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<title>Unlambda</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Unlambda</span></span>

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</style><table class="infobox vevent"><tbody><tr><th colspan="2" class="infobox-above" style="background-color:#e0e0e0;">Unlambda</th></tr><tr><th scope="row" class="infobox-label"><a href="Programming_paradigm" title="Programming paradigm">Paradigm</a></th><td class="infobox-data">Nearly <a href="Purely_functional_programming" title="Purely functional programming">pure</a> <a href="Functional_programming" title="Functional programming">functional</a></td></tr><tr><th scope="row" class="infobox-label"><a href="Software_design" title="Software design">Designed by</a></th><td class="infobox-data">David Madore</td></tr><tr><th scope="row" class="infobox-label"><a href="Software_developer" class="mw-redirect" title="Software developer">Developer</a></th><td class="infobox-data organiser">David Madore</td></tr><tr><th scope="row" class="infobox-label">First appeared</th><td class="infobox-data">28 June 1999<span style="display:none"> (<span class="bday dtstart published updated">1999-06-28</span>)</span></td></tr><tr><td colspan="2" class="infobox-full-data"></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="Software_release_life_cycle" title="Software release life cycle">Stable release</a></th><td class="infobox-data"><div style="margin:0px;">2.0.0

/ 20 December 1999<span style="display:none"> (<span class="bday dtstart published updated">1999-12-20</span>)</span></div></td></tr><tr style="display:none"><td colspan="2">

</td></tr><tr><th scope="row" class="infobox-label"><a href="Type_system" title="Type system">Typing discipline</a></th><td class="infobox-data"><a href="Type_system" title="Type system">Untyped</a></td></tr><tr><th scope="row" class="infobox-label">Implementation language</th><td class="infobox-data"><a href="Scheme_(programming_language)" title="Scheme (programming language)">Scheme</a>, <a href="C_(programming_language)" title="C (programming language)">C</a>, <a href="Java_(programming_language)" title="Java (programming language)">Java</a></td></tr><tr><th scope="row" class="infobox-label"><a href="Software_license" title="Software license">License</a></th><td class="infobox-data"><a href="GNU_General_Public_License" title="GNU General Public License">GPL</a> 2.0 or later</td></tr><tr><th scope="row" class="infobox-label">Website</th><td class="infobox-data"><span class="url"><a rel="nofollow" class="external text" href="http://www.madore.org/~david/programs/unlambda">www<wbr>.madore<wbr>.org<wbr>/~david<wbr>/programs<wbr>/unlambda</a></span></td></tr></tbody></table>

<p><b>Unlambda</b> is a minimal, "nearly <a href="Purely_functional_language" class="mw-redirect" title="Purely functional language">pure</a>"<sup id="cite_ref-chu2006_1-0" class="reference"><a href="#cite_note-chu2006-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <a href="Functional_programming_language" class="mw-redirect" title="Functional programming language">functional programming language</a> invented by David Madore. It is based on <a href="Combinatory_logic" title="Combinatory logic">combinatory logic</a>, an expression system without the <a href="Lambda_calculus" title="Lambda calculus">lambda operator</a> or free variables. It relies mainly on two built-in functions (<code>s</code> and <code>k</code>) and an apply operator (written <code>`</code>, the <a href="Backquote" class="mw-redirect" title="Backquote">backquote</a> character). These alone make it <a href="Turing-complete" class="mw-redirect" title="Turing-complete">Turing-complete</a>, but there are also some <a href="Input/output" title="Input/output">input/output</a> (I/O) functions to enable interacting with the user, some shortcut functions, and a <a href="Lazy_evaluation" title="Lazy evaluation">lazy evaluation</a> function. Variables are unsupported.

</p><p>Unlambda is <a href="Free_and_open-source_software" title="Free and open-source software">free and open-source software</a> distributed under a <a href="GNU_General_Public_License" title="GNU General Public License">GNU General Public License</a> (GPL) 2.0 or later.

</p>

<div class="mw-heading mw-heading2"><h2 id="Basic_principles">Basic principles</h2></div>

<p>As an <a href="Esoteric_programming_language" title="Esoteric programming language">esoteric programming language</a>, Unlambda is meant as a demonstration of very pure functional programming rather than for practical use. Its main feature is the lack of conventional operators and data types—the only kind of data in the program are one-parameter functions. Data can nevertheless be simulated with appropriate functions as in the <a href="Lambda_calculus" title="Lambda calculus">lambda calculus</a>. Multi-parameter functions can be represented via the method of <a href="Currying" title="Currying">currying</a>.

</p><p>Unlambda is based on the principle of <a href="Abstraction_elimination" class="mw-redirect" title="Abstraction elimination">abstraction elimination</a>, or the elimination of all saved variables, including functions. As a purely functional language, Unlambda's functions are <a href="First-class_object" class="mw-redirect" title="First-class object">first-class objects</a>, and are the <i>only</i> such objects.

</p><p>Here is an implementation of a <a href="Hello_world_program" class="mw-redirect" title="Hello world program">hello world program</a> in Unlambda:<sup id="cite_ref-chu2006_1-1" class="reference"><a href="#cite_note-chu2006-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

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<pre>`r```````````.H.e.l.l.o. .w.o.r.l.di

</pre>

<div class="mw-heading mw-heading2"><h2 id="Original_built-in_functions">Original built-in functions</h2></div>

<p>The notation <code>.<i>x</i></code> denotes a function which takes one argument and returns it unchanged, printing the single character <i>x</i> as a side effect when it is invoked. <code>i</code> represents the version of the identity function that has no such side effect; it is used here as a dummy argument. The program <code>`.di</code> applies the <code>d</code>-printing function to a dummy argument of <code>i</code>, returning <code>i</code> and printing the letter <code>d</code> as a side effect. Similarly, <code>``.l.di</code> first applies <code>.l</code> to <code>.d</code>, printing the letter <code>l</code> and returning <code>.d</code>; this result of <code>.d</code> is then applied to <code>i</code> as in the previous example. The function <code>r</code> is <a href="Syntactic_sugar" title="Syntactic sugar">syntactic sugar</a> for the function that prints a newline character.

</p><p>Other important features provided by Unlambda include the <code>k</code> and <code>s</code> functions. <code>k</code> manufactures constant functions: the result of <code>`k<i>x</i></code> is a function which, when invoked, returns <i>x</i>. Thus the value of <code>``k<i>xy</i></code> is <i>x</i> for any <i>x</i> and <i>y</i>.

</p><p><code>s</code> is a generalized evaluation operator. <code>```s<i>xyz</i></code> evaluates to <code>``<i>xz</i>`<i>yz</i></code> for any <i>x</i>, <i>y</i>, and <i>z</i>. It is a remarkable fact that <code>s</code> and <code>k</code> are sufficient to perform any calculation, as described in <a href="SKI_combinator_calculus" title="SKI combinator calculus">SKI combinator calculus</a>. As a brief example, the identity function <code>i</code> can be implemented as <code>``skk</code>, since <code>```skk<i>x</i></code> yields <i>x</i> for all <i>x</i>.

</p><p>Unlambda's one flow control construct is <a href="Call_with_current_continuation" class="mw-redirect" title="Call with current continuation">call with current continuation</a>, denoted <code>c</code>. When an expression of the form <code>`c<i>x</i></code> is evaluated, a special <i>continuation</i> object is constructed, representing the state of the interpreter at that moment. Then <i>x</i> is evaluated, and then the result is given the continuation object as an argument. If the continuation is never applied to an argument, the value of the <code>`c<i>x</i></code> expression is the same as the value of <i>x</i>. But if the continuation object is applied to a value <i>y</i>, execution of <i>x</i> is immediately aborted, and the value of the entire <code>`c<i>x</i></code> expression is <i>y</i>.

</p><p>Unlambda's execution semantics are normally <a href="Eager_evaluation" class="mw-redirect" title="Eager evaluation">eager evaluation</a>, but a <a href="Lazy_evaluation" title="Lazy evaluation">lazy evaluation</a> option exists, indicated by the use of the <code>d</code> operator. Usually, to evaluate an expression of the form <code>`<i>xy</i></code>, unlambda first evaluates <i>x</i>, then <i>y</i>, and then applies <i>x</i> to <i>y</i>. However, if <i>x</i> evaluates to the special value <code>d</code>, then <i>y</i> is <i>not</i> evaluated; instead, the value of the expression <code>`d<i>y</i></code> is a special "delayed computation" object, which, when applied to an argument <i>z</i>, evaluates <i>y</i>, and then applies its value to <i>z</i>. In the absence of side effects, this is exactly the same as <code>`i<i>y</i></code>. The difference is that <code>`i<i>y</i></code> executes any side effects in <i>y</i> immediately, whereas <code>`d<i>y</i></code> defers the side effects until the result is applied to another argument.

