id -package:llvm-hs-pure -package:faktory package:foundation

the identity morphism

Represent types that supports an euclidian division

(x ‘div‘ y) * y + (x ‘mod‘ y) == x

Identity functor and monad. (a non-strict monad)

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

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.

Identity element over multiplication

Possible failure related to validating bytes of UTF8 sequences.