<!DOCTYPE html>
<html class="client-nojs vector-feature-night-mode-disabled vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-sticky-header-enabled" lang="en" dir="ltr"><head>
<meta charset="UTF-8">
<title>Applicative computing systems</title>
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<link rel="canonical" href="https://en.wikipedia.org/wiki/Applicative_computing_systems"> <link href="./mw/ext.cite.styles.css" rel="stylesheet" type="text/css">
<link href="./mw/skins.vector.icons.css" rel="stylesheet" type="text/css">
<link href="./mw/skins.vector.search.codex.styles.css" rel="stylesheet" type="text/css">
<link href="./mw/skins.vector.styles.css" rel="stylesheet" type="text/css">
<link href="./mw/user.styles.css" rel="stylesheet" type="text/css">
<meta name="ResourceLoaderDynamicStyles" content="">
<link rel="stylesheet" type="text/css" href="./mw/site.styles.css">
<link rel="stylesheet" type="text/css" href="./mw/noscript.css">
<link rel="stylesheet" type="text/css" href="./footer.css">
<link rel="stylesheet" type="text/css" href="./vector-2022.css">
</head>
<body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Applicative_computing_systems rootpage-Applicative_computing_systems skin-vector-2022 action-view">
<div class="mw-page-container">
<div class="mw-page-container-inner">
<div class="mw-content-container">
<main id="content" class="mw-body">
<header class="mw-body-header vector-page-titlebar">
<h1 id="firstHeading" class="firstHeading mw-first-heading">
<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Applicative computing systems</span></span>
</h1>
</header>
<a id="top"></a>
<div id="bodyContent" class="vector-body ve-init-mw-desktopArticleTarget-targetContainer" aria-labelledby="firstHeading" data-mw-ve-target-container="">
<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="en" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p><b>Applicative computing systems</b>, or <b>ACS</b> are the systems of object calculi founded on <a href="Combinatory_logic" title="Combinatory logic">combinatory logic</a> and <a href="Lambda_calculus" title="Lambda calculus">lambda calculus</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>
The only essential notion which is under consideration in these systems is the representation of <a href="Object_(computer_science)" title="Object (computer science)">object</a>. In <a href="Combinatory_logic" title="Combinatory logic">combinatory logic</a> the only metaoperator is <a href="Function_application" title="Function application">application</a> in a sense of applying one object to other. In <a href="Lambda_calculus" title="Lambda calculus">lambda calculus</a> two metaoperators are used: <a href="Function_application" title="Function application">application</a> – the same as in combinatory logic, and <a href="Functional_abstraction" class="mw-redirect" title="Functional abstraction">functional abstraction</a> which binds the only variable in one object.
</p>
<meta property="mw:PageProp/toc">
<div class="mw-heading mw-heading2"><h2 id="Features">Features</h2></div>
<p>The objects generated in these systems are the functional entities with the following features:
</p>
<ol><li>the number of argument places, or object arity is not fixed but is enabling step by step in interoperations with other objects;</li>
<li>in a process of generating the compound object one of its counterparts—function—is applied to other one—argument—but in other contexts they can change their roles, i.e. functions and arguments are considered on the equal rights;</li>
<li>the self-applying of functions is allowed, i.e. any object can be applied to itself.</li></ol>
<p>ACS give a sound ground for <a href="Applicative_programming_language" title="Applicative programming language">applicative approach</a> to programming.
</p>
<div class="mw-heading mw-heading2"><h2 id="Research_challenge">Research challenge</h2></div>
<p>Applicative computing systems' lack of storage and history sensitivity is the basic reason they have not provided a foundation for computer design. Moreover, most applicative systems employ the substitution operation of the <a href="Lambda_calculus" title="Lambda calculus">lambda calculus</a> as their basic operation. This operation is one of virtually unlimited power, but its complete and efficient realization presents great difficulties to the machine designer.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="Applicative_programming_language" title="Applicative programming language">Applicative programming language</a></li>
<li><a href="Categorical_abstract_machine" title="Categorical abstract machine">Categorical abstract machine</a></li>
<li><a href="Combinatory_logic" title="Combinatory logic">Combinatory logic</a></li>
<li><a href="Functional_programming" title="Functional programming">Functional programming</a></li>
<li><a href="Lambda_calculus" title="Lambda calculus">Lambda calculus</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
<div class="mw-references-wrap"><ol class="references">
<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Wolfengagen V.E. <i>Methods and means for computations with objects. Applicative Computational Systems.</i> — M.: JurInfoR Ltd., «Center JurInfoR», 2004. — xvi+789 pp. <style data-mw-deduplicate="TemplateStyles:r1238218222">
/* start https://en.wikipedia.org/ */
.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("./mw/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("./mw/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("./mw/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("./mw/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}
/* end https://en.wikipedia.org/ */
</style><a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>5-89158-100-0</bdi>.</span>
</li>
<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFBackus1978" class="citation journal cs1"><a href="John_Backus" title="John Backus">Backus, J.</a> (1978). <a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F359576.359579">"1977 Turing Award Lecture: Can Programming Be Liberated from the von Neumann Style? A Functional Style and Its Algebra of Programs"</a>. <i>Commun. ACM</i>. <b>2</b> (8): <span class="nowrap">613–</span>641. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F359576.359579">10.1145/359576.359579</a></span>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:16367522">16367522</a>.</cite></span>
</li>
</ol></div>
<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>
<ul><li><cite id="CITEREFHindleySeldin1980" class="citation cs2"><a href="J._Roger_Hindley" title="J. Roger Hindley">Hindley, J. Roger</a>; Seldin, Jonathan P., eds. (September 1980), <i>To H. B. Curry: Essays on combinatory logic, lambda calculus and formalism</i>, Boston, MA: <a href="Academic_Press" title="Academic Press">Academic Press</a>, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-12-349050-6</bdi></cite> [This volume reflects the research program and philosophy of <a href="Haskell_Curry" title="Haskell Curry">H. Curry</a>, one of the founders of <a href="Computational_models" class="mw-redirect" title="Computational models">computational models</a> and the deductive framework for reasoning in terms of objects.]</li></ul>
<ul><li><cite id="CITEREFWolfengagen2003" class="citation book cs1">Wolfengagen, V.E. (2003). <i>Combinatory logic in programming. Computations with objects through examples and exercises</i> (2nd ed.). JurInfoR. <a href="CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.62.4421">10.1.1.62.4421</a></span>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9785891581265</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/491339472">491339472</a>.</cite></li></ul></div><!--htdig_noindex--><div><div class="zim-footer">
This article is issued from <a class="external text" title="Last edited on 2023-03-19" href="https://en.wikipedia.org/wiki/?title=Applicative_computing_systems&oldid=1145432491">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.
</div>
</div><!--/htdig_noindex--></div>
</div>
</main>
</div>
</div>
</div>
</body></html>