This article describes the features in Haskell98.
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A simple example that is often used to demonstrate the syntax of functional languages is the factorial function for non-negative integers, shown in Haskell:
factorial :: Integer -> Integer factorial 0 = 1 factorial n | n > 0 = n * factorial (n-1)
Or in one line:
factorial n = if n > 0 then n * factorial (n-1) else 1
This describes the factorial as a recursive function, with one terminating base case. It is similar to the descriptions of factorials found in mathematics textbooks. Much of Haskell code is similar to standard mathematical notation in facility and syntax.
The first line of the factorial function describes the type of this function; while it is optional, it is considered to be good style[1] to include it. It can be read as the function factorial (factorial) has type (::) from integer to integer (Integer -> Integer). That is, it takes an integer as an argument, and returns another integer. The type of a definition is inferred automatically if the programmer didn't supply a type annotation.
The second line relies on pattern matching, an important feature of Haskell. Note that parameters of a function are not in parentheses but separated by spaces. When the function's argument is 0 (zero) it will return the integer 1 (one). For all other cases the third line is tried. This is the recursion, and executes the function again until the base case is reached.
A guard protects the third line from negative numbers for which a factorial is undefined. Without the guard this function would, if called with a negative number, recurse through all negative numbers without ever reaching the base case of 0. As it is, the pattern matching is not complete: if a negative integer is passed to the factorial function as an argument, the program will fail with a runtime error. A final case could check for this error condition and print an appropriate error message instead.
Using the product function from the Prelude, a number of small functions analogous to C's standard library, and using the Haskell syntax for arithmetic sequences, the factorial function can be expressed in Haskell as follows:
factorial n = product [1..n]
Here [1..n] denotes the arithmetic sequence 1, 2, …, n in list form. Using the Prelude function enumFromTo, the expression [1..n] can be written as enumFromTo 1 n, allowing the factorial function to be expressed as
factorial n = product (enumFromTo 1 n)
which, using the function composition operator (expressed as a dot in Haskell) to compose the product function with the curried enumeration function can be rewritten in point-free style:[2]
factorial = product . enumFromTo 1
In the Hugs interpreter, one often needs to define the function and use it on the same line separated by a where or let..in. For example, to test the above examples and see the output 120:
let { factorial n | n > 0 = n * factorial (n-1); factorial _ = 1 } in factorial 5
or
factorial 5 where factorial = product . enumFromTo 1
The GHCi interpreter doesn't have this restriction and function definitions can be entered on one line (with the let syntax without the in part), and referenced later.
In the Haskell source immediately below, "::" can be read as "has type"; "a —> b" can be read as "is a function from a to b". (Thus the Haskell "calc :: String —> [Float]" can be read as "calc has type of function from Strings to lists of Floats".) In the second line "calc = ... " the equals sign can be read as "can be"; thus multiple lines with "calc = ... " can be read as multiple possible values for calc, depending on the circumstance detailed in each line.
A simple Reverse Polish notation calculator expressed with the higher-order function foldl whose argument f is defined in a where clause using pattern matching and the type class Read:
calc :: String -> [Float] calc = foldl f [] . words where f (x:y:zs) "+" = (y + x):zs f (x:y:zs) "-" = (y - x):zs f (x:y:zs) "*" = (y * x):zs f (x:y:zs) "/" = (y / x):zs f (x:y:zs) "FLIP" = y:x:zs f xs y = read y : xs
The empty list is the initial state, and f interprets one word at a time, either as a function name, taking two numbers from the head of the list and pushing the result back in, or parsing the word as a floating-point number and prepending it to the list.
The following definition produces the list of Fibonacci numbers in linear time:
fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
The infinite list is produced by corecursion — the latter values of the list are computed on demand starting from the initial two items 0 and 1. This kind of a definition relies on lazy evaluation, an important feature of Haskell programming. For an example of how the evaluation evolves, the following illustrates the values of fibs and tail fibs after the computation of six items and shows how zipWith (+) has produced four items and proceeds to produce the next item:
fibs = 0 : 1 : 1 : 2 : 3 : 5 : ...
+ + + + + +
tail fibs = 1 : 1 : 2 : 3 : 5 : ...
