Pure (programming language)

{{Short description|Functional programming language}} {{redirect|Pure (language)|the linguistic notions|Linguistic purism|and|Adamic language}} {{Infobox programming language |name = Pure |logo = |screenshot = Pure with texmacs.png |screenshot caption = Using Pure with [[TeXmacs]] |paradigm = [[Functional programming|Functional]], [[Declarative programming|declarative]], [[term rewriting]] |designer = Albert Gräf |developer = Albert Gräf |released = {{Start date and age|2008}} |latest release version = 0.68 |latest release date = {{Start date and age|2018|04|11|df=yes}} |typing = [[Strong and weak typing|strong]], [[Type system#DYNAMIC|dynamic]] |implementations = |dialects = |operating system = [[Cross-platform software|Cross-platform]]: [[FreeBSD]], [[Linux]], [[macOS]], [[Microsoft Windows|Windows]] |license = [[GNU Lesser General Public License]] |influenced by = Q (equational language), [[Haskell]], [[Lisp (programming language)|Lisp]], [[Alice (programming language)|Alice]], [[MATLAB]] |influenced = |website = {{URL|agraef.github.io/pure-lang}} }}

'''Pure''', successor to the equational language '''Q''', is a dynamically typed, [[Functional programming|functional]] [[programming language]] based on [[term rewriting]]. It has facilities for user-defined [[Operator (computer programming)|operator]] [[Syntax (programming languages)|syntax]], [[Macro (computer science)|macros]], [[arbitrary-precision arithmetic]] (multiple-precision numbers), and compiling to native code through the [[LLVM]]. Pure is [[free and open-source software]] distributed (mostly) under the [[GNU Lesser General Public License]] version 3 or later.

== Overview == Pure comes with an [[Interpreter (computing)|interpreter]] and [[debugger]], provides [[Garbage collection (computer science)|automatic memory management]], has powerful functional and symbolic programming abilities, and interfaces to [[Library (computing)|libraries]] in [[C (programming language)|C]] (e.g., for numerics, low-level protocols, and other such tasks). At the same time, Pure is a ''small'' language designed from scratch; its interpreter is not large, and the library modules are written in Pure. The syntax of Pure resembles that of [[Miranda (programming language)|Miranda]] and [[Haskell]], but it is a [[free-format language]] and thus uses explicit [[delimiter]]s (rather than [[off-side rule]] indents) to denote program structure.

The Pure language is a successor of the equational programming language Q,<ref> Q-Equational-Programming-Language https://q-lang.sourceforge.net/</ref> previously created by the same author, Albert Gräf at the [[University of Mainz]], Germany. Relative to Q, it offers some important new features (such as local functions with [[lexical scoping]], efficient vector and matrix support, and the built-in C interface) and programs run much faster as they are [[Just-in-time compilation|compiled just-in-time]] to native code on the fly. Pure is mostly aimed at mathematical applications and [[scientific computing]] currently, but its interactive interpreter environment, the C interface and the growing set of addon modules make it suitable for a variety of other uses, such as [[artificial intelligence]], symbolic computation,<ref>{{Cite web |title=REDUCE Related Projects |url=https://reduce-algebra.sourceforge.io/projects.php |access-date=2025-01-19 |website=REDUCE Computer Algebra System}}</ref> and real-time multimedia processing <ref>FAUST https://faust.grame.fr/.</ref>

Pure [[Plug-in (computing)|plug-ins]] are available for the [[Gnumeric]] spreadsheet and Miller Puckette's [[Pure Data]] graphical multimedia software, which make it possible to extend these programs with functions written in the Pure language. Interfaces are also provided as library modules to [[GNU Octave]], [[OpenCV]], [[OpenGL]], the [[GNU Scientific Library]], [[FAUST (programming language)|FAUST]], [[SuperCollider]], and liblo (for [[Open Sound Control]] (OSC)).

==Examples== The [[Fibonacci numbers]] (naive version):

Better ([[tail-recursive]] and [[linear-time]]) version:

Compute the first 20 Fibonacci numbers:

An [[algorithm]] for the [[Eight queens puzzle|n queens problem]] which employs a [[list comprehension]] to organize the backtracking search:

<syntaxhighlight lang="q"> queens n = search n 1 [] with search n i p = [reverse p] if i>n; = cat [search n (i+1) ((i,j):p) | j = 1..n; safe (i,j) p]; safe (i,j) p = ~any (check (i,j)) p; check (i1,j1) (i2,j2) = i1==i2 || j1==j2 || i1+j1==i2+j2 || i1-j1==i2-j2; end; </syntaxhighlight>

While Pure uses [[eager evaluation]] by default, it also supports [[Lazy evaluation|lazy]] data structures such as streams (lazy [[List (computing)|lists]]). For instance, [[David Turner (computer scientist)|David Turner]]'s algorithm<ref>Turner, David A. SASL language manual. Tech. rept. CS/75/1. Department of Computational Science, University of St. Andrews 1975.</ref> for computing the stream of [[prime numbers]] by [[trial division]] can be expressed in Pure:

