather than the contentious task of 'haskell-ification' of  
> the standard lib.

Certainly. I wasn't suggesting that the standard library necessarily  
needs these things in it. Merely that, where the standard library DOES  
choose to implement algebraic abstractions, it takes some care to get  
them right, so they can be built upon cleanly by others.

In particular I wasn't suggesting borrowing wholesale from haskell -  
haskell gets quite a few things wrong, eg its 'Num' class.

Cheers
-Matt