= = = = = =
zipWith ... = 1 : 2 : 3 : 5 : 8 : ...
fibs = 0 : 1 : 1 : 2 : 3 : 5 : 8 : ...
The same function, written using GHC's parallel list comprehension syntax (GHC extensions must be enabled using a special command-line flag '-fglasgow-exts'; see GHC's manual for more):
fibs = 0 : 1 : [ a+b | a <- fibs | b <- tail fibs ]
or with regular list comprehensions:
fibs = 0 : 1 : [ a+b | (a,b) <- zip fibs (tail fibs) ]
or directly self-referencing:
fibs = 0 : 1 : next fibs where next (a: t@(b:_)) = (a+b):next t
With generating function:
fibs = fibgen (0,1) where fibgen (a,b) = a:fibgen (b,a+b)
or with unfoldr:
fibs = unfoldr (\(a,b)->Just(a,(b,a+b))) (0,1)
The factorial we saw previously can be written as a sequence of functions:
factorial n = (foldr (.) id [\x -> x*k | k <- [1..n]]) 1
A remarkably concise function that returns the list of Hamming numbers in order:
hamming = 1 : map (2*) hamming `union` map (3*) hamming `union` map (5*) hamming
Like the various fibs solutions displayed above, this uses corecursion to produce a list of numbers on demand, starting from the base case of 1 and building new items based on the preceding part of the list.
Here the function union is used as an operator by enclosing it in back-quotes. Its case clauses define how it merges two ascending lists into one ascending list without duplicate items. The function name merge ought to be reserved for use with mergesort definition, which ought to be stable (i.e. preserving of the original order of otherwise equal elements in a list to be sorted, so should not skip duplicates). The function minus computes the difference of two ascending lists:
union (x:xs) (y:ys) = case compare x y of LT -> x : union xs (y:ys) EQ -> x : union xs ys GT -> y : union (x:xs) ys union a [] = a union [] b = b minus (x:xs) (y:ys) = case compare x y of LT -> x : minus xs (y:ys) EQ -> minus xs ys GT -> minus (x:xs) ys minus a b = a
Here is that mergesort function, using guards:
mergesortBy less [] = [] mergesortBy less xs = head $ until (null.tail) pairs [[x] | x <- xs] where pairs (x:y:t) = merge x y : pairs t pairs xs = xs merge (x:xs) (y:ys) | less y x = y : merge (x:xs) ys | otherwise = x : merge xs (y:ys) merge xs ys = xs ++ ys
(better, more complex, definition is at Data.List.Ordered package which does much better job at initial partitioning of the list).
Optimal trial division:
primeNums = 2 : [n | n <- [3,5..], isPrime primeNums n] isPrime primes n = foldr (\p r-> p*p>n || (rem n p /= 0 && r)) True primes
Segmented trial division sieve:
primesST () = 2 : primes' where primes' = 3 : sieve 5 9 (tail primes') 0 sieve x q ps k = let fs = take k primes' in [n | n <- [x,x+2..q-2], and [rem n f /= 0 | f <- fs]] ++ sieve (q+2) (head ps^2) (tail ps) (k+1)
A simple sieve of Eratosthenes definition is
primesTo m = 2 : sieve [3,5..m] where sieve (p:xs) | p*p>m = p : xs | True = p : sieve (xs `minus` [p*p, p*p+2*p..])
or a faster one, corecursive and unbounded, with very low space complexity (achieved through double-staged production):
primes () = 2 : ([3,5..] `minus` unionAll [[p*p, p*p+2*p..] | p <- primes']) where primes' = 3 : ([5,7..] `minus` unionAll [[p*p, p*p+2*p..] | p <- primes']) unionAll ((x:xs):t) = x : union xs (unionAll (pairs t)) pairs ((x:xs):ys:t) = (x : union xs ys) : pairs t
where unionAll is equivalent to foldi (\(x:xs) -> (x:) . union xs) [], with foldi a kind of tree-like fold for infinite (i.e. indefinitely defined) lists.
Haskell allows indentation to be used to indicate the beginning of a new declaration. For example, in a where clause:
product xs = prod xs 1 where prod [] a = a prod (x:xs) a = prod xs (a*x)
The two equations for the nested function prod are aligned vertically, which allows the semi-colon separator to be omitted. In Haskell, indentation can be used in several syntactic constructs, including do, let, case, class, and instance.
