Safe Haskell | Safe |
---|---|

Language | Haskell2010 |

A subset of the Prelude motivated by deeply embedded domain-specific languages

- data Bool :: *
- data Double :: *
- data Either a b :: * -> * -> *
- type FilePath = String
- data Float :: *
- data Int :: *
- data IO a :: * -> *
- data Integer :: *
- data Maybe a :: * -> *
- type String = [Char]
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- class Functor f => Applicative f where
- class Bounded a where
- class Fractional a => Floating a where
- class Num a => Fractional a where
- (/) :: a -> a -> a
- recip :: a -> a
- fromRational :: Rational -> a

- class Functor f where
- class Applicative m => Monad m where
- class Num a where
- class Read a where
- class Show a where
- (.) :: (b -> c) -> (a -> b) -> a -> c
- ($) :: (a -> b) -> a -> b
- asTypeOf :: a -> a -> a
- const :: a -> b -> a
- curry :: ((a, b) -> c) -> a -> b -> c
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- flip :: (a -> b -> c) -> b -> a -> c
- fst :: (a, b) -> a
- id :: a -> a
- maybe :: b -> (a -> b) -> Maybe a -> b
- otherwise :: Bool
- print :: Show a => a -> IO ()
- putStr :: String -> IO ()
- putStrLn :: String -> IO ()
- readFile :: FilePath -> IO String
- snd :: (a, b) -> b
- subtract :: Num a => a -> a -> a
- toInteger :: Integral a => a -> Integer
- toRational :: Real a => a -> Rational
- uncurry :: (a -> b -> c) -> (a, b) -> c
- undefined :: a
- writeFile :: FilePath -> String -> IO ()

# Documentation

data Double :: *

Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.

data Either a b :: * -> * -> *

The `Either`

type represents values with two possibilities: a value of
type

is either `Either`

a b

or `Left`

a

.`Right`

b

The `Either`

type is sometimes used to represent a value which is
either correct or an error; by convention, the `Left`

constructor is
used to hold an error value and the `Right`

constructor is used to
hold a correct value (mnemonic: "right" also means "correct").

#### Examples

The type

is the type of values which can be either
a `Either`

`String`

`Int`

`String`

or an `Int`

. The `Left`

constructor can be used only on
`String`

s, and the `Right`

constructor can be used only on `Int`

s:

`>>>`

`let s = Left "foo" :: Either String Int`

`>>>`

Left "foo"`s`

`>>>`

`let n = Right 3 :: Either String Int`

`>>>`

Right 3`n`

`>>>`

s :: Either String Int`:type s`

`>>>`

n :: Either String Int`:type n`

The `fmap`

from our `Functor`

instance will ignore `Left`

values, but
will apply the supplied function to values contained in a `Right`

:

`>>>`

`let s = Left "foo" :: Either String Int`

`>>>`

`let n = Right 3 :: Either String Int`

`>>>`

Left "foo"`fmap (*2) s`

`>>>`

Right 6`fmap (*2) n`

The `Monad`

instance for `Either`

allows us to chain together multiple
actions which may fail, and fail overall if any of the individual
steps failed. First we'll write a function that can either parse an
`Int`

from a `Char`

, or fail.

`>>>`

`import Data.Char ( digitToInt, isDigit )`

`>>>`

let parseEither :: Char -> Either String Int parseEither c | isDigit c = Right (digitToInt c) | otherwise = Left "parse error"`:{`

`>>>`

`:}`

The following should work, since both `'1'`

and `'2'`

can be
parsed as `Int`

s.

`>>>`

let parseMultiple :: Either String Int parseMultiple = do x <- parseEither '1' y <- parseEither '2' return (x + y)`:{`

`>>>`

`:}`

`>>>`

Right 3`parseMultiple`

But the following should fail overall, since the first operation where
we attempt to parse `'m'`

as an `Int`

will fail:

`>>>`

let parseMultiple :: Either String Int parseMultiple = do x <- parseEither 'm' y <- parseEither '2' return (x + y)`:{`

`>>>`

`:}`

`>>>`

Left "parse error"`parseMultiple`

File and directory names are values of type `String`

, whose precise
meaning is operating system dependent. Files can be opened, yielding a
handle which can then be used to operate on the contents of that file.

data Float :: *

Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.

data Int :: *

data IO a :: * -> *

A value of type

is a computation which, when performed,
does some I/O before returning a value of type `IO`

a`a`

.

There is really only one way to "perform" an I/O action: bind it to
`Main.main`

in your program. When your program is run, the I/O will
be performed. It isn't possible to perform I/O from an arbitrary
function, unless that function is itself in the `IO`

monad and called
at some point, directly or indirectly, from `Main.main`

.

