lecture 02 + lab 01

lab01/expo.ml

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+(** [fact n] calculates the factorial of [n]; non tail recursive *)
+let rec fact n =
+  if n = 0. then 1.
+  else n *. fact(n -. 1.);;
+
+(**/**)
+let test_fact () =
+  assert (fact 0. = 1.);
+  assert (fact 3. = 6.);
+  assert (fact 5. = 120.)
+(**/**)
+
+(** [fact_tr n] calculates the factorial of [n]; tail recursive *)
+let fact_tr n =
+  let rec fact_tr' acc i =
+    if i = 0. then acc
+    else fact_tr' (i *. acc) (i -. 1.)
+  in
+  fact_tr' 1. n;;
+
+(**/**)
+let test_fact_tr () =
+  assert (fact_tr 0. = 1.);
+  assert (fact_tr 3. = 6.);
+  assert (fact_tr 5. = 120.)
+(**/**)
+
+(** [pow_tr a b] calculates [a] to the power of [b]; non tail recursive *)
+let rec pow a b =
+  if b = 0. then 1.
+  else a *. pow a (b -. 1.);;
+
+(**/**)
+let test_pow () =
+  assert (pow 0. 1. = 0.);
+  assert (pow 0. 5. = 0.);
+  assert (pow 1. 0. = 1.);
+  assert (pow 5. 0. = 1.);
+  assert (pow 1. 1. = 1.);
+  assert (pow 5. 1. = 5.);
+  assert (pow 2. 3. = 8.)
+(**/**)
+
+(** [pow_tr a b] calculates [a] to the power of [b]; tail recursive *)
+let pow_tr a b =
+  let rec pow_tr' acc i =
+    if i = 0. then acc
+    else pow_tr' (acc *. a) (i -. 1.)
+  in
+  pow_tr' 1. b;;
+
+(**/**)
+let test_pow_tr () =
+  assert (pow_tr 0. 1. = 0.);
+  assert (pow_tr 0. 5. = 0.);
+  assert (pow_tr 1. 0. = 1.);
+  assert (pow_tr 5. 0. = 1.);
+  assert (pow_tr 1. 1. = 1.);
+  assert (pow_tr 5. 1. = 5.);
+  assert (pow_tr 2. 3. = 8.)
+(**/**)
+
+(** [expo_tr n x] calculates the approximation of e to the power of [x];
+  * with a max iteration detail of [n]; non tail recursive
+  * Require: [n] >= 1
+  *)
+let rec expo n x =
+  if n = 0 then 1.
+  else pow x (float_of_int n) /. fact (float_of_int n) +.
+    expo (n - 1) x;;
+
+(**/**)
+let test_expo () =
+  let tolerance = 1e-6 in
+  let diff = abs_float (expo 20 1. -. exp 1.) in
+  assert (diff < tolerance);
+  let diff = abs_float (expo 20 2. -. exp 2.) in
+  assert (diff < tolerance);
+  let diff = abs_float (expo 20 3. -. exp 3.) in
+  assert (diff < tolerance)
+(**/**)
+
+(** [expo_tr n x] calculates the approximation of e to the power of [x];
+  * with a max iteration detail of [n]; tail recursive
+  * Require: [n] >= 1
+  *)
+let expo_tr n x =
+  let rec expo_tr' acc i =
+    if i = 0 then acc
+    else expo_tr' (acc +. pow_tr x (float_of_int i) /.
+      fact_tr (float_of_int i)) (i - 1)
+  in
+  expo_tr' 1. n;;
+
+(**/**)
+let test_expo_tr () =
+  let tolerance = 1e-6 in
+  let diff = abs_float (expo_tr 20 1. -. exp 1.) in
+  assert (diff < tolerance);
+  let diff = abs_float (expo_tr 20 2. -. exp 2.) in
+  assert (diff < tolerance);
+  let diff = abs_float (expo_tr 20 3. -. exp 3.) in
+  assert (diff < tolerance)
+(**/**)
+
+(**/**)
+let run_all_tests () =
+  test_fact();
+  test_fact_tr();
+  test_pow();
+  test_pow_tr();
+  test_expo();
+  test_expo_tr()
+(**/**)

