On Oct 24, 2010, at 8:52 AM, wren ng thornton wrote:
But then, how should we decide whether the additive or multiplicative structure is more "neutral"?
On Oct 24, 2010, at 7:08 AM, Jacques Carette wrote:
People usually use additive notation for commutative monoids, and multiplicative notation for generic monoids. It's a convention, nothing else.
I recently used class Monoid m where one :: m (*) :: m -> m -> m class CommutativeMonoid m where zero :: m (+) :: m -> m -> m class (Monoid s, CommutativeMonoid s) => Semiring s (The `Semiring` class only serves as a contract for additional laws.) Considering the convention Jaques mentions and my wish for splitting the two monoids underlying a semiring into separate classes, it seemed natural to use multiplicative notation for the "neutral" case. Sebastian