`IO`

is a monad, so `IO`

actions can be combined using either the do-notation
or the `>>`

and `>>=`

operations from the `Monad`

class.

data Integer :: *

data Maybe a :: * -> *

The `Maybe`

type encapsulates an optional value. A value of type

either contains a value of type `Maybe`

a`a`

(represented as

),
or it is empty (represented as `Just`

a`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 `Either`

type.

Monad Maybe | |

Functor Maybe | |

Applicative Maybe | |

Alternative Maybe | |

MonadPlus Maybe | |

Eq a => Eq (Maybe a) | |

Ord a => Ord (Maybe a) | |

Read a => Read (Maybe a) | |

Show a => Show (Maybe a) | |

Monoid a => Monoid (Maybe a) | Lift a semigroup into |

type (==) (Maybe k) a b = EqMaybe k a b |

(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4

An infix synonym for `fmap`

.

#### Examples

Convert from a

to a `Maybe`

`Int`

using `Maybe`

`String`

`show`

:

`>>>`

Nothing`show <$> Nothing`

`>>>`

Just "3"`show <$> Just 3`

Convert from an

to an `Either`

`Int`

`Int`

`Either`

`Int`

`String`

using `show`

:

`>>>`

Left 17`show <$> Left 17`

`>>>`

Right "17"`show <$> Right 17`

Double each element of a list:

`>>>`

[2,4,6]`(*2) <$> [1,2,3]`

Apply `even`

to the second element of a pair:

`>>>`

(2,True)`even <$> (2,2)`

class Functor f => Applicative f where

A functor with application, providing operations to

A minimal complete definition must include implementations of these functions satisfying the following laws:

*identity*`pure`

`id`

`<*>`

v = v*composition*`pure`

(.)`<*>`

u`<*>`

v`<*>`

w = u`<*>`

(v`<*>`

w)*homomorphism*`pure`

f`<*>`

`pure`

x =`pure`

(f x)*interchange*u

`<*>`

`pure`

y =`pure`

(`$`

y)`<*>`

u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

As a consequence of these laws, the `Functor`

instance for `f`

will satisfy

If `f`

is also a `Monad`

, it should satisfy

(which implies that `pure`

and `<*>`

satisfy the applicative functor laws).

pure :: a -> f a

Lift a value.

(<*>) :: f (a -> b) -> f a -> f b infixl 4

Sequential application.

(*>) :: f a -> f b -> f b infixl 4

Sequence actions, discarding the value of the first argument.

(<*) :: f a -> f b -> f a infixl 4

Sequence actions, discarding the value of the second argument.

Applicative [] | |

Applicative IO | |

Applicative Maybe | |

Applicative ((->) a) | |

Applicative (Either e) | |

Monoid a => Applicative ((,) a) |

class Bounded a where

The `Bounded`

class is used to name the upper and lower limits of a
type. `Ord`

is not a superclass of `Bounded`

since types that are not
totally ordered may also have upper and lower bounds.

The `Bounded`

class may be derived for any enumeration type;
`minBound`

is the first constructor listed in the `data`

declaration
and `maxBound`

is the last.
`Bounded`

may also be derived for single-constructor datatypes whose
constituent types are in `Bounded`

.

class Fractional a => Floating a where

Trigonometric and hyperbolic functions and related functions.

class Num a => Fractional a where

Fractional numbers, supporting real division.

fromRational, (recip | (/))

(/) :: a -> a -> a infixl 7

fractional division

recip :: a -> a

reciprocal fraction

fromRational :: Rational -> a

Conversion from a `Rational`

(that is

).
A floating literal stands for an application of `Ratio`

`Integer`

`fromRational`

to a value of type `Rational`

, so such literals have type
`(`

.`Fractional`

a) => a

Integral a => Fractional (Ratio a) |

class Functor f where

The `Functor`

class is used for types that can be mapped over.
Instances of `Functor`

should satisfy the following laws:

fmap id == id fmap (f . g) == fmap f . fmap g

The instances of `Functor`

for lists, `Maybe`

and `IO`

satisfy these laws.

class Applicative m => Monad m where

The `Monad`

class defines the basic operations over a *monad*,
a concept from a branch of mathematics known as *category theory*.
From the perspective of a Haskell programmer, however, it is best to
think of a monad as an *abstract datatype* of actions.
Haskell's `do`

expressions provide a convenient syntax for writing
monadic expressions.

Instances of `Monad`

should satisfy the following laws:

Furthermore, the `Monad`

and `Applicative`

operations should relate as follows:

The above laws imply:

and that `pure`

and (`<*>`

) satisfy the applicative functor laws.

The instances of `Monad`

for lists, `Maybe`

and `IO`

defined in the Prelude satisfy these laws.

