Inverse

The Inverse type class describes an associative binary operator for a type A that has an identity element and an inverse binary operator. Combining any value with itself with the inverse operator must return the identity element. For example, for integer addition zero is an identity element and subtraction is an inverse operation, because subtracting any value from itself always returns zero.

Because Inverse defines a binary rather than a unary operator it can be used to describe inverse operations for types that do not have inverse values. For example, the natural numbers do not have inverses because the set of natural numbers does not include negative numbers. But we can still define a subtraction operation that is the inverse of addition for the natural numbers, since subtracting a number from itself always returns zero.