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{{Short description|Functional programming language}}

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{{redirect|Pure (language)|the linguistic notions|Linguistic purism|and|Adamic language}}

{{more footnotes|date=September 2016}}

{{notability|date=September 2016}}

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{{Infobox programming language

|name = Pure

|logo = Pure lang logo.png

|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 = 0.2368

|latest release date = {{Start date and age|20172018|0104|1011|df=yes}}

|typing = [[Strong and weak typing|Strongstrong]], [[Type system#DYNAMIC|dynamic]]

|implementations =

|dialects =

|operating system = [[Cross-platform software|Cross-platform]]: [[FreeBSD]], GNU/[[Linux]], [[macOS]], [[Microsoft Windows|Windows]]

|license = [[GNU Lesser General Public License]]

|influenced by = Q, [[HaskellQ (programming language from Kx Systems)|Q]], [[Haskell]], [[Lisp (programming language)|Lisp]], [[Alice (programming language)|Alice]], [[MATLAB]]

|influenced =

|website = {{URL|https://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 [[operatorOperator (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 and debugger, provides 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 (programming language)|Haskell]], but it is a [[free-format language]] and thus uses explicit delimiters (rather than [[off-side rule]] indents) to denote program structure.

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> createdQ-Equational-Programming-Language formerlyhttps://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 applicationsuses, 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):

<syntaxhighlight lang="q">

<pre>

fib 0 = 0;

fib 1 = 1;

fib n = fib (n-2) + fib (n-1) if n>1;

</syntaxhighlight>

</pre>

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

<syntaxhighlight lang="q">

<pre>

fib n = fibs (0,1) n with

fibs (a,b) n = if n<=0 then a else fibs (b,a+b) (n-1);

end;

</syntaxhighlight>

</pre>

Compute the first 20 Fibonacci numbers:

<syntaxhighlight lang="q">

<pre>

map fib (1..20);

</syntaxhighlight>

</pre>

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

<syntaxhighlight lang="q">

<pre>

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>

</pre>

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">

<pre>

primes = sieve (2..inf) with

sieve (p:qs) = p : sieve [q | q = qs; q mod p] &;

end;

</syntaxhighlight>

</pre>

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">

<pre>

primes!!(0..99); // yields the first 100 primes

</syntaxhighlight>

</pre>

Pure has efficient support for vectors and matrices (similar to that of [[MATLAB]] and [[GNU Octave]]), including vector and matrix comprehensions. E.g., a [[Gaussian elimination]] algorithm with [[partial pivoting]] can be implemented in Pure thusly:

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>

<pre>

gauss_elimination x::matrix = p,x

when n,m = dim x; p,_,x = foldl step (0..n-1,0,x) (0..m-1) end;

step (p,i,x) j

= if max_x==0 then p,i,x else

// updated row permutation and index:

transp i max_i p, i+1,

{// the top rows of the matrix remain unchanged:

x!!(0..i-1,0..m-1);

// the pivot row, divided by the pivot element:

{x!(i,l)/x!(i,j) | l=0..m-1};

// subtract suitable multiples of the pivot row:

{{x!(k,l)-x!(k,j)*x!(i,l)/x!(i,j) | k=i+1..n-1; l=0..m-1}}

when

n,m = dim x; max_i, max_x = pivot i (col x j);

x = if max_x>0 then swap x i max_i else x;

end with

pivot i x = foldl max (0,0) [j,abs (x!j)|j=i..#x-1];

max (i,x) (j,y) = if x<y then j,y else i,x;

end;

/* Swap rows i and j of the matrix x. */

swap x i j = x!!(transp i j (0..n-1),0..m-1) when n,m = dim x end;

/* Apply a transposition to a permutation. */

transp i j p = [p!tr k | k=0..#p-1]

with tr k = if k==i then j else if k==j then i else k end;

/* Example: */

let x = dmatrix {2,1,-1,8; -3,-1,2,-11; -2,1,2,-3};

x; gauss_elimination x;

</pre>

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">

<pre>

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

</pre>

factor = reduce with

Calling [[C (programming language)|C]] functions from Pure is very easy. E.g., 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:

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==

Line 149 ⟶ 139:

* [[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|purelanghttps://agraef.bitbucketgithub.io/pure-lang}}

* [https://github.com/agraef/pure-lang Pure at Github]

* [http://puredocs.bitbucket.org/ Pure language and library documentation]

* [httphttps://purelangagraef.bitbucketgithub.org/quickrefio/pure-quickrefdocs/pure.pdfhtml The Pure quickManual reference(html)]

* [httphttps://codeagraef.googlegithub.com/pio/pure-langdocs/wiki/PurePrimer0purelib.html The Pure PrimerLibrary 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]

{{Programming languages}}