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
>>>
s
Left "foo">>>
let n = Right 3 :: Either String Int
>>>
n
Right 3>>>
:type s
s :: Either String Int>>>
:type n
n :: Either String Int
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
>>>
fmap (*2) s
Left "foo">>>
fmap (*2) n
Right 6
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)>>>
:}
>>>
parseMultiple
Right 3
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)>>>
:}
>>>
parseMultiple
Left "parse error"
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
aa
.
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
aa
(represented as
),
or it is empty (represented as Just
aNothing
). 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 |
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4
An infix synonym for fmap
.
Examples
Convert from a
to a Maybe
Int
using Maybe
String
show
:
>>>
show <$> Nothing
Nothing>>>
show <$> Just 3
Just "3"
Convert from an
to an Either
Int
Int
Either
Int
String
using show
:
>>>
show <$> Left 17
Left 17>>>
show <$> Right 17
Right "17"
Double each element of a list:
>>>
(*2) <$> [1,2,3]
[2,4,6]
Apply even
to the second element of a pair:
>>>
even <$> (2,2)
(2,True)
class Functor f => Applicative f where
A functor with application, providing operations to
A minimal complete definition must include implementations of these functions satisfying the following laws:
- identity
pure
id
<*>
v = v- composition
pure
(.)<*>
u<*>
v<*>
w = u<*>
(v<*>
w)- homomorphism
pure
f<*>
pure
x =pure
(f x)- interchange
u
<*>
pure
y =pure
($
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 thand
(associativity is ignored). Thus, ifd
is0
then the result is never surrounded in parentheses; ifd
is11
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 stringshow
(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
aa
;
if it is
, apply the second function to Right
bb
.
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
>>>
either length (*2) s
3>>>
either length (*2) n
6
flip :: (a -> b -> c) -> b -> a -> c
takes its (first) two arguments in the reverse order of flip
ff
.
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:
>>>
maybe False odd (Just 3)
True
>>>
maybe False odd Nothing
False
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 )
>>>
maybe 0 (*2) (readMaybe "5")
10>>>
maybe 0 (*2) (readMaybe "")
0
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":
>>>
maybe "" show (Just 5)
"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