[Haskell-cafe] [Haskell-beginners] For class Monoid; better names than mempty & mappend might have been: mid (mident) & mbinop

[wren ng thornton]

On 7/24/11 2:29 PM, Julian Porter wrote:
> On 24 Jul 2011, at 19:19, KC wrote:
>> A lot of math books use "+" or "x" enclosed in a circle to indicate
>> that the usual meaning of "+" nor "x" is intended for the meaning of
>> the binary operation.
>
> Er no.  Both symbols have extremely precise meanings.  $\oplus$ is the
direct sum of two modules and $\otimes$ is their tensor product.

Well, they mean that if you're off in module/vector land; but they don't
mean that everywhere. Another place they're used frequently is for
semirings: with $\oplus$ the associative monoid and $\otimes$ the other
monoid. While the tourism board for semirings is less well funded than the
one for vectors, it's a beautiful locale with rich history. Natural
language processing, graph theory, Boolean algebras, and related logics
are nothing to scoff at.

-- 
Live well,
~wren