Haskell Cookbook

How it works...

The Monoid class is defined as follows:

    class Monoid a where      mempty :: a      mappend :: a -> a -> a      mconcat :: [a] -> a

The mempty function defines a default value. The mappend function defines that as a result of combining two values of a, we will get a single value of type a. mconcat indicates that we can combine all the values in the list to produce a single value of type a. To define a Monoid instance, we need to define at least mempty and mappend functions: 

Laws of Monoid--The monoid instance should follow this law: 

• mappend x mempty = x  (Appending the default value should not change the value)

• mappend mempty x = x (Appending a value to the default value is the same as value)

• mappend x (mappend y z) = mappend (mappend ...