Monoid package:Cabal-syntax

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:

• Right identity x <> mempty = x
• Left identity mempty <> x = x
• Associativity x <> (y <> z) = (x <> y) <> z (Semigroup law)
• Concatenation mconcat = foldr (<>) mempty

You can alternatively define mconcat instead of mempty, in which case the laws are:

• Unit mconcat (pure x) = x
• Multiplication mconcat (join xss) = mconcat (fmap mconcat xss)
• Subclass mconcat (toList xs) = sconcat xs

The method names refer to the monoid of lists under concatenation, but there are many other instances. Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product. NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

Field which can be define multiple times, and the results are mappended.

Monoidal field. Values are combined with mappend. Note: optionalFieldAla is a monoidalField with Last monoid.