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<div id="content">
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orge252066">1. Introduction</a>
<ul>
<li><a href="#orge006232">1.1. A Set of Search Tools</a></li>
</ul>
</li>
<li><a href="#orgffca9f6">2. Common Lisp</a>
<ul>
<li><a href="#org33b98eb">2.1. tree search</a></li>
<li><a href="#org31f014b">2.2. goal-p</a></li>
<li><a href="#org87a1804">2.3. successors</a></li>
<li><a href="#org32e2b29">2.4. depth first search</a></li>
<li><a href="#org8845270">2.5. breadth first search</a></li>
<li><a href="#org7ca8b17">2.6. Helpers</a>
<ul>
<li><a href="#org0e78457">2.6.1. auto-generation header</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#org12262a4">3. Python</a>
<ul>
<li><a href="#orge9e4201">3.1. tree search</a></li>
<li><a href="#orgb587e84">3.2. goal p</a></li>
<li><a href="#orgdd128bb">3.3. successors</a></li>
<li><a href="#org26910c2">3.4. infinite binary tree</a></li>
<li><a href="#org70e009a">3.5. finite binary tree</a></li>
<li><a href="#org7ef2f15">3.6. depth first search</a></li>
<li><a href="#org91c1920">3.7. breadth first search</a></li>
<li><a href="#org1519765">3.8. helpers</a>
<ul>
<li><a href="#org3c03438">3.8.1. auto-generation header</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#orgcfbdf06">4. Smalltalk</a></li>
</ul>
</div>
</div>
<div id="outline-container-orge252066" class="outline-2">
<h2 id="orge252066"><span class="section-number-2">1</span> Introduction</h2>
<div class="outline-text-2" id="text-1">
<p>
Back in 2014, I tried taking <a href="https://www.coursera.org/instructor/~1289035">Pascal Van Hentenryck</a>'s Coursera course on <a href="https://www.coursera.org/learn/discrete-optimization">Discreet Optimization</a>. It was well over my head, but I feel like I learned a lot watching the videos and trying unsuccessfully to complete the early assignments. Later I came across {Norvig's Book}.
</p>
<div class="inlinetask">
<b><span class="todo TODO">TODO</span> create link for {Norvig's Book}.</b><br />
nil</div>
<p>
Much of Van Hentenryck's course is what was once artificial intelligence. The first important topic is search. Although I had written depth first and breadth first search algorithms in Racket for Tim Roughgarden's <a href="https://lagunita.stanford.edu/courses/course-v1:Engineering+Algorithms1+SelfPaced/about">Alogorithms Design and Analysis</a> course on Coursera, I didn't understand how to manipulate the implementation. {Norvig's Book} has a very clear modular approach to search and provides several techniques to potentially improve its performance.
</p>
</div>
<div id="outline-container-orge006232" class="outline-3">
<h3 id="orge006232"><span class="section-number-3">1.1</span> A Set of Search Tools</h3>
<div class="outline-text-3" id="text-1-1">
<p>
Search can be described as [see {Norvig's Book} section 6.4]:
</p>
<ul class="org-ul">
<li>A start state</li>
<li>A goal state</li>
<li>The successors, or states that can be reached from any other state</li>
<li>The strategy for determining the order in which we search</li>
</ul>
</div>
</div>
</div>
<div id="outline-container-orgffca9f6" class="outline-2">
<h2 id="orgffca9f6"><span class="section-number-2">2</span> Common Lisp</h2>
<div class="outline-text-2" id="text-2">
<p>
This is the base implementation since {Norvig's Book} is informing the design.
</p>
<div class="org-src-container">
<pre class="src src-lisp"><<cl-auto-generated-note>>
<<cl-tree-search>>
<<cl-successors>>
<<cl-depth-first>>
<<cl-breadth-first>>
<<cl-helpers>>
</pre>
</div>
</div>
<div id="outline-container-org33b98eb" class="outline-3">
<h3 id="org33b98eb"><span class="section-number-3">2.1</span> tree search</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-lisp" id="org50c552e">(defun tree-search (states goal-p successors combiner)
"Find a state that satisfies goal-p. Start with states.
and search according to successors and combiner."
(dbg :search "~&;; Search: ~a" states)
(cond
((null states) ;nothing left to search
fail)
((funcall goal-p (first-states)) ;found a goal state
(first states))
(t
(tree-search
(funcall combiner
(funcall successors (first states))
(rest states))
goal-p successors combiner))))
</pre>
</div>
</div>
</div>
<div id="outline-container-org31f014b" class="outline-3">
<h3 id="org31f014b"><span class="section-number-3">2.2</span> goal-p</h3>
<div class="outline-text-3" id="text-2-2">
<p>
One of the things Common Lisp emphasizes is good names. A good name for a predicate generator is <code>is</code> …depending on how 'is' is defined.
</p>
<div class="org-src-container">
<pre class="src src-lisp" id="org6e82021">(defun is (value)
#'(lambda (x) (eql x value)))
</pre>
</div>
</div>
</div>
<div id="outline-container-org87a1804" class="outline-3">
<h3 id="org87a1804"><span class="section-number-3">2.3</span> successors</h3>
<div class="outline-text-3" id="text-2-3">
<div class="org-src-container">
<pre class="src src-lisp" id="orgfc98f74">;;;;;;;;;;;;;;;;
;; SUCCESSORS ;;
;;;;;;;;;;;;;;;;
<<cl-inifinite-binary-tree>>
<<cl-finite-binary-tree>>
</pre>
</div>
<p>
As always, Common Lisp has a way of challenging me. Rather than defining a data set to search, Norvig defines a binary tree with a function. Although now that I think about it, that's how we really want to think about search – we want to think about search over a stream that might be infinite rather than a haystack of fixed size. Even when the stream of possible solutions is bounded, combinatorial explosion produces a solution space that is for practical purposes equivalent to an infinite one.
</p>
<div class="org-src-container">
<pre class="src src-lisp" id="orgc4d9aeb">(defun binary-tree (x)
(list (* 2 x) (+ 1 (* 2 x))))
</pre>
</div>
<p>
For testing it makes sense to have a finite binary tree as well. Again, the tree is generated with a function (that's the idea of successors), but it prunes the successors that don't meet the criteria. <b>The important point here, is that <code>successor</code> does the pruning.</b> That was hard to see when I was trying to right these functions previously.
</p>
<div class="org-src-container">
<pre class="src src-lisp" id="org0f260e9">(defun finite-binary-tree (n)
"Return a successor function that generates a binary tree with n nodes."
#'(lambda (x)
(remove-if #'(lambda (child) (> child n))
(binary-tree x))))
</pre>
</div>
</div>
</div>
<div id="outline-container-org32e2b29" class="outline-3">
<h3 id="org32e2b29"><span class="section-number-3">2.4</span> depth first search</h3>
<div class="outline-text-3" id="text-2-4">
<div class="org-src-container">
<pre class="src src-lisp" id="orgcc84f04">(defun depth-first-search (start goal-p successors)
"Search new states first until goal is reached."
(tree-search (list start) goal-p successors #'append))
</pre>
</div>
</div>
</div>
<div id="outline-container-org8845270" class="outline-3">
<h3 id="org8845270"><span class="section-number-3">2.5</span> breadth first search</h3>
<div class="outline-text-3" id="text-2-5">
<p>
The difference between depth first and breadth first search is that earlier successors are searched before later successors. To create this, use a simple analog to <code>append</code>.
</p>
<div class="org-src-container">
<pre class="src src-lisp" id="org09a68bb">(defun prepend (x y)
"Prepend y to the start of x."
(append y x))
</pre>
</div>
<p>
Defining a breadth first search from tree search becomes:
</p>
<div class="org-src-container">
<pre class="src src-lisp" id="orgafa403c">(defun breadth-first-search (start goal-p successors)
"Search oldest states first until goal is reached."
(tree-search (list start) goal-p successors #'prepend))
</pre>
</div>
</div>
</div>
<div id="outline-container-org7ca8b17" class="outline-3">
<h3 id="org7ca8b17"><span class="section-number-3">2.6</span> Helpers</h3>
<div class="outline-text-3" id="text-2-6">
<div class="org-src-container">
<pre class="src src-lisp" id="org803970e">;;;;;;;;;;;;;
;; HELPERS ;;
;;;;;;;;;;;;;
<<cl-is>>
<<cl-prepend>>
</pre>
</div>
</div>
<div id="outline-container-org0e78457" class="outline-4">
<h4 id="org0e78457"><span class="section-number-4">2.6.1</span> auto-generation header</h4>
<div class="outline-text-4" id="text-2-6-1">
<div class="org-src-container">
<pre class="src src-lisp" id="org055d61e">;;; This file was autogenerated using org-babel-tangle
;;; on the literate programming document located in the
;;; root directory of the git repository.
