[Haskell-cafe] Categorical description for vector-space instance of AdditiveGroup (Maybe a)

[trevor cook]

Here's that vector-space code, formatted better.


-- Maybe is handled like the Maybe-of-Sum monoid
instance AdditiveGroup a => AdditiveGroup (Maybe a) where
  zeroV = Nothing  Nothing ^+^ b' = b'
  a' ^+^ Nothing      = a'
  Just a' ^+^ Just b' = Just (a' ^+^ b')
  negateV = fmap negateV

{- Alexey Khudyakov wrote:

I looked through vector-space package and found lawless instance. Namely
Maybe's AdditiveGroup instance  It's group so following relation is
expected to hold. Otherwise it's not a group.

> x ^+^ negateV x == zeroV

Here is counterexample:

> let x = Just 2 in x ^+^ negateV x == zeroV
False

I think it's not possible to sensibly define group instance for Maybe a at
all.I see that the problem here is in distinguishing 'Just zeroV'
fromNothing. I could fix the Just + Just line to use Nothing instead of
JustzeroV when a' ^+^ b' == zeroV, although doing so would require Eq a
andhence lose some generality. Even so, the abstraction leak would
probablyshow up elsewhere.Hm.
-}
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