(>>=) :: m a -> (a -> m b) -> m b infixl 1

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

(>>) :: m a -> m b -> m b infixl 1

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

return :: a -> m a

Inject a value into the monadic type.

Fail with a message. This operation is not part of the
mathematical definition of a monad, but is invoked on pattern-match
failure in a `do`

expression.

class Num a where

Basic numeric class.

(+) :: a -> a -> a infixl 6

(-) :: a -> a -> a infixl 6

(*) :: a -> a -> a infixl 7

negate :: a -> a

Unary negation.

abs :: a -> a

Absolute value.

signum :: a -> a

Sign of a number.
The functions `abs`

and `signum`

should satisfy the law:

abs x * signum x == x

For real numbers, the `signum`

is either `-1`

(negative), `0`

(zero)
or `1`

(positive).

fromInteger :: Integer -> a

Conversion from an `Integer`

.
An integer literal represents the application of the function
`fromInteger`

to the appropriate value of type `Integer`

,
so such literals have type `(`

.`Num`

a) => a

class Read a where

Parsing of `String`

s, producing values.

Derived instances of `Read`

make the following assumptions, which
derived instances of `Show`

obey:

- If the constructor is defined to be an infix operator, then the
derived
`Read`

instance will parse only infix applications of the constructor (not the prefix form). - Associativity is not used to reduce the occurrence of parentheses, although precedence may be.
- If the constructor is defined using record syntax, the derived
`Read`

will parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration. - The derived
`Read`

instance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.

For example, given the declarations

infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a

the derived instance of `Read`

in Haskell 2010 is equivalent to

instance (Read a) => Read (Tree a) where readsPrec d r = readParen (d > app_prec) (\r -> [(Leaf m,t) | ("Leaf",s) <- lex r, (m,t) <- readsPrec (app_prec+1) s]) r ++ readParen (d > up_prec) (\r -> [(u:^:v,w) | (u,s) <- readsPrec (up_prec+1) r, (":^:",t) <- lex s, (v,w) <- readsPrec (up_prec+1) t]) r where app_prec = 10 up_prec = 5

Note that right-associativity of `:^:`

is unused.

The derived instance in GHC is equivalent to

instance (Read a) => Read (Tree a) where readPrec = parens $ (prec app_prec $ do Ident "Leaf" <- lexP m <- step readPrec return (Leaf m)) +++ (prec up_prec $ do u <- step readPrec Symbol ":^:" <- lexP v <- step readPrec return (u :^: v)) where app_prec = 10 up_prec = 5 readListPrec = readListPrecDefault

:: Int | the operator precedence of the enclosing
context (a number from |

-> ReadS a |

attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.

Derived instances of `Read`

and `Show`

satisfy the following:

That is, `readsPrec`

parses the string produced by
`showsPrec`

, and delivers the value that
`showsPrec`

started with.

Read Bool | |

Read Char | |

Read Double | |

Read Float | |

Read Int | |

Read Integer | |

Read Ordering | |

Read Word | |

Read () | |

Read Lexeme | |

Read a => Read [a] | |

(Integral a, Read a) => Read (Ratio a) | |

Read a => Read (Maybe a) | |

(Read a, Read b) => Read (Either a b) | |

(Read a, Read b) => Read (a, b) | |

(Ix a, Read a, Read b) => Read (Array a b) | |

(Read a, Read b, Read c) => Read (a, b, c) | |

(~) k a b => Read ((:~:) k a b) | |

(Read a, Read b, Read c, Read d) => Read (a, b, c, d) | |

(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) | |

(Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |

class Show a where

Conversion of values to readable `String`

s.

Derived instances of `Show`

have the following properties, which
are compatible with derived instances of `Read`

:

- The result of
`show`

is a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used. - If the constructor is defined to be an infix operator, then
`showsPrec`

will produce infix applications of the constructor. - the representation will be enclosed in parentheses if the
precedence of the top-level constructor in
`x`

is less than`d`

(associativity is ignored). Thus, if`d`

is`0`

then the result is never surrounded in parentheses; if`d`

is`11`

it is always surrounded in parentheses, unless it is an atomic expression. - If the constructor is defined using record syntax, then
`show`

will produce the record-syntax form, with the fields given in the same order as the original declaration.

For example, given the declarations

infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a

the derived instance of `Show`

is equivalent to

instance (Show a) => Show (Tree a) where showsPrec d (Leaf m) = showParen (d > app_prec) $ showString "Leaf " . showsPrec (app_prec+1) m where app_prec = 10 showsPrec d (u :^: v) = showParen (d > up_prec) $ showsPrec (up_prec+1) u . showString " :^: " . showsPrec (up_prec+1) v where up_prec = 5

Note that right-associativity of `:^:`

is ignored. For example,

produces the string`show`

(Leaf 1 :^: Leaf 2 :^: Leaf 3)`"Leaf 1 :^: (Leaf 2 :^: Leaf 3)"`

.

