Category:Monads

In functional programming, the Monad pattern is a general solution to the problem of nesting (or 'composing') functions when the data to which they apply is enclosed in some kind of useful wrapping. It involves implementing two higher-order functions which, between them, can take care of ensuring that the nested (data-transforming) functions are not choked by being called on unexpected types of data. (Wrapped data, when they were expecting something raw and unwrapped).

The two higher-order functions which make up the monad pattern handle the details of: 1. wrapping and unwrapping data, and 2. Providing other functions with direct access to the unwrapped data contents. Delegating the mechanics to these two meta-functions allows the programmer to work with a simple and well-understood generic model, and to nest functions transparently.

The two monad functions are sometimes named as follows:

1. 'Return' or 'unit' which wraps a piece of raw data, returning the wrapped 'monadic' form.
2. 'Bind' which applies some other function directly to the contents of a monadic wrapper, obtains a result, and returns a wrapped form of that result.

(The term monad derives from a concept in category theory. In ancient Greek the word μοναδικος means 'consisting of units').

Commonly used monads include the Maybe monad, (in which the wrapper encodes whether or not the raw content is a legal value for a particular type of function), and the List monad, in which raw data is simply contained in a list. When lists are used to represent a range of possible values for a variable name, nesting functions which act on these lists allows a convenient encoding of cartesian products and set comprehensions. In this context, the two higher order monad functions ensure that each data-transforming function (in a nest or composition of such functions) gets the right kind of argument (Raw atomic values versus one or more values 'wrapped in' a list).

(Other frequently used monads are the IO monad and the State monad)