The Maybe type and operations

The Maybe type encapsulates an optional value. A value of type Maybe a either contains a value of type a (represented as Just a), or it is empty (represented as Nothing). Using Maybe is a good way to deal with errors or exceptional cases without resorting to drastic measures such as error.

The Maybe type is also a monad. It is a simple kind of error monad, where all errors are represented by Nothing. A richer error monad can be built using the Data.Either.Either type

The maybe function takes a default value, a function, and a Maybe value. If the Maybe value is Nothing, the function returns the default value. Otherwise, it applies the function to the value inside the Just and returns the result.

The isJust function returns True iff its argument is of the form Just _.

The isNothing function returns True iff its argument is Nothing.

The fromJust function extracts the element out of a Just and throws an error if its argument is Nothing.

The fromMaybe function takes a default value and and Maybe value. If the Maybe is Nothing, it returns the default values; otherwise, it returns the value contained in the Maybe.

The listToMaybe function returns Nothing on an empty list or Just a where a is the first element of the list.

The maybeToList function returns an empty list when given Nothing or a singleton list when not given Nothing.

The catMaybes function takes a list of Maybes and returns a list of all the Just values.

The mapMaybe function is a version of map which can throw out elements. In particular, the functional argument returns something of type Maybe b. If this is Nothing, no element is added on to the result list. If it just Just b, then b is included in the result list.