simpleprelude-1.0.1.0: A simplified Haskell prelude for teaching

Prelude

Contents

Synopsis

Standard types, classes and related functions

Basic data types

data Bool

Constructors

False 
True 

(&&) :: Bool -> Bool -> Bool

Boolean "and"

(||) :: Bool -> Bool -> Bool

Boolean "or"

not :: Bool -> Bool

Boolean "not"

otherwise :: Bool

otherwise is defined as the value True. It helps to make guards more readable. eg.

  f x | x < 0     = ...
      | otherwise = ...

data Maybe a

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.

Constructors

Nothing 
Just a 

Instances

Monad Maybe 
Functor Maybe 
MonadPlus Maybe 
Eq a => Eq (Maybe a) 
Ord a => Ord (Maybe a) 
Read a => Read (Maybe a) 
Show a => Show (Maybe a) 
Generic (Maybe a) 

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.

data Either a b

The Either type represents values with two possibilities: a value of type Either a b is either Left a or 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").

Constructors

Left a 
Right b 

Instances

Typeable2 Either 
(Eq a, Eq b) => Eq (Either a b) 
(Ord a, Ord b) => Ord (Either a b) 
(Read a, Read b) => Read (Either a b) 
(Show a, Show b) => Show (Either a b) 
Generic (Either a b) 

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

Case analysis for the Either type. If the value is Left a, apply the first function to a; if it is Right b, apply the second function to b.

data Char

The character type Char is an enumeration whose values represent Unicode (or equivalently ISO/IEC 10646) characters (see http://www.unicode.org/ for details). This set extends the ISO 8859-1 (Latin-1) character set (the first 256 charachers), which is itself an extension of the ASCII character set (the first 128 characters). A character literal in Haskell has type Char.

To convert a Char to or from the corresponding Int value defined by Unicode, use Prelude.toEnum and Prelude.fromEnum from the Prelude.Enum class respectively (or equivalently ord and chr).

type String = [Char]

A String is a list of characters. String constants in Haskell are values of type String.

Tuples

fst :: (a, b) -> a

Extract the first component of a pair.

snd :: (a, b) -> b

Extract the second component of a pair.

curry :: ((a, b) -> c) -> a -> b -> c

curry converts an uncurried function to a curried function.

uncurry :: (a -> b -> c) -> (a, b) -> c

uncurry converts a curried function to a function on pairs.

Basic type classes

class Enum a where

Class Enum defines operations on sequentially ordered types.

The enumFrom... methods are used in Haskell's translation of arithmetic sequences.

Instances of Enum may be derived for any enumeration type (types whose constructors have no fields). The nullary constructors are assumed to be numbered left-to-right by fromEnum from 0 through n-1. See Chapter 10 of the Haskell Report for more details.

For any type that is an instance of class Bounded as well as Enum, the following should hold:

    enumFrom     x   = enumFromTo     x maxBound
    enumFromThen x y = enumFromThenTo x y bound
      where
        bound | fromEnum y >= fromEnum x = maxBound
              | otherwise                = minBound

Methods

succ :: a -> a

the successor of a value. For numeric types, succ adds 1.

pred :: a -> a

the predecessor of a value. For numeric types, pred subtracts 1.

toEnum :: Int -> a

Convert from an Int.

fromEnum :: a -> Int

Convert to an Int. It is implementation-dependent what fromEnum returns when applied to a value that is too large to fit in an Int.

enumFrom :: a -> [a]

Used in Haskell's translation of [n..].

enumFromThen :: a -> a -> [a]

Used in Haskell's translation of [n,n'..].

enumFromTo :: a -> a -> [a]

Used in Haskell's translation of [n..m].

enumFromThenTo :: a -> a -> a -> [a]

Used in Haskell's translation of [n,n'..m].

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.

Methods

minBound :: a

maxBound :: a

Instances

Bounded Bool 
Bounded Char 
Bounded Int 
Bounded Ordering 
Bounded () 
(Bounded a, Bounded b) => Bounded (a, b) 
(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) 
(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) 

Numbers

Numeric types

data Integer

Arbitrary-precision integers.

Numeric type classes

Numeric functions

fromIntegral :: (Integral a, Num b) => a -> b

general coercion from integral types

Monads and functors

class 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.

Minimal complete definition: >>= and return.

Instances of Monad should satisfy the following laws:

 return a >>= k  ==  k a
 m >>= return  ==  m
 m >>= (\x -> k x >>= h)  ==  (m >>= k) >>= h

Instances of both Monad and Functor should additionally satisfy the law:

 fmap f xs  ==  xs >>= return . f

The instances of Monad for lists, Data.Maybe.Maybe and System.IO.IO defined in the Prelude satisfy these laws.

Methods

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

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

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

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 :: String -> m a

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.

Instances

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, Data.Maybe.Maybe and System.IO.IO satisfy these laws.

Methods

fmap :: (a -> b) -> f a -> f b

mapM :: Monad m => (a -> m b) -> [a] -> m [b]

mapM f is equivalent to sequence . map f.

mapM_ :: Monad m => (a -> m b) -> [a] -> m ()

mapM_ f is equivalent to sequence_ . map f.

sequence :: Monad m => [m a] -> m [a]

Evaluate each action in the sequence from left to right, and collect the results.

sequence_ :: Monad m => [m a] -> m ()

Evaluate each action in the sequence from left to right, and ignore the results.

(=<<) :: Monad m => (a -> m b) -> m a -> m b

Same as >>=, but with the arguments interchanged.

Miscellaneous functions

id :: a -> a

Identity function.

const :: a -> b -> a

Constant function.

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

Function composition.

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

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

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

Application operator. This operator is redundant, since ordinary application (f x) means the same as (f $ x). However, $ 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) xs, or Data.List.zipWith ($) fs xs.

until :: (a -> Bool) -> (a -> a) -> a -> a

until p f yields the result of applying f until p holds.

asTypeOf :: a -> a -> a

asTypeOf is a type-restricted version of const. It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the second.

error :: [Char] -> a

error stops execution and displays an error message.

undefined :: a

A special case of error. It is expected that compilers will recognize this and insert error messages which are more appropriate to the context in which undefined appears.

seq :: a -> b -> b

Evaluates its first argument to head normal form, and then returns its second argument as the result.

($!) :: (a -> b) -> a -> b

Strict (call-by-value) application, defined in terms of seq.

List operations

map :: (a -> b) -> [a] -> [b]

map f xs is the list obtained by applying f to each element of xs, i.e.,

 map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
 map f [x1, x2, ...] == [f x1, f x2, ...]

(++) :: [a] -> [a] -> [a]

Append two lists, i.e.,

 [x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
 [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]

If the first list is not finite, the result is the first list.

filter :: (a -> Bool) -> [a] -> [a]

filter, applied to a predicate and a list, returns the list of those elements that satisfy the predicate; i.e.,

 filter p xs = [ x | x <- xs, p x]

head :: [a] -> a

Extract the first element of a list, which must be non-empty.

last :: [a] -> a

Extract the last element of a list, which must be finite and non-empty.

tail :: [a] -> [a]

Extract the elements after the head of a list, which must be non-empty.

init :: [a] -> [a]

Return all the elements of a list except the last one. The list must be non-empty.

null :: [a] -> Bool

Test whether a list is empty.

(!!) :: [a] -> Integer -> aSource

reverse :: [a] -> [a]

reverse xs returns the elements of xs in reverse order. xs must be finite.

Reducing lists (folds)

foldl :: (a -> b -> a) -> a -> [b] -> a

foldl, applied to a binary operator, a starting value (typically the left-identity of the operator), and a list, reduces the list using the binary operator, from left to right:

 foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn

The list must be finite.

foldl1 :: (a -> a -> a) -> [a] -> a

foldl1 is a variant of foldl that has no starting value argument, and thus must be applied to non-empty lists.

foldr :: (a -> b -> b) -> b -> [a] -> b

foldr, applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:

 foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)

foldr1 :: (a -> a -> a) -> [a] -> a

foldr1 is a variant of foldr that has no starting value argument, and thus must be applied to non-empty lists.