The use of indentation to indicate program structure originates in Landin's ISWIM language, where it was called the off-side rule. This was later adopted by Miranda, and Haskell adopted a similar (but rather more complicated) version of Miranda's off-side rule, which it called "layout". Other languages to adopt whitespace-sensitive syntax include Python and F#.
The use of layout in Haskell is optional. For example, the function product above can also be written:
product xs = prod xs 1 where { prod [] a = a; prod (x:xs) a = prod xs (a*x) }
The explicit open brace after the where keyword indicates that the programmer has opted to use explicit semi-colons to separate declarations, and that the declaration-list will be terminated by an explicit closing brace. One reason for wanting support for explicit delimiters is that it makes automatic generation of Haskell source code easier.
Haskell's layout rule has been criticised for its complexity. In particular, the definition states that if the parser encounters a parse error during processing of a layout section, then it should try inserting a close brace (the "parse error" rule). Implementing this rule in a traditional parsing/lexical-analysis combination requires two-way cooperation between the parser and lexical analyser, whereas in most languages these two phases can be considered independently.
Applying a function f to a value x is expressed as simply f x.
Haskell distinguishes function calls from infix operators syntactically, but not semantically. Function names which are composed of punctuation characters can be used as operators, as can other function names if surrounded with backticks; and operators can be used in prefix notation if surrounded with parentheses.
This example shows the ways that functions can be called:
add a b = a + b ten1 = 5 + 5 ten2 = (+) 5 5 ten3 = add 5 5 ten4 = 5 `add` 5
Functions which are defined as taking several parameters can always be partially applied. Binary operators can be partially applied using section notation:
ten5 = (+ 5) 5 ten6 = (5 +) 5 addfive = (5 +) ten7 = addfive 5
See List_comprehension#Overview for the Haskell example.
Pattern matching is used to match on the different constructors of algebraic data types. Here are some functions, each using pattern matching on each of the types above:
-- This type signature says that empty takes a list containing any type, and returns a Bool empty :: [a] -> Bool empty (x:xs) = False empty [] = True -- Will return a value from a Maybe a, given a default value in case a Nothing is encountered fromMaybe :: a -> Maybe a -> a fromMaybe x (Just y) = y fromMaybe x Nothing = x isRight :: Either a b -> Bool isRight (Right _) = True isRight (Left _) = False getName :: Person -> String getName (Person name _ _) = name getSex :: Person -> Sex getSex (Person _ sex _) = sex getAge :: Person -> Int getAge (Person _ _ age) = age
Using the above functions, along with the map function, we can apply them to each element of a list, to see their results:
map empty [[1,2,3],[],[2],[1..]] -- returns [False,True,False,False] map (fromMaybe 0) [Just 2,Nothing,Just 109238, Nothing] -- returns [2,0,109238,0] map isRight [Left "hello", Right 6, Right 23, Left "world"] -- returns [False, True, True, False] map getName [Person "Sarah" Female 20, Person "Alex" Male 20, tom] -- returns ["Sarah", "Alex", "Tom"], using the definition for tom above
Tuples in haskell can be used to hold a fixed number of elements. They are used to group pieces of data of differing types:
account :: (String, Integer, Double) -- The type of a three-tuple, representing a name, balance, interest rate account = ("John Smith",102894,5.25)
Tuples are commonly used in the zip* functions to place adjacent elements in separate lists together in tuples (zip4 to zip7 are provided in the Data.List module):
-- The definition of the zip function. Other zip* functions are defined similarly zip :: [x] -> [y] -> [(x,y)] zip (x:xs) (y:ys) = (x,y) : zip xs ys zip _ _ = [] zip [1..5] "hello" -- returns [(1,'h'),(2,'e'),(3,'l'),(4,'l'),(5,'o')] -- and has type [(Integer, Char)] zip3 [1..5] "hello" [False, True, False, False, True] -- returns [(1,'h',False),(2,'e',True),(3,'l',False),(4,'l',False),(5,'o',True)] -- and has type [(Integer,Char,Bool)]
In the GHC compiler, tuples are defined with sizes from 2 elements up to 62 elements.
