| Safe Haskell | Safe |
|---|---|
| Language | Haskell2010 |
Prelude.EDSL
Description
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 Either a bLeft aRight 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 Either String IntString or an Int. The Left constructor can be used only on
Strings, and the Right constructor can be used only on Ints:
>>>let s = Left "foo" :: Either String Int>>>sLeft "foo">>>let n = Right 3 :: Either String Int>>>nRight 3>>>:type ss :: Either String Int>>>:type nn :: 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) sLeft "foo">>>fmap (*2) nRight 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 Ints.
>>>:{let parseMultiple :: Either String Int parseMultiple = do x <- parseEither '1' y <- parseEither '2' return (x + y)>>>:}
>>>parseMultipleRight 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)>>>:}
>>>parseMultipleLeft "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 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
Maybe aa (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.
Instances
| 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 |
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4
An infix synonym for fmap.
Examples
Convert from a Maybe IntMaybe Stringshow:
>>>show <$> NothingNothing>>>show <$> Just 3Just "3"
Convert from an Either Int IntEither IntString using show:
>>>show <$> Left 17Left 17>>>show <$> Right 17Right "17"
Double each element of a list:
>>>(*2) <$> [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>even <$> (2,2)(2,True)
class Functor f => Applicative f where
A functor with application, providing operations to
A minimal complete definition must include implementations of these functions satisfying the following laws:
- identity
pureid<*>v = v- composition
pure(.)<*>u<*>v<*>w = u<*>(v<*>w)- homomorphism
puref<*>purex =pure(f x)- interchange
u
<*>purey =pure($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).
Methods
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.
Instances
| 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.
Instances
class Fractional a => Floating a where
Trigonometric and hyperbolic functions and related functions.
Minimal complete definition
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
class Num a => Fractional a where
Fractional numbers, supporting real division.
Minimal complete definition
fromRational, (recip | (/))
Methods
(/) :: a -> a -> a infixl 7
fractional division
recip :: a -> a
reciprocal fraction
fromRational :: Rational -> a
Conversion from a Rational (that is Ratio IntegerfromRational
to a value of type Rational, so such literals have type
(.Fractional a) => a
Instances
| 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.
Minimal complete definition
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.
Minimal complete definition
Methods
(>>=) :: 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.
Methods
(+) :: 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 Strings, 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
Readinstance 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
Readwill parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration. - The derived
Readinstance 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 = 5Note 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 = readListPrecDefaultMethods
Arguments
| :: 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.
Instances
| 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 Strings.
Derived instances of Show have the following properties, which
are compatible with derived instances of Read:
- The result of
showis 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
showsPrecwill produce infix applications of the constructor. - the representation will be enclosed in parentheses if the
precedence of the top-level constructor in
xis less thand(associativity is ignored). Thus, ifdis0then the result is never surrounded in parentheses; ifdis11it is always surrounded in parentheses, unless it is an atomic expression. - If the constructor is defined using record syntax, then
showwill 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 = 5Note that right-associativity of :^: is ignored. For example,
show(Leaf 1 :^: Leaf 2 :^: Leaf 3)"Leaf 1 :^: (Leaf 2 :^: Leaf 3)".
Methods
Arguments
| :: 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.
Instances
| 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 map ($ 0) xszipWith ($) 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 Left aa;
if it is Right bb.
Examples
We create two values of type Either String IntLeft 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) s3>>>either length (*2) n6
flip :: (a -> b -> c) -> b -> a -> c
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 NothingFalse
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