Special folds

and :: [Bool] -> Bool

and returns the conjunction of a Boolean list. For the result to be True, the list must be finite; False, however, results from a False value at a finite index of a finite or infinite list.

or :: [Bool] -> Bool

or returns the disjunction of a Boolean list. For the result to be False, the list must be finite; True, however, results from a True value at a finite index of a finite or infinite list.

any :: (a -> Bool) -> [a] -> Bool

Applied to a predicate and a list, any determines if any element of the list satisfies the predicate. For the result to be False, the list must be finite; True, however, results from a True value for the predicate applied to an element at a finite index of a finite or infinite list.

all :: (a -> Bool) -> [a] -> Bool

Applied to a predicate and a list, all determines if all elements of the list satisfy the predicate. For the result to be True, the list must be finite; False, however, results from a False value for the predicate applied to an element at a finite index of a finite or infinite list.

concat :: [[a]] -> [a]

Concatenate a list of lists.

concatMap :: (a -> [b]) -> [a] -> [b]

Map a function over a list and concatenate the results.

maximum :: Ord a => [a] -> a

maximum returns the maximum value from a list, which must be non-empty, finite, and of an ordered type. It is a special case of maximumBy, which allows the programmer to supply their own comparison function.

minimum :: Ord a => [a] -> a

minimum returns the minimum value from a list, which must be non-empty, finite, and of an ordered type. It is a special case of minimumBy, which allows the programmer to supply their own comparison function.

Building lists

Scans

scanl :: (a -> b -> a) -> a -> [b] -> [a]

scanl is similar to foldl, but returns a list of successive reduced values from the left:

 scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]

Note that

 last (scanl f z xs) == foldl f z xs.

scanl1 :: (a -> a -> a) -> [a] -> [a]

scanl1 is a variant of scanl that has no starting value argument:

 scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]

scanr :: (a -> b -> b) -> b -> [a] -> [b]

scanr is the right-to-left dual of scanl. Note that

 head (scanr f z xs) == foldr f z xs.

scanr1 :: (a -> a -> a) -> [a] -> [a]

scanr1 is a variant of scanr that has no starting value argument.

Infinite lists

iterate :: (a -> a) -> a -> [a]

iterate f x returns an infinite list of repeated applications of f to x:

 iterate f x == [x, f x, f (f x), ...]

repeat :: a -> [a]

repeat x is an infinite list, with x the value of every element.

replicate :: Int -> a -> [a]

replicate n x is a list of length n with x the value of every element. It is an instance of the more general Data.List.genericReplicate, in which n may be of any integral type.

cycle :: [a] -> [a]

cycle ties a finite list into a circular one, or equivalently, the infinite repetition of the original list. It is the identity on infinite lists.

Sublists

take, drop :: Integer -> [a] -> [a]Source

splitAt :: Int -> [a] -> ([a], [a])

splitAt n xs returns a tuple where first element is xs prefix of length n and second element is the remainder of the list:

 splitAt 6 "Hello World!" == ("Hello ","World!")
 splitAt 3 [1,2,3,4,5] == ([1,2,3],[4,5])
 splitAt 1 [1,2,3] == ([1],[2,3])
 splitAt 3 [1,2,3] == ([1,2,3],[])
 splitAt 4 [1,2,3] == ([1,2,3],[])
 splitAt 0 [1,2,3] == ([],[1,2,3])
 splitAt (-1) [1,2,3] == ([],[1,2,3])

It is equivalent to (take n xs, drop n xs) when n is not _|_ (splitAt _|_ xs = _|_). splitAt is an instance of the more general Data.List.genericSplitAt, in which n may be of any integral type.

takeWhile :: (a -> Bool) -> [a] -> [a]

takeWhile, applied to a predicate p and a list xs, returns the longest prefix (possibly empty) of xs of elements that satisfy p:

 takeWhile (< 3) [1,2,3,4,1,2,3,4] == [1,2]
 takeWhile (< 9) [1,2,3] == [1,2,3]
 takeWhile (< 0) [1,2,3] == []

dropWhile :: (a -> Bool) -> [a] -> [a]

dropWhile p xs returns the suffix remaining after takeWhile p xs:

 dropWhile (< 3) [1,2,3,4,5,1,2,3] == [3,4,5,1,2,3]
 dropWhile (< 9) [1,2,3] == []
 dropWhile (< 0) [1,2,3] == [1,2,3]

span :: (a -> Bool) -> [a] -> ([a], [a])

span, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that satisfy p and second element is the remainder of the list:

 span (< 3) [1,2,3,4,1,2,3,4] == ([1,2],[3,4,1,2,3,4])
 span (< 9) [1,2,3] == ([1,2,3],[])
 span (< 0) [1,2,3] == ([],[1,2,3])

span p xs is equivalent to (takeWhile p xs, dropWhile p xs)

break :: (a -> Bool) -> [a] -> ([a], [a])

break, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that do not satisfy p and second element is the remainder of the list:

 break (> 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4])
 break (< 9) [1,2,3] == ([],[1,2,3])
 break (> 9) [1,2,3] == ([1,2,3],[])

break p is equivalent to span (not . p).

Searching lists

elem :: Eq a => a -> [a] -> Bool

elem is the list membership predicate, usually written in infix form, e.g., x `elem` xs. For the result to be False, the list must be finite; True, however, results from an element equal to x found at a finite index of a finite or infinite list.

notElem :: Eq a => a -> [a] -> Bool

notElem is the negation of elem.

lookup :: Eq a => a -> [(a, b)] -> Maybe b

lookup key assocs looks up a key in an association list.

Zipping and unzipping lists

zip :: [a] -> [b] -> [(a, b)]

zip takes two lists and returns a list of corresponding pairs. If one input list is short, excess elements of the longer list are discarded.

zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]

zip3 takes three lists and returns a list of triples, analogous to zip.

zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]

zipWith generalises zip by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two lists to produce the list of corresponding sums.

zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]

The zipWith3 function takes a function which combines three elements, as well as three lists and returns a list of their point-wise combination, analogous to zipWith.

unzip :: [(a, b)] -> ([a], [b])

unzip transforms a list of pairs into a list of first components and a list of second components.

unzip3 :: [(a, b, c)] -> ([a], [b], [c])

The unzip3 function takes a list of triples and returns three lists, analogous to unzip.

Functions on strings

lines :: String -> [String]

lines breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.

words :: String -> [String]

words breaks a string up into a list of words, which were delimited by white space.

unlines :: [String] -> String

unlines is an inverse operation to lines. It joins lines, after appending a terminating newline to each.

unwords :: [String] -> String

unwords is an inverse operation to words. It joins words with separating spaces.

Converting to and from String

Converting to String

type ShowS = String -> String

The shows functions return a function that prepends the output String to an existing String. This allows constant-time concatenation of results using function composition.

class Show a where

Conversion of values to readable Strings.

Minimal complete definition: showsPrec or show.

Derived instances of Show have the following properties, which are compatible with derived instances of Text.Read.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,

  • show (Leaf 1 :^: Leaf 2 :^: Leaf 3) produces the string "Leaf 1 :^: (Leaf 2 :^: Leaf 3)".

Methods

showsPrec

Arguments

:: Int

the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.

-> a

the value to be converted to a String

-> 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 Text.Read.Read and Show satisfy the following:

  • (x,"") is an element of (Text.Read.readsPrec d (showsPrec d x "")).

That is, Text.Read.readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.

show :: a -> String

A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String.

showList :: [a] -> ShowS

The method showList is provided to allow the programmer to give a specialised way of showing lists of values. For example, this is used by the predefined Show instance of the Char type, where values of type String should be shown in double quotes, rather than between square brackets.

Instances

Show Bool 
Show Char 
Show Double 
Show Float 
Show Int 
Show Integer 
Show Ordering 
Show () 
Show BlockedIndefinitelyOnMVar 
Show BlockedIndefinitelyOnSTM 
Show Deadlock 
Show AssertionFailed 
Show AsyncException 
Show ArrayException 
Show ExitCode 
Show IOErrorType 
Show MaskingState 
Show IOException 
Show Arity 
Show Fixity 
Show Associativity 
Show a => Show [a] 
Integral 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 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) 

shows :: Show a => a -> ShowS

equivalent to showsPrec with a precedence of 0.

showChar :: Char -> ShowS

utility function converting a Char to a show function that simply prepends the character unchanged.

showString :: String -> ShowS

utility function converting a String to a show function that simply prepends the string unchanged.

showParen :: Bool -> ShowS -> ShowS

utility function that surrounds the inner show function with parentheses when the Bool parameter is True.

Converting from String

type ReadS a = String -> [(a, String)]

A parser for a type a, represented as a function that takes a String and returns a list of possible parses as (a,String) pairs.

