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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Walther recursion</span></span>
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<p>In computer programming, <b>Walther recursion</b> (named after <a href="Christoph_Walther" title="Christoph Walther">Christoph Walther</a>) is a method of analysing recursive functions that can determine if the function is definitely <a href="Terminating" class="mw-redirect" title="Terminating">terminating</a>, given finite inputs. It allows a more natural style of expressing computation than simply using <a href="Primitive_recursive_function" title="Primitive recursive function">primitive recursive functions</a>.
</p><p>Since the <a href="Halting_problem" title="Halting problem">halting problem</a> cannot be solved in general, there must still be programs that terminate, but which Walther recursion cannot prove to terminate. Walther recursion may be used in <a href="Total_functional_programming" title="Total functional programming">total functional languages</a> in order to allow a more liberal style of showing primitive recursion.
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<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="BlooP_and_FlooP" title="BlooP and FlooP">BlooP and FlooP</a></li>
<li><a href="Termination_analysis" title="Termination analysis">Termination analysis</a></li>
<li><a href="Total_Turing_machine" class="mw-redirect" title="Total Turing machine">Total Turing machine</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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</style><cite id="CITEREFWalther1991" class="citation journal cs1"><a href="Christoph_Walther" title="Christoph Walther">Walther, Christoph</a> (1991). <a rel="nofollow" class="external text" href="https://www.researchgate.net/profile/Christoph-Walther/publication/220545855_On_Proving_the_Termination_of_Algorithms_by_Machine/links/5a974a8eaca27214056b3bf4/On-Proving-the-Termination-of-Algorithms-by-Machine.pdf">"On Proving the Termination of Algorithms by Machine"</a> <span class="cs1-format">(PDF)</span>. <i><a href="Artificial_Intelligence_(journal)" title="Artificial Intelligence (journal)">Artificial Intelligence</a></i>. <b>70</b> (1). <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0004-3702%2894%2990063-9">10.1016/0004-3702(94)90063-9</a>.</cite></li>
<li><cite id="CITEREFWu1994" class="citation thesis cs1">Wu, Alexander (1994). <a rel="nofollow" class="external text" href="http://dspace.mit.edu/handle/1721.1/35388"><i>Automated termination proofs using Walther recursion</i></a> (Thesis). <a href="Massachusetts_Institute_of_Technology" title="Massachusetts Institute of Technology">Massachusetts Institute of Technology</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2014-09-15</span></span>.</cite></li>
<li><cite id="CITEREFMcAllesterArkoudas1996" class="citation conference cs1"><a href="David_A._McAllester" title="David A. McAllester">McAllester, David</a>; Arkoudas, Kostas (1996). McRobbie, Michael A.; Slaney, J.K. (eds.). <a rel="nofollow" class="external text" href="http://ttic.uchicago.edu/~dmcallester/walther.ps"><i>Walther recursion</i></a>. <a rel="nofollow" class="external text" href="https://www.springer.com/computer/ai/book/978-3-540-61511-8">13th International Conference on Automated Deduction (CADE-13)</a>. LNCS. Vol. 1104. New Brunswick, NJ, USA: Springer-Verlag. pp. <span class="nowrap">643–</span>657. <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=10.1.1.46.5487">10.1.1.46.5487</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F3-540-61511-3_119">10.1007/3-540-61511-3_119</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>3-540-61511-3</bdi>.</cite></li></ul>
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