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<h2 section-num="1" id="introduction"><span class="section-number">1 </span>Introduction</h2>
<p>Like the Lambda Calculus, <a href="http://en.wikipedia.org/wiki/Combinatory_logic">Combinatory Logic</a> is a mathematical notation that is powerful enough to handle set theory and issues in computability.</p>
<blockquote>
<p>Combinatory logic is a notation introduced by <a href="http://en.wikipedia.org/wiki/Moses_Sch&#xE23;&#xE16;nfinkel">Moses Sch&#xE23;&#xE16;nfinkel</a> and <a href="http://en.wikipedia.org/wiki/Haskell_Curry">Haskell Curry</a> to eliminate the need for variables in mathematical logic. It has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming languages. It is based on combinators. A combinator is a higher-order function that uses only function application and earlier defined combinators to define a result from its arguments.</p>
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<p>In this book, we&#x2019;re going to meet some of the standard combinators, and for each one we&#x2019;ll explore some of its ramifications when writing programs using the Ruby programming language. In Combinatory logic, combinators combine and alter each other, and our Ruby examples will focus on combining and altering Ruby code. From simple examples like the K Combinator and Ruby&#x2019;s <code>.tap</code> method, we&#x2019;ll work our way up to meta-programming with aspects and recursive combinators.</p>
<p>
<strong>about the bird names</strong>
</p>
<p>When Combinatory Logic was first invented by Haskell Curry, the standard combinators were given upper-case letters. For example, the two combinators needed to express everything in the Lambda Calculus and in Set Theory are the <code>S</code> and <code>K</code> combinators. In 1985, Raymond Smullyan published <a href="http://en.wikipedia.org/wiki/To_Mock_a_Mockingbird">To Mock a Mockingbird</a>, an exploration of combinatory logic for the recreational layman. Smullyan used a forest full of songbirds as a metaphor, with each of the combinators given the name of a songbird rather than a single letter. For example, the <code>S</code> and <code>K</code> combinators became the Starling and Kestrel, the <code>I</code> combinator became the Idiot bird, and so forth.</p>
<p>These ornithological nicknames have become part of the standard lexicon for combinatory logic.</p>
<p>
<strong>thanks</strong>
</p>
<p>There are too many people to name,but amongst the crowd, Alan Smith stands out.</p>
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<h2>Table of Contents</h2>
<ol class="toc">
<li class="section"><a href="chap00.html#the-mit-license"><span class="section-number">0.1 </span>The MIT License</a></li>
<li class="section"><a href="chap00.html#preface"><span class="section-number">0.2 </span>Preface</a></li>
<li class="chapter"><a href="chap01.html#introduction"><span class="section-number">1 </span>Introduction</a></li>
<li class="chapter"><a href="chap02.html#kestrels"><span class="section-number">2 </span>Kestrels</a></li>
<li class="section"><a href="chap02.html#object-initializer-blocks"><span class="section-number">2.1 </span>Object initializer blocks</a></li>
<li class="section"><a href="chap02.html#inside-an-idiomatic-ruby-kestrel"><span class="section-number">2.2 </span>Inside, an idiomatic Ruby Kestrel</a></li>
<li class="section"><a href="chap02.html#the-enchaining-kestrel"><span class="section-number">2.3 </span>The Enchaining Kestrel</a></li>
<li class="section"><a href="chap02.html#the-obdurate-kestrel"><span class="section-number">2.4 </span>The Obdurate Kestrel</a></li>
<li class="section"><a href="chap02.html#kestrels-on-rails"><span class="section-number">2.5 </span>Kestrels on Rails</a></li>
<li class="section"><a href="chap02.html#rewriting-returning-in-rails"><span class="section-number">2.6 </span>Rewriting &#x201C;Returning&#x201D; in Rails</a></li>
<li class="chapter"><a href="chap03.html#the-thrush"><span class="section-number">3 </span>The Thrush</a></li>
<li class="section"><a href="chap03.html#let"><span class="section-number">3.1 </span>Let</a></li>
<li class="chapter"><a href="chap04.html#songs-of-the-cardinal"><span class="section-number">4 </span>Songs of the Cardinal</a></li>
<li class="section"><a href="chap04.html#building-a-cardinal-in-ruby"><span class="section-number">4.1 </span>Building a Cardinal in Ruby</a></li>
<li class="chapter"><a href="chap05.html#quirky-birds-and-meta-syntactic-programming"><span class="section-number">5 </span>Quirky Birds and Meta-Syntactic Programming</a></li>
<li class="section"><a href="chap05.html#a-limited-interpretation-of-the-quirky-bird-in-ruby"><span class="section-number">5.1 </span>A limited interpretation of the Quirky Bird in Ruby</a></li>
<li class="section"><a href="chap05.html#embracing-the-quirky-bird"><span class="section-number">5.2 </span>Embracing the Quirky Bird</a></li>
<li class="section"><a href="chap05.html#andand-even-more"><span class="section-number">5.3 </span>Andand even more</a></li>
<li class="chapter"><a href="chap06.html#aspect-oriented-programming-in-ruby-using-combinator-birds"><span class="section-number">6 </span>Aspect-Oriented Programming in Ruby using Combinator Birds</a></li>
