Definitions

# recurse

Haskell is a standardized purely functional programming language with non-strict semantics, named after the logician Haskell Curry.

## History

Following the release of Miranda by Research Software Ltd, in 1985, interest in lazy functional languages proliferated. By 1987, more than a dozen non-strict, purely functional programming languages existed. Of these Miranda was much the most widely used, but was not in the public domain. At the conference on Functional Programming Languages and Computer Architecture (FPCA '87) in Portland, Oregon, a meeting was held during which strong consensus was found among the participants that a committee should be formed to define an open standard for such languages. This would have the express purpose of consolidating the existing languages into a common one that would serve as a basis for future research in language design. The first version of Haskell ("Haskell 1.0") was defined in 1990. The committee's efforts resulted in a series of language definitions, which in late 1997, culminated in Haskell 98, intended to specify a stable, minimal, portable version of the language and an accompanying standard library for teaching, and as a base for future extensions. The committee expressly welcomed the creation of extensions and variants of Haskell 98 via adding and incorporating experimental features.

In January 1999, the Haskell 98 language standard was originally published as "The Haskell 98 Report". In January 2003, a revised version was published as "Haskell 98 Language and Libraries: The Revised Report". The language continues to evolve rapidly, with the Hugs and GHC implementation (see below) representing the current de facto standard. In early 2006, the process of defining a successor to the Haskell 98 standard, informally named Haskell′ ("Haskell Prime"), was begun. This process is intended to produce a minor revision of Haskell 98.

## Features and extensions

Characteristic features of Haskell include pattern matching, currying, list comprehensions , guards, definable operators, and single assignment. The language also supports recursive functions and algebraic data types, as well as lazy evaluation. Unique concepts include monads, and type classes. The combination of such features can make functions which would be difficult to write in a procedural programming language almost trivial to implement in Haskell.

Several variants have been developed: parallelizable versions from MIT and Glasgow University, both called Parallel Haskell; more parallel and distributed versions called Distributed Haskell (formerly Goffin) and Eden; a speculatively evaluating version called Eager Haskell and several object oriented versions: Haskell++, O'Haskell and Mondrian.

Concurrent Clean is a close relative of Haskell, whose biggest deviation from Haskell is in the use of uniqueness types for input instead of monads.

## Applications

Haskell's strengths have been well applied to a few projects. Audrey Tang's Pugs is an implementation for the long-forthcoming Perl 6 language with an interpreter and compilers that proved useful already after just a few months of its writing; similarly, GHC is often a testbed for advanced functional programming features and optimizations. Darcs is a revision control system, with several innovative features. Linspire GNU/Linux chose Haskell for system tools development. Xmonad is a window manager for the X Window System, written entirely in Haskell. Bluespec SystemVerilog is a language for semiconductor design that is an extension of Haskell. Additionally, Bluespec, Inc.'s tools are implemented in Haskell.

## Examples

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 types of this function; while it is optional, it is considered to be good style 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 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 fac 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.

The "Prelude" is a number of small functions analogous to C's standard library. Using the Prelude and writing in the point-free style of unspecified arguments, it becomes:

`fac = product . enumFromTo 1`

The above is close to mathematical definitions such as $f = g circ h$ (see function composition) with the dot acting as the function composition operator, and indeed, it is not an assignment of a numeric value to a variable.

In the Hugs interpreter, you often need to define the function and use it on the same line separated by a where or let..in, meaning you need to enter this to test the above examples and see the output 120: let { fac 0 = 1; fac n | n > 0 = n * fac (n-1) } in fac 5 or

`fac 5 where fac = product . enumFromTo 1`

The GHCi interpreter doesn't have this restriction and function definitions can be entered on one line and referenced later.

### More complex examples

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 xs y = read y : xs`

The empty list is the initial state, and f interprets one word at a time, either matching 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 ]`

The factorial we saw previously can be written as a sequence of functions:

`fac n = (foldl (.) 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 `merge` map (3*) hamming `merge` map (5*) hamming`
`     where merge (x:xs) (y:ys)`
`            | x < y = x : xs `merge` (y:ys)`
`            | x > y = y : (x:xs) `merge` ys`
`            | otherwise = x : xs `merge` ys`

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.

In this case the producer `merge` is defined in a `where` clause and used as an operator by enclosing it in back-quotes. The branches of the guards define how `merge` merges two ascending lists into one ascending list without duplicate items.

## Criticism

Jan-Willem Maessen, in 2002, and Simon Peyton Jones, in 2003, discussed problems associated with lazy evaluation while also acknowledging the theoretical motivation for it, in addition to purely practical considerations such as improved performance. They note that, in addition to adding some performance overhead, laziness makes it more difficult for programmers to reason about the performance of their code (specifically with regard to space usage).

Bastiaan Heeren, Daan Leijen, and Arjan van IJzendoorn in 2003 also observed some stumbling blocks for Haskell learners, "The subtle syntax and sophisticated type system of Haskell are a double edged sword—highly appreciated by experienced programmers but also a source of frustration among beginners, since the generality of Haskell often leads to cryptic error messages." To address these, they developed an advanced interpreter called Helium which improved the user-friendliness of error messages by limiting the generality of some Haskell features, and in particular removing support for type classes.

## Implementations

• The Glasgow Haskell Compiler compiles to native code on a number of different architectures—as well as to ANSI C—using C-- as an intermediate language. GHC is probably the most popular Haskell compiler, and there are quite a few useful libraries (e.g. bindings to OpenGL) that will work only with GHC.
• Gofer was an educational dialect of Haskell, with a feature called "constructor classes", developed by Mark Jones. It was supplanted by Hugs (see below).
• is another native-code Haskell compiler. It has not been actively developed for some time but is still usable.
• Helium is a newer dialect of Haskell. The focus is on making it easy to learn by providing clearer error messages. It currently lacks typeclasses, rendering it incompatible with many Haskell programs.
• Hugs, the Haskell User's Gofer System, is a bytecode interpreter. It offers fast compilation of programs and reasonable execution speed. It also comes with a simple graphics library. Hugs is good for people learning the basics of Haskell, but is by no means a "toy" implementation. It is the most portable and lightweight of the Haskell implementations.
• is a Haskell compiler written by John Meacham emphasising speed and efficiency of generated programs as well as exploration of new program transformations.
• is another bytecode compiler, but the bytecode runs significantly faster than with Hugs. Nhc98 focuses on minimizing memory usage, and is a particularly good choice for older, slower machines.
• Yhc, the York Haskell Compiler is a fork of nhc98, with the goals of being simpler, more portable, more efficient, and integrating support for Hat, the Haskell tracer. It also features a JavaScript backend allowing users to run Haskell programs in a web browser