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From James Carman <ja...@carmanconsulting.com>
Subject Re: [Graph] On graph weight type(s)
Date Thu, 15 Dec 2011 13:20:20 GMT
We may be modeling the domain properly with all of this terminology, but is
this going to be understandable to the common user?
On Dec 15, 2011 7:38 AM, "Matthew Pocock" <turingatemyhamster@gmail.com>
wrote:

> Hi,
>
> On 15 December 2011 11:35, James Carman <james@carmanconsulting.com>
> wrote:
>
>
> > public interface BinaryOperation<T>
> > {
> >  public T execute(T operand1, T operand2);
> > }
> >
> > Perhaps we can come up with an interface that combines the two
> > aspects.  I'm trying to think of mathematically what that would be
> > called.  By the way, what do you need to know "HasZero"?  A sum
> > operation has to have a "zero", doesn't it?
>
>
> The mathematical hierarchy goes: semigroup -> monoid.
>
> http://en.wikipedia.org/wiki/Semigroup
> http://en.wikipedia.org/wiki/Monoid
>
> You don't need a full group here as you are only interested in a single
> operation, not a pair of interacting operations. There are several
> JVM-hosted libraries that model this hierarchy to a greater or lesser
> degree. scalaz uses:
>
> trait Semigroup[S] {
>  def append(s1: S
> <
> http://scalaz.googlecode.com/svn/continuous/latest/browse.sxr/scalaz/Semigroup.scala.html#22357
> >,
> s2: => S): S <
> http://scalaz.googlecode.com/svn/continuous/latest/browse.sxr/scalaz/Semigroup.scala.html#22357
> >
> }
>
> trait Zero[Z] {
>  val zero: Z <
> http://scalaz.googlecode.com/svn/continuous/latest/browse.sxr/scalaz/Zero.scala.html#22160
> >
> }
>
> trait Monoid[M] extends Zero
> <
> http://scalaz.googlecode.com/svn/continuous/latest/browse.sxr/scalaz/Zero.scala.html#17945
> >[M]
> with Semigroup <
> http://scalaz.googlecode.com/svn/continuous/latest/browse.sxr/scalaz/Semigroup.scala.html#15476
> >[M]
>
>
> http://scalaz.googlecode.com/svn/continuous/latest/browse.sxr/scalaz/Semigroup.scala.html
>
> http://scalaz.googlecode.com/svn/continuous/latest/browse.sxr/scalaz/Zero.scala.html
>
> http://scalaz.googlecode.com/svn/continuous/latest/browse.sxr/scalaz/Monoid.scala.html
>
> If you're not used to reading scala, here's the essentially equivalent
> definitions in Java:
>
> public interface Semigroup<S> {
>  public S append(S s1, S s2);
> }
>
> public interface Zero<Z> {
>
>  public Z zero();
> }
>
> public interface Monoid<M> extends
> Zero<
> http://scalaz.googlecode.com/svn/continuous/latest/browse.sxr/scalaz/Zero.scala.html#17945
> ><M>,
> Semigroup<
> http://scalaz.googlecode.com/svn/continuous/latest/browse.sxr/scalaz/Semigroup.scala.html#15476
> >
> <M>
>
>
> So, given that you have Ordering<O> already (or is that Comparator<C>?),
> I'd say that Weight is defined as:
>
> // insert comments here about the consistency of append and compare
> public interface Weight<W> extends Monoid<W>, Ordered<W>
>
> Of course, a sensible default implementation of Weight would delegate to
> Monoid and Ordered instances and you can then pray to the gods of hotspot
> to inline this all away.
>
> public <W> Weight<W> weight(Monoid<W> m, Ordered<W> o) {
>  new Weight<W>() {
>    public W zero() { return m.zero(); }
>    ...
>  }
> }
>
> Matthew
>
> --
> Dr Matthew Pocock
> Integrative Bioinformatics Group, School of Computing Science, Newcastle
> University
> mailto: turingatemyhamster@gmail.com
> gchat: turingatemyhamster@gmail.com
> msn: matthew_pocock@yahoo.co.uk
> irc.freenode.net: drdozer
> skype: matthew.pocock
> tel: (0191) 2566550
> mob: +447535664143
>

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