<li class="section"><a href="chap06.html#giving-methods-advice"><span class="section-number">6.1 </span>Giving methods advice</a></li>
<li class="section"><a href="chap06.html#the-super-keyword-perhaps-youve-heard-of-it"><span class="section-number">6.2 </span>The super keyword, perhaps you&#x2019;ve heard of it?</a></li>
<li class="section"><a href="chap06.html#the-queer-bird"><span class="section-number">6.3 </span>The Queer Bird</a></li>
<li class="chapter"><a href="chap07.html#mockingbirds"><span class="section-number">7 </span>Mockingbirds</a></li>
<li class="section"><a href="chap07.html#duplicative-combinators"><span class="section-number">7.1 </span>Duplicative Combinators</a></li>
<li class="section"><a href="chap07.html#recursive-lambdas-in-ruby"><span class="section-number">7.2 </span>Recursive Lambdas in Ruby</a></li>
<li class="section"><a href="chap07.html#recursive-combinatorics"><span class="section-number">7.3 </span>Recursive Combinatorics</a></li>
<li class="section"><a href="chap07.html#recursive-combinators-in-idiomatic-ruby"><span class="section-number">7.4 </span>Recursive Combinators in Idiomatic Ruby</a></li>
<li class="section"><a href="chap07.html#the-mockingbird"><span class="section-number">7.5 </span>The Mockingbird</a></li>
<li class="chapter"><a href="chap08.html#refactoring-methods-with-recursive-combinators"><span class="section-number">8 </span>Refactoring Methods with Recursive Combinators</a></li>
<li class="section"><a href="chap08.html#divide-and-conquer"><span class="section-number">8.1 </span>Divide and Conquer</a></li>
<li class="section"><a href="chap08.html#the-merge-sort"><span class="section-number">8.2 </span>The Merge Sort</a></li>
<li class="section"><a href="chap08.html#separating-declaration-from-implementation"><span class="section-number">8.3 </span>Separating Declaration from Implementation</a></li>
<li class="section"><a href="chap08.html#practical-recursive-combinators"><span class="section-number">8.4 </span>Practical Recursive Combinators</a></li>
<li class="section"><a href="chap08.html#spicing-things-up"><span class="section-number">8.5 </span>Spicing things up</a></li>
<li class="section"><a href="chap08.html#building-on-a-legacy"><span class="section-number">8.6 </span>Building on a legacy</a></li>
<li class="section"><a href="chap08.html#seriously"><span class="section-number">8.7 </span>Seriously</a></li>
<li class="section"><a href="chap08.html#separating-implementation-from-declaration"><span class="section-number">8.8 </span>Separating Implementation from Declaration</a></li>
<li class="section"><a href="chap08.html#a-really-simple-recursive-combinator"><span class="section-number">8.9 </span>A Really Simple Recursive Combinator</a></li>
<li class="chapter"><a href="chap09.html#you-cant-be-serious"><span class="section-number">9 </span>You can&#x2019;t be serious!?</a></li>
<li class="section"><a href="chap09.html#string-to-proc"><span class="section-number">9.1 </span>String to Proc</a></li>
<li class="section"><a href="chap09.html#the-message"><span class="section-number">9.2 </span>The Message</a></li>
<li class="chapter"><a href="chap10.html#the-hopelessly-egocentric-book-chapter"><span class="section-number">10 </span>The Hopelessly Egocentric Book Chapter</a></li>
<li class="section"><a href="chap10.html#object-oriented-egocentricity"><span class="section-number">10.1 </span>Object-oriented egocentricity</a></li>
<li class="chapter"><a href="chap11.html#bonus-chapter-separating-concerns-in-coffeescript-using-aspect-oriented-programming"><span class="section-number">11 </span>Bonus Chapter: Separating Concerns in Coffeescript using Aspect-Oriented Programming</a></li>
<li class="chapter"><a href="chap12.html#appendix-finding-joy-in-combinators"><span class="section-number">12 </span>Appendix: Finding Joy in Combinators</a></li>
<li class="section"><a href="chap12.html#languages-for-combinatorial-logic"><span class="section-number">12.1 </span>Languages for combinatorial logic</a></li>
<li class="section"><a href="chap12.html#concatenative-languages"><span class="section-number">12.2 </span>Concatenative languages</a></li>
<li class="chapter"><a href="chap13.html#appendix-source-code"><span class="section-number">13 </span>Appendix: Source Code</a></li>
<li class="section"><a href="chap13.html#kestrels-1"><span class="section-number">13.1 </span>kestrels</a></li>
<li class="section"><a href="chap13.html#thrushes"><span class="section-number">13.2 </span>thrushes</a></li>
<li class="section"><a href="chap13.html#the-cardinal"><span class="section-number">13.3 </span>the cardinal</a></li>
<li class="section"><a href="chap13.html#quirky-birds"><span class="section-number">13.4 </span>quirky birds</a></li>
<li class="section"><a href="chap13.html#bluebirds"><span class="section-number">13.5 </span>bluebirds</a></li>
<li class="chapter"><a href="chap14.html#about-the-author"><span class="section-number">14 </span>About The Author</a></li>
<li class="section"><a href="chap14.html#contact"><span class="section-number">14.1 </span>contact</a></li>
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