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ksiazka tytuł: Foundations of Combinatory Logic autor: Curry Haskell

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Foundations of Combinatory Logic

(Grundlagen der kombinatorischen Logik)
Wersja papierowa
Wydawnictwo: College Publications
ISBN: 978-18-489-0202-2
Tłumaczenie: Kamareddine Fairouz
Format: 15.6x23.4cm
Liczba stron: 176
Oprawa: Miękka
Wydanie: 2017 r.
Język: angielski

Dostępność: dostępny
74,40 zł 70,70 zł

<p>Curry&#39;s PhD dissertation &nbsp;<em>Introduction</em> <em>to Combinatory Logic</em>, represents a first major work on a new subject. &nbsp;Curry&#39;s interest in the subject started when he noticed the complicated form of substitution in Principia Mathematica and set about trying &nbsp; to find a simpler form &nbsp;of this rule. This led him by 1926 to some of the combinators. In 1928 Curry went to G\'ottingen and completed his dissertation in 1929 under the direction of David Hilbert. &nbsp;This book is a translation of the dissertation.&nbsp;</p><p>&nbsp;Curry&#39;s dissertation was the first publication to give a complete formal &nbsp;development of combinatory logic as a formal system in which the terms are built up from &nbsp;<em>variables</em>&nbsp;and a number of &nbsp;constants (combinators including <em>B, C&nbsp;</em>and <em>K</em>) by means of <em>application</em>. The proof of the consistency of the system faced the &nbsp;major difficulty &nbsp;that the only reduction relation Curry had was what we now call weak reduction. &nbsp;This made it impossible to prove the Church-Rosser Theorem, which is now the standard way one proves the consistency of systems of this kind. &nbsp;Instead, Curry was looking at sequences based on what we now call weak contractions with strings of variables added on the right.&nbsp;</p><p>After his dissertation, Curry developed further ground-breaking ideas &nbsp;that continue to be very influential. &nbsp;These include, <em>functionality</em>&nbsp;(which became the basis of what we now call type assignment), the correspondence between types and implication formulas &nbsp;(the beginning of the idea of 'propositions as types') and generalised functionality (a form of &nbsp;dependent types in modern type systems). &nbsp; &nbsp;Curry&#39;s ideas continue to influence developments in mathematics, logic and computation. &nbsp;</p><p><br />
We hope that making his original thesis available in English will help make his ideas clearer.&nbsp;<br />
We have made use of all information we could find by Curry, mostly from marginal notes in his copy of the dissertation, indicating corrections to the original German.</p>



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