Hi,
On 15 December 2011 11:35, James Carman <[email protected]> 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
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