Monads: Difference between revisions

In functional programming, the [[wp:Monad_(functional_programming)|Monad]] pattern is a general solution to the problem of nesting (or 'composing') functions when the data which they apply to is contained 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 to the 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:

# 'Return' which wraps a piece of raw data, returning the wrapped 'monadic' form

# 'Bind' which applies some other function directly to the contents of a monadic wrapper, obtains a result, and returns a wrapped monadic form of that result.

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 convenenient encoding of cartesian products and set comprehensions. In this context, the two higher order monad functions ensure that each data-transforming function gets and returns 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)