:: Int | the operator precedence of the enclosing
context (a number from |

-> a | the value to be converted to a |

-> ShowS |

Convert a value to a readable `String`

.

`showsPrec`

should satisfy the law

showsPrec d x r ++ s == showsPrec d x (r ++ s)

Derived instances of `Read`

and `Show`

satisfy the following:

That is, `readsPrec`

parses the string produced by
`showsPrec`

, and delivers the value that `showsPrec`

started with.

Show Bool | |

Show Char | |

Show Int | |

Show Integer | |

Show Ordering | |

Show Word | |

Show () | |

Show MaskingState | |

Show a => Show [a] | |

(Integral a, Show a) => Show (Ratio a) | |

Show a => Show (Maybe a) | |

(Show a, Show b) => Show (Either a b) | |

(Show a, Show b) => Show (a, b) | |

(Show a, Show b, Show c) => Show (a, b, c) | |

Show ((:~:) k a b) | |

(Show a, Show b, Show c, Show d) => Show (a, b, c, d) | |

(Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e) | |

(Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f) | |

(Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g) | |

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h) => Show (a, b, c, d, e, f, g, h) | |

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i) => Show (a, b, c, d, e, f, g, h, i) | |

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j) => Show (a, b, c, d, e, f, g, h, i, j) | |

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k) => Show (a, b, c, d, e, f, g, h, i, j, k) | |

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l) => Show (a, b, c, d, e, f, g, h, i, j, k, l) | |

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m) | |

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n, Show o) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |

(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9

Function composition.

($) :: (a -> b) -> a -> b infixr 0

Application operator. This operator is redundant, since ordinary
application `(f x)`

means the same as `(f `

. However, `$`

x)`$`

has
low, right-associative binding precedence, so it sometimes allows
parentheses to be omitted; for example:

f $ g $ h x = f (g (h x))

It is also useful in higher-order situations, such as

,
or `map`

(`$`

0) xs

.`zipWith`

(`$`

) fs xs

asTypeOf :: a -> a -> a

const :: a -> b -> a

Constant function.

either :: (a -> c) -> (b -> c) -> Either a b -> c

Case analysis for the `Either`

type.
If the value is

, apply the first function to `Left`

a`a`

;
if it is

, apply the second function to `Right`

b`b`

.

#### Examples

We create two values of type

, one using the
`Either`

`String`

`Int`

`Left`

constructor and another using the `Right`

constructor. Then
we apply "either" the `length`

function (if we have a `String`

)
or the "times-two" function (if we have an `Int`

):

`>>>`

`let s = Left "foo" :: Either String Int`

`>>>`

`let n = Right 3 :: Either String Int`

`>>>`

3`either length (*2) s`

`>>>`

6`either length (*2) n`

flip :: (a -> b -> c) -> b -> a -> c

takes its (first) two arguments in the reverse order of `flip`

f`f`

.

fst :: (a, b) -> a

Extract the first component of a pair.

id :: a -> a

Identity function.

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

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.

#### Examples

Basic usage:

`>>>`

True`maybe False odd (Just 3)`

`>>>`

False`maybe False odd Nothing`

Read an integer from a string using `readMaybe`

. If we succeed,
return twice the integer; that is, apply `(*2)`

to it. If instead
we fail to parse an integer, return `0`

by default:

`>>>`

`import Text.Read ( readMaybe )`

`>>>`

10`maybe 0 (*2) (readMaybe "5")`

`>>>`

0`maybe 0 (*2) (readMaybe "")`

Apply `show`

to a `Maybe Int`

. If we have `Just n`

, we want to show
the underlying `Int`

`n`

. But if we have `Nothing`

, we return the
empty string instead of (for example) "Nothing":

`>>>`

"5"`maybe "" show (Just 5)`

`>>>`

""`maybe "" show Nothing`

The `print`

function outputs a value of any printable type to the
standard output device.
Printable types are those that are instances of class `Show`

; `print`

converts values to strings for output using the `show`

operation and
adds a newline.

For example, a program to print the first 20 integers and their powers of 2 could be written as:

main = print ([(n, 2^n) | n <- [0..19]])

readFile :: FilePath -> IO String

The `readFile`

function reads a file and
returns the contents of the file as a string.
The file is read lazily, on demand, as with `getContents`

.

snd :: (a, b) -> b

Extract the second component of a pair.

toRational :: Real a => a -> Rational

the rational equivalent of its real argument with full precision

undefined :: a