</p><p>Unlambda's next built-in operator is <code>v</code>, which ignores its argument and returns <code>v</code>. This feature is not strictly necessary, since <code>v</code> could be implemented as <code>``s`k``s``s`kskk`k``s``s`kskk</code>, but it is supplied as a convenience. (This expression above is simply <code>`Yk</code>, where <code>Y</code> denotes a <a href="Fixed_point_combinator" class="mw-redirect" title="Fixed point combinator">fixed point combinator</a>.)

</p>

<div class="mw-heading mw-heading2"><h2 id="Version_2_built-in_functions">Version 2 built-in functions</h2></div>

<p>More built-ins were introduced in Unlambda version 2. <a href="Input/output" title="Input/output">Input</a> is facilitated by operators <code>@</code> and <code>?<i>u</i></code>. When <code>@</code> is applied to a function <i>x</i>, a character is read from input, and stored as the "current character"; then <i>x</i> is applied to <code>i</code>. However, if no more characters were available on input, the <i>current character</i> is left undefined, and <i>x</i> is applied to <code>v</code> instead. When a function <code>?<i>u</i></code> is applied to a function <i>x</i>, the result is the evaluation of <code>`<i>x</i>i</code> if the current character is <i>u</i>, otherwise <code>`<i>x</i>v</code> is evaluated.

</p><p>There is also a "reprint" operator <code>|</code>. When <code>`|<i>x</i></code> is evaluated, the function <i>x</i> is applied to <code>.<i>u</i></code> if <i>u</i> is the current character, or to <code>v</code> if there is no current character.

</p><p>Finally, there is an exit operator <code>e</code>. When <code>e</code> is applied to <i>x</i>, the execution of the program is terminated, and <i>x</i> is taken as the result of the program (most of the currently existing interpreters ignore the result anyway).

</p>

<li><a href="SKI_combinator_calculus" title="SKI combinator calculus">SKI combinator calculus</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFChu-Carroll2006" class="citation web cs1">Chu-Carroll, Mark C. (2006-08-11). <a rel="nofollow" class="external text" href="http://scienceblogs.com/goodmath/2006/08/11/friday-pathological-programmin-3/">"Friday Pathological Programming: Unlambda, or Programming Without Variables"</a>. <i>Good Math, Bad Math (blog)</i>. ScienceBlogs.</cite></span>

</li>

</ol></div></div>

<ul><li>Felix-Hernandez Campos (1 April 2002), <i><a rel="nofollow" class="external text" href="http://www.cs.unc.edu/~stotts/144/lectures/lect28apr.pdf">Lecture 28: More on functional programming</a></i>, University of North Carolina COMP144</li>

<li><cite id="CITEREF原_悠_(Yutaka_Hara)2008" class="citation book cs1 cs1-prop-foreign-lang-source">原悠 (Yutaka Hara) (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=LlR6__OpAxoC&dq=%22Unlambda%22&pg=PA205"><i>Rubyで作る奇妙なプログラミング言語</i></a> (in Japanese). Tōkyō: Mainichikomyunikēshonzu. pp. <span class="nowrap">205–</span>214. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-4-8399-2784-4</bdi>.</cite><span class="cs1-maint citation-comment"><code class="cs1-code">{{cite book}}</code>: CS1 maint: publisher location (link)</span></li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><span class="official-website"><span class="url"><a rel="nofollow" class="external text" href="http://www.madore.org/~david/programs/unlambda">Official website</a></span></span></li></ul>

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</style><div id="Esoteric_programming_languages165" style="font-size:114%;margin:0 4em"><a href="Esoteric_programming_language" title="Esoteric programming language">Esoteric programming languages</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Beatnik_(programming_language)" title="Beatnik (programming language)">Beatnik</a></li>

<li><a href="Befunge" title="Befunge">Befunge</a></li>

<li><a href="Brainfuck" title="Brainfuck">Brainfuck</a></li>

<li><a href="FRACTRAN" title="FRACTRAN">FRACTRAN</a></li>

<li><a href="INTERCAL" title="INTERCAL">INTERCAL</a></li>

<li><a href="JSFuck" title="JSFuck">JSFuck</a></li>

<li><a href="LOLCODE" title="LOLCODE">LOLCODE</a></li>

<li><a href="Malbolge" title="Malbolge">Malbolge</a></li>

<li><a href="One-instruction_set_computer" title="One-instruction set computer">One-instruction set computer</a></li>

<li><a href="Shakespeare_Programming_Language" title="Shakespeare Programming Language">Shakespeare Programming Language</a></li>

<li><a href="Whitespace_(programming_language)" title="Whitespace (programming language)">Whitespace</a></li></ul>

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