</pre>
</div>
</div>
</div>
</div>
</div>
<div id="outline-container-org12262a4" class="outline-2">
<h2 id="org12262a4"><span class="section-number-2">3</span> Python</h2>
<div class="outline-text-2" id="text-3">
<div class="org-src-container">
<pre class="src src-python"><<python-auto-generated-note>>
<<python-tree-search>>
<<python-successors>>
<<python-depth-first>>
<<python-breadth-first>>
<<python-helpers>>
</pre>
</div>
</div>
<div id="outline-container-orge9e4201" class="outline-3">
<h3 id="orge9e4201"><span class="section-number-3">3.1</span> tree search</h3>
<div class="outline-text-3" id="text-3-1">
<div class="org-src-container">
<pre class="src src-python" id="orge15ee93">def tree_search(states, goal_p, successors, combiner):
"""Find a state that satisfies goal_p. Start with states and search according to successors and combiner."""
if not states:
return fail
elif goal_p(states[0]):
return states[0]
else:
tree_search(combiner(successors(first states), rest(states)), goal_p, successors, combiner)
</pre>
</div>
</div>
</div>
<div id="outline-container-orgb587e84" class="outline-3">
<h3 id="orgb587e84"><span class="section-number-3">3.2</span> goal p</h3>
<div class="outline-text-3" id="text-3-2">
<div class="org-src-container">
<pre class="src src-python" id="orgf1ec332"></pre>
</div>
</div>
</div>
<div id="outline-container-orgdd128bb" class="outline-3">
<h3 id="orgdd128bb"><span class="section-number-3">3.3</span> successors</h3>
<div class="outline-text-3" id="text-3-3">
<div class="org-src-container">
<pre class="src src-python" id="orgc1faf1e"><<python-inifinite-binary-tree>>
<<python-finite-binary-tree>>
</pre>
</div>
</div>
</div>
<div id="outline-container-org26910c2" class="outline-3">
<h3 id="org26910c2"><span class="section-number-3">3.4</span> infinite binary tree</h3>
<div class="outline-text-3" id="text-3-4">
<div class="org-src-container">
<pre class="src src-python" id="orgb6ef1ca"></pre>
</div>
</div>
</div>
<div id="outline-container-org70e009a" class="outline-3">
<h3 id="org70e009a"><span class="section-number-3">3.5</span> finite binary tree</h3>
<div class="outline-text-3" id="text-3-5">
<div class="org-src-container">
<pre class="src src-python" id="org0fd768d"></pre>
</div>
</div>
</div>
<div id="outline-container-org7ef2f15" class="outline-3">
<h3 id="org7ef2f15"><span class="section-number-3">3.6</span> depth first search</h3>
<div class="outline-text-3" id="text-3-6">
<div class="org-src-container">
<pre class="src src-python" id="orgca5f2a5"></pre>
</div>
</div>
</div>
<div id="outline-container-org91c1920" class="outline-3">
<h3 id="org91c1920"><span class="section-number-3">3.7</span> breadth first search</h3>
<div class="outline-text-3" id="text-3-7">
<div class="org-src-container">
<pre class="src src-python" id="org93e0d82"></pre>
</div>
</div>
</div>
<div id="outline-container-org1519765" class="outline-3">
<h3 id="org1519765"><span class="section-number-3">3.8</span> helpers</h3>
<div class="outline-text-3" id="text-3-8">
<div class="org-src-container">
<pre class="src src-python" id="org1836ad0"><<python-is>>
<<python-prepend>>
</pre>
</div>
</div>
<div id="outline-container-org3c03438" class="outline-4">
<h4 id="org3c03438"><span class="section-number-4">3.8.1</span> auto-generation header</h4>
<div class="outline-text-4" id="text-3-8-1">
<div class="org-src-container">
<pre class="src src-python" id="org8150b8e">"""This file was autogenerated using org-babel-tangle
on the literate programming document located in the
root directory of the git repository."""
</pre>
</div>
</div>
</div>
</div>
</div>
<div id="outline-container-orgcfbdf06" class="outline-2">
<h2 id="orgcfbdf06"><span class="section-number-2">4</span> Smalltalk</h2>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: benrudgers</p>
<p class="date">Created: 2017-07-13 Thu 15:18</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>