Note that this kind of backtracking parser is very inefficient; reading a large structure may be quite slow (cf ReadP).

class Read a where

Parsing of Strings, producing values.

Minimal complete definition: readsPrec (or, for GHC only, readPrec)

Derived instances of Read make the following assumptions, which derived instances of Text.Show.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 98 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

Methods

readsPrec

Arguments

:: Int

the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.

-> 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 Text.Show.Show satisfy the following:

  • (x,"") is an element of (readsPrec d (Text.Show.showsPrec d x "")).

That is, readsPrec parses the string produced by Text.Show.showsPrec, and delivers the value that Text.Show.showsPrec started with.

readList :: ReadS [a]

The method readList is provided to allow the programmer to give a specialised way of parsing lists of values. For example, this is used by the predefined Read instance of the Char type, where values of type String should be are expected to use double quotes, rather than square brackets.

Instances

Read Bool 
Read Char 
Read Double 
Read Float 
Read Int 
Read Integer 
Read Ordering 
Read () 
Read ExitCode 
Read Lexeme 
Read Arity 
Read Fixity 
Read Associativity 
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) 
(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) 

reads :: Read a => ReadS a

equivalent to readsPrec with a precedence of 0.

readParen :: Bool -> ReadS a -> ReadS a

readParen True p parses what p parses, but surrounded with parentheses.

readParen False p parses what p parses, but optionally surrounded with parentheses.

read :: Read a => String -> a

The read function reads input from a string, which must be completely consumed by the input process.

lex :: ReadS String

The lex function reads a single lexeme from the input, discarding initial white space, and returning the characters that constitute the lexeme. If the input string contains only white space, lex returns a single successful `lexeme' consisting of the empty string. (Thus lex "" = [("","")].) If there is no legal lexeme at the beginning of the input string, lex fails (i.e. returns []).

This lexer is not completely faithful to the Haskell lexical syntax in the following respects:

  • Qualified names are not handled properly
  • Octal and hexadecimal numerics are not recognized as a single token
  • Comments are not treated properly

Basic Input and output

data IO a

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

Instances

Simple I/O operations

Output functions

putChar :: Char -> IO ()

Write a character to the standard output device (same as hPutChar stdout).

putStr :: String -> IO ()

Write a string to the standard output device (same as hPutStr stdout).

putStrLn :: String -> IO ()

The same as putStr, but adds a newline character.

print :: Show a => a -> IO ()

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]])

Input functions

getChar :: IO Char

Read a character from the standard input device (same as hGetChar stdin).

getLine :: IO String

Read a line from the standard input device (same as hGetLine stdin).

getContents :: IO String

The getContents operation returns all user input as a single string, which is read lazily as it is needed (same as hGetContents stdin).

interact :: (String -> String) -> IO ()

The interact function takes a function of type String->String as its argument. The entire input from the standard input device is passed to this function as its argument, and the resulting string is output on the standard output device.

Files

type FilePath = String

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.

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.

writeFile :: FilePath -> String -> IO ()

The computation writeFile file str function writes the string str, to the file file.

appendFile :: FilePath -> String -> IO ()

The computation appendFile file str function appends the string str, to the file file.

Note that writeFile and appendFile write a literal string to a file. To write a value of any printable type, as with print, use the show function to convert the value to a string first.

 main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])

readIO :: Read a => String -> IO a

The readIO function is similar to read except that it signals parse failure to the IO monad instead of terminating the program.

readLn :: Read a => IO a

The readLn function combines getLine and readIO.

Exception handling in the I/O monad

type IOError = IOException

The Haskell 98 type for exceptions in the IO monad. Any I/O operation may raise an IOError instead of returning a result. For a more general type of exception, including also those that arise in pure code, see Control.Exception.Exception.

In Haskell 98, this is an opaque type.

ioError :: IOError -> IO a

Raise an IOError in the IO monad.

userError :: String -> IOError

Construct an IOError value with a string describing the error. The fail method of the IO instance of the Monad class raises a userError, thus:

 instance Monad IO where 
   ...
   fail s = ioError (userError s)

catch :: IO a -> (IOError -> IO a) -> IO a

The catch function is deprecated. Please use the new exceptions variant, Control.Exception.catch from Control.Exception, instead.