On Dec 19, 2011, at 1:03 PM, Alexander Solla wrote:
> The "incidental" comment is significantly more clear than an English
> description.
That is only true for someone who has already seen a sentence like that one
before and so can immediately pick up what it is getting at. :-) In
particular, if one has never heard of a semigroup then the sentence is not very
helpful.
> I would rather see commutative diagrams (or what amounts to the same, usage
> examples) that describe the behavior than a "plain English" description.
I find it amusing that anyone would consider commutative diagram to be the same
thing as usage examples for anyone other than a mathematician. :-)
Nonetheless, I see your point that examples may be clearer than English, so how
about:
================================================================
This instance satisfies the property that, for all x any y:
(1) Nothing `mappend` Nothing = Nothing
(2) Just x `mappend` Nothing = Just x
(3) Nothing `mappend` Just y = Just y
(4) Just x `mappend` Just y = Just (x `mappend` y)
(Warning: Note that rule (4) for this instance is different from the
case of the MonadPlus/Alternative instances where the Just y value is discarded
so that Just x `mplus` Just y = Just x <|> Just y = Just x.)
Formally, this instance performs the standard procedure of turning an
arbitrary semigroup into a monoid by simply adding a new element to the
semigroup to serve as the identity element, where in this case the identity
element is the Nothing value of Maybe; unfortunately, since the base libraries
do not come with a Semigroup typeclass, this process is expressed in code as
lifting from the Monoid typeclass.
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