モノイド的構造

Monoid

• Ordering (文字列順序)
• () (自明)
• Any (or)
• All (and)
• Semigroupの一点モノイド化 (e*s = s = s*e)
• Last (Maybe a)
• First (Maybe a)
• Product
• Sum
• Endo
• Max (Ord, Bounded)
• Min (Ord, Bounded)

Semigroup

• Void
• NonEmpty
• Last (a)
• First (a)
• Max (Ord)
• Min (Ord)
• Either (Alt Maybeと同様、先頭を取る)

Alternative, MonadPlus (Alt)

• []
• Maybe
• IO (例外で連結)
• Parser

Applicative

• Monoid m => Const * m

Apply (Semigroup)

• IntMap
• Map k
• HashMap k

その他

• (Monoid a, Applicative f) => Monoid (f a)
• Monoid m => Monoid (Dual m) (左右交換)