# Maybe

(Difference between revisions)
 Revision as of 22:18, 5 March 2006 (edit) (Adding a page for the lovely Maybe type.)← Previous diff Current revision (13:53, 30 April 2012) (edit) (undo) (removed redundant nowiki tag) (10 intermediate revisions not shown.) Line 1: Line 1: - {{Standard type|Maybe|module=Data.Maybe|module-doc=Control-Maybe|package=base}} + {{Standard type|Maybe|module=Data.Maybe|module-doc=Data-Maybe|package=base}} The '''Maybe''' type is defined as follows: The '''Maybe''' type is defined as follows: - + data Maybe a = Just a | Nothing data Maybe a = Just a | Nothing deriving (Eq, Ord) deriving (Eq, Ord) - + It allows the programmer to specify something may not be there. It allows the programmer to specify something may not be there. - ==Type Equation== + ==Type equation== - '''Maybe''' satisfies the [[type]] equation [itex]F X = 1 + F X[/itex], where the functor [itex]F[/itex] takes a set to a point plus that set. + '''Maybe''' satisfies the [[type]] equation [itex]F X = 1 + X[/itex], where the functor [itex]F[/itex] takes a set to a point plus that set. ==Comparison to imperative languages== ==Comparison to imperative languages== - Most imperative languages will ignore this, or allow one to use ''NULL'' (defined in some manner) to specify a value might not be there. + Imperative languages may support this by rewriting as a ''union'' or allow one to use / return ''NULL'' (defined in some manner) to specify a value might not be there. ==Classes== ==Classes== Line 23: Line 23: always be '''Nothing'''. always be '''Nothing'''. - ===Usage example=== + ===Maybe as a Monad=== Using the [[Monad]] class definition can lead to much more compact code. For example: Using the [[Monad]] class definition can lead to much more compact code. For example: - + f::Int -> Maybe Int f::Int -> Maybe Int f 0 = Nothing f 0 = Nothing Line 42: Line 42: h' x = do n <- f x h' x = do n <- f x g n g n - + The functions h and h' will give the same results. ([itex]h 0 = h' 0 = h 100 = h' 100 = Nothing;\ h x = h' x = Just\, x[/itex]). In this case the savings in code size is quite modest, stringing together multiple functions like f and g will be more noticeable. The functions h and h' will give the same results. ([itex]h 0 = h' 0 = h 100 = h' 100 = Nothing;\ h x = h' x = Just\, x[/itex]). In this case the savings in code size is quite modest, stringing together multiple functions like f and g will be more noticeable. + + ==Library functions== + When the module is imported, it supplies a variety of useful functions including: + ;maybe :: b->(a->b) -> Maybe a -> b :Applies the second argument to the third, when it is ''Just x'', otherwise returns the first argument. + ;isJust, isNothing :Test the argument, returing a Bool based on the constructor. + ;listToMaybe, maybeToList :Convert to/from a one element or empty list. + ;mapMaybe : A different way to filter a list. + + See the documentation for [http://www.haskell.org/ghc/docs/latest/html/libraries/base/Data-Maybe.html Data.Maybe] for more explanation and other functions. + [[Category:Monad]]

## Current revision

 import Data.Maybe

The Maybe type is defined as follows:

```data Maybe a = Just a | Nothing
deriving (Eq, Ord)```

It allows the programmer to specify something may not be there.

## 1 Type equation

Maybe satisfies the type equation FX = 1 + X, where the functor F takes a set to a point plus that set.

## 2 Comparison to imperative languages

Imperative languages may support this by rewriting as a union or allow one to use / return NULL (defined in some manner) to specify a value might not be there.

## 3 Classes

As one can see from the type definition, Maybe will be an instance of Eq and Ord when the base type is. As well, instances of Functor and Monad are defined for Maybe.

For Functor, the `fmap` function moves inside the Just constructor and is identity on the Nothing constructor.

For Monad, the bind operation passes through Just, while Nothing will force the result to always be Nothing.

### 3.1 Maybe as a Monad

Using the Monad class definition can lead to much more compact code. For example:

```f::Int -> Maybe Int
f 0 = Nothing
f x = Just x

g :: Int -> Maybe Int
g 100 = Nothing
g x = Just x

h ::Int -> Maybe Int
h x = case f x of
Just n -> g n
Nothing -> Nothing

h' :: Int -> Maybe Int
h' x = do n <- f x
g n```

The functions `h` and `h'` will give the same results. ($h 0 = h' 0 = h 100 = h' 100 = Nothing;\ h x = h' x = Just\, x$). In this case the savings in code size is quite modest, stringing together multiple functions like `f` and `g` will be more noticeable.

## 4 Library functions

When the module is imported, it supplies a variety of useful functions including:

maybe :: b->(a->b) -> Maybe a -> b

Applies the second argument to the third, when it is Just x, otherwise returns the first argument.
isJust
,
isNothing

Test the argument, returing a Bool based on the constructor.
listToMaybe
,
maybeToList

Convert to/from a one element or empty list.
mapMaybe

A different way to filter a list.

See the documentation for Data.Maybe for more explanation and other functions.