[Haskell-cafe] Join and it's relation to >>= and return

[ajb at spamcop.net]

G'day all.

Quoting Rik van Ginneken <ginneken at math.kun.nl>:

> It is more even subtle if one considers the rotation group.
> The unit is keeping an object on its place.
> The multiplication is doing rotations sequently.
> Allright, one has an inverse here, but
> the rule (a*b)*c = a*(b*c) doesn't occur; try it with a
> banana or an apple!

Wrong.  Rotations do indeed form a group.  In three dimensions, it's
isomorphic to the unit quaternion group.  I think you're thinking of unit
octonions, which don't form a group because octonion multiplication is not
associative in general.

> Please make a distinction betwixt "monoids" and "monads".
> The first is a group without an invertion.

...or a semigroup with an identity.

> The latter is a construction in category theory (=abstract nonsense),

Them's fighting words!

Cheers,
Andrew Bromage