<syntaxhighlight lang="q"> primes = sieve (2..inf) with sieve (p:qs) = p : sieve [q | q = qs; q mod p] &; end; </syntaxhighlight>

Use of the <code>&</code> operator turns the tail of the sieve into a [[thunk]] to delay its computation. The thunk is evaluated implicitly and then [[Memoization|memoized]] (using [[call by need]] evaluation) when the corresponding part of the list is accessed, e.g.:

<syntaxhighlight lang="q"> primes!!(0..99); // yields the first 100 primes </syntaxhighlight>

Pure has efficient support for vectors and matrices (similar to that of [[MATLAB]] and [[GNU Octave]]), including vector and matrix comprehensions.

Namespaces, types and interfaces belong to the standard repertoire:

<syntaxhighlight lang="q"> nonfix nil; type bintree nil | bintree (bin x left right);

outfix « »; namespace foo (« »); infixr (::^) ^; x^y = 2*x+y; namespace;

interface stack with push s::stack x; pop s::stack; top s::stack; end;

type stack [];

push xs@[] x | push xs@(_:_) x = x:xs; pop (x:xs) = xs; top (x:xs) = x; </syntaxhighlight>

As a language based on [[term rewriting]], Pure fully supports [[symbolic computation]] with expressions. Here is an example showing the use of local rewriting rules to [[polynomial expansion|expand]] and [[factorization|factor]] simple arithmetic expressions:

<syntaxhighlight lang="q"> expand = reduce with (a+b)*c = a*c+b*c; a*(b+c) = a*b+a*c; end;

factor = reduce with a*c+b*c = (a+b)*c; a*b+a*c = a*(b+c); end;

expand ((a+b)*2); // yields a*2+b*2 factor (a*2+b*2); // yields (a+b)*2 </syntaxhighlight>

Calling [[C (programming language)|C]] functions from Pure is very easy. E.g., for a [["Hello, World!" program]], the following imports the <code>puts</code> function from the [[C library]] and uses it to print the string <code>"Hello, world!"</code> on the terminal:

<syntaxhighlight lang="c"> extern int puts(char*); hello = puts "Hello, world!"; hello; </syntaxhighlight>

Instead of manually compiling source files to LLVM bitcode modules, one can also place the source code into a Pure script, enclosing it in %< ... %> (inline code, e.g. C, Fortran 77/90 and so on).

==See also== {{Portal|Free and open-source software}} * [[Functional programming]] * [[:Category: Functional languages|Functional languages]] * [[Clean (programming language)]]

== References == * Albert Gräf. "Signal Processing in the Pure Programming Language". ''Linux Audio Conference 2009''. * Michael Riepe. [http://www.heise.de/ix/artikel/Rein-ins-Vergnuegen-856225.html "Pure – eine einfache funktionale Sprache"] {{Webarchive|url=https://web.archive.org/web/20110319165239/http://www.heise.de/ix/artikel/Rein-ins-Vergnuegen-856225.html |date=2011-03-19 }}. ''Heise''. * [https://web.archive.org/web/20130808212022/http://blueparen.com/node/6 "Interview With Albert Gräf"]. blueparen. * Mark Boady, [https://www.cs.drexel.edu/~mwb33/posters/teach_pres/mwb33_teaching_presentation.pdf Introduction to Term Rewrite Systems and their Applications]

== Notes == {{Reflist}}

==External links== * {{Official website|https://agraef.github.io/pure-lang}} * [https://github.com/agraef/pure-lang Pure at Github] * [https://agraef.github.io/pure-docs/pure.html The Pure Manual (html)] * [https://agraef.github.io/pure-docs/purelib.html The Pure Library Manual (html)] * [https://agraef.github.io/pure-docs/ Documentation Overview (html)] * [https://agraef.github.io/pure-docs/pure-reduce.html Computer Algebra with Pure: A Reduce Interface] * [https://agraef.github.io/pure-lang/quickref/pure-quickref.pdf Pure quick reference] * [https://github.com/agraef/pure-lang/wiki/UsingPure Using the Pure Interpreter] * [https://github.com/agraef/pure-lang/wiki/TeXmacs Using Pure with TeXmacs] * [https://github.com/agraef/pure-lang/wiki/pure-texmacs.en.pdf The Pure TeXmacs Plugin]

[[Category:Dynamically typed programming languages]] [[Category:Functional languages]] [[Category:Term-rewriting programming languages]] [[Category:Programming languages created in 2008]] [[Category:High-level programming languages]] [[Category:2008 software]] [[Category:Cross-platform free software]] [[Category:Cross-platform software]]  [[Category:Articles with example code]]