Alternate Semigroup instance: SearchResult

[k0ral]

Consider the following data type:

-- | Either a, or b, or both a and b
data SearchResult a b = Scanned a | Found b | ScannedAndFound a b

-- | Accumulate 'a's from left to right, until one 'b' is found
instance Semigroup a => Semigroup (SearchResult a b) where
  ScannedAndFound a b <> _ = ScannedAndFound a b
  Found b <> _ = Found b
  Scanned a <> Scanned a' = Scanned (a <> a')
  Scanned a <> Found b = ScannedAndFound a b
  Scanned a <> ScannedAndFound a' b = ScannedAndFound (a <> a') b

The type definition is identical to These, but the Semigroup semantics differ. Do you think it could/should be integrated to these library, e.g. as a newtype over These ?

Rationale: as the name suggests, this type is useful in search algorithms to return both the search result and a semigroup of traversed items.

[phadej]

This is different from These a (First b) as This part turns into First too, when there is first That found. In current form it's a bit ad-hoc, I wonder if it can be generalised

[phadej]

I'm still undecided. Maybe if you make a module Data.These.SearchResult. I guess most instances can be derived using GeneralizedNewtypeDeriving.