In the #More_complex_examples section above, calc is used in two senses, showing that there is a Haskell type class namespace and also a namespace for values:
Algebraic data types are used extensively in Haskell. Some examples of these are the built in list, Maybe and Either types:
-- A list of a's ([a]) is either an a consed (:) onto another list of a's, or an empty list ([]) data [a] = a : [a] | [] -- Something of type Maybe a is either Just something, or Nothing data Maybe a = Just a | Nothing -- Something of type Either atype btype is either a Left atype, or a Right btype data Either a b = Left a | Right b
Users of the language can also define their own abstract data types. An example of an ADT used to represent a person's name, sex and age might look like:
data Sex = Male | Female data Person = Person String Sex Int -- Notice that Person is both a constructor and a type -- An example of creating something of type Person tom :: Person tom = Person "Tom" Male 27
The ST monad allows programmers to write imperative algorithms in Haskell, using mutable variables (STRef's) and mutable arrays (STArrays and STUArrays). The advantage of the ST monad is that it allows programmers to write code that has internal side effects, such as destructively updating mutable variables and arrays, while containing these effects inside the monad. The result of this is that functions written using the ST monad appear completely pure to the rest of the program. This allows programmers to produce imperative code where it may be impractical to write functional code, while still keeping all the safety that pure code provides.
Here is an example program (taken from the Haskell wiki page on the ST monad) that takes a list of numbers, and sums them, using a mutable variable:
import Control.Monad.ST import Data.STRef import Control.Monad sumST :: Num a => [a] -> a sumST xs = runST $ do -- runST takes stateful ST code and makes it pure. summed <- newSTRef 0 -- Create an STRef (a mutable variable) forM_ xs $ \x -> do -- For each element of the argument list xs .. modifySTRef summed (+x) -- add it to what we have in n. readSTRef summed -- read the value of n, which will be returned by the runST above.
The STM monad is an implementation of Software Transactional Memory in Haskell. It is implemented in the GHC compiler, and allows for mutable variables to be modified in transactions.
As Haskell is a pure functional language, functions cannot have side effects. Being non-strict, it also does not have a well-defined evaluation order. This is a challenge for real programs, which among other things need to interact with an environment. Haskell solves this with monadic types that leverage the type system to ensure the proper sequencing of imperative constructs. The typical example is I/O, but monads are useful for many other purposes, including mutable state, concurrency and transactional memory, exception handling, and error propagation.
Haskell provides a special syntax for monadic expressions, so that side-effecting programs can be written in a style similar to current imperative programming languages; no knowledge of the mathematics behind monadic I/O is required for this. The following program reads a name from the command line and outputs a greeting message:
main = do putStrLn "What's your name?" name <- getLine putStr ("Hello, " ++ name ++ "!\n")
The do-notation eases working with monads. This do-expression is equivalent to, but (arguably) easier to write and understand than, the de-sugared version employing the monadic operators directly:
main = putStrLn "What's your name?" >> getLine >>= \ name -> putStr ("Hello, " ++ name ++ "!\n")
The Haskell language definition itself does not include either concurrency or parallelism, although GHC supports both.
Concurrent Haskell is an extension to Haskell that provides support for threads and synchronization.[3] GHC's implementation of Concurrent Haskell is based on multiplexing lightweight Haskell threads onto a few heavyweight OS threads,[4] so that Concurrent Haskell programs run in parallel on a multiprocessor. The runtime can support millions of simultaneous threads.[5]
The GHC implementation employs a dynamic pool of OS threads, allowing a Haskell thread to make a blocking system call without blocking other running Haskell threads.[6] Hence the lightweight Haskell threads have the characteristics of heavyweight OS threads, and the programmer is unaware of the implementation details.
Recently, Concurrent Haskell has been extended with support for Software Transactional Memory (STM), which is a concurrency abstraction in which compound operations on shared data are performed atomically, as transactions.[7] GHC's STM implementation is the only STM implementation to date to provide a static compile-time guarantee preventing non-transactional operations from being performed within a transaction. The Haskell STM library also provides two operations not found in other STMs: retry and orElse, which together allow blocking operations to be defined in a modular and composable fashion.