lab01/lab1.ml

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+(** [reverse l] returns the reverse order of list [l]; non tail recursive *)
+let rec reverse l =
+  match l with
+  | [] -> []
+  | x :: xs -> reverse xs @ [x];;
+
+(**/**)
+let test_reverse () =
+  assert (reverse [] = []);
+  assert (reverse [1] = [1]);
+  assert (reverse [1; 2] = [2; 1])
+(**/**)
+
+(** [reverse_tr l] returns the reverse order of list [l]; tail recursive *)
+let reverse_tr l =
+  let rec reverse_tr' acc l =
+    match l with
+    | [] -> acc
+    | x :: xs -> reverse_tr' (x :: acc) xs
+  in
+  reverse_tr' [] l;;
+
+(**/**)
+let test_reverse_tr () =
+  assert (reverse_tr [] = []);
+  assert (reverse_tr [1] = [1]);
+  assert (reverse_tr [1; 2] = [2; 1])
+(**/**)
+
+(** [zip l1 l2] combines elements from [l1] and [l2] into a
+  * new list of tuples; non tail recursive
+  *)
+let rec zip l1 l2 =
+  match l1, l2 with
+  | [], _ | _, [] -> [] (* if l1 or l2 is empty, return empty *)
+  | x1 :: xs1, x2 :: xs2 ->
+    (x1, x2) :: zip xs1 xs2;;
+
+(**/**)
+let test_zip () =
+  assert (zip [] [] = []);
+  assert (zip [1] [] = []);
+  assert (zip [] ['a'] = []);
+  assert (zip [1; 2; 3] ['a'; 'b'] = [(1, 'a'); (2, 'b')]);
+  assert (zip [1; 2; 3] ['a'; 'b'; 'c'] = [(1, 'a'); (2, 'b'); (3, 'c')])
+(**/**)
+
+(** [zip_tr l1 l2] combines elements from [l1] and [l2] into a
+  * new list of tuples; tail recursive
+  *)
+let zip_tr l1 l2 =
+  let rec zip_tr' acc l1 l2 =
+    match l1, l2 with
+    | [], _ | _, [] -> reverse_tr acc (* if l1 or l2 is empty, return empty *)
+    | x1 :: xs1, x2 :: xs2 ->
+      zip_tr' ((x1, x2) :: acc) xs1 xs2
+  in
+  zip_tr' [] l1 l2;;
+
+(**/**)
+let test_zip_tr () =
+  assert (zip_tr [] [] = []);
+  assert (zip_tr [1] [] = []);
+  assert (zip_tr [] ['a'] = []);
+  assert (zip_tr [1; 2; 3] ['a'; 'b'] = [(1, 'a'); (2, 'b')]);
+  assert (zip_tr [1; 2; 3] ['a'; 'b'; 'c'] = [(1, 'a'); (2, 'b'); (3, 'c')])
+(**/**)
+
+(** [unzip l] takes in a list of tuples [l] where each tuple is
+  * a pair, we seperate the pairs (x, y) into sepeate lists, ([x], [y])
+  * and return a tuple of both lists; non tail recursive *)
+let rec unzip l =
+  match l with
+  | [] -> ([], [])
+  | (x, y) :: xys ->
+    let (l1, l2) = unzip xys in
+      x :: l1, y :: l2;;
+
+(**/**)
+let test_unzip () =
+  assert (unzip [] = ([], []));
+  assert (unzip [(1, 'a')] = ([1], ['a']));
+  assert (unzip [(1, 'a'); (2, 'b')] = ([1; 2], ['a'; 'b']))
+(**/**)
+
+(** [unzip_tr l] takes in a list of tuples [l] where each tuple is
+  * a pair, we seperate the pairs (x, y) into sepeate lists, ([x], [y])
+  * and return a tuple of both lists; tail recursive *)
+let unzip_tr l =
+  let rec unzip_tr' (a1, a2) l =
+    match l with
+    | [] -> (a1, a2)
+    | (x, y) :: xys ->
+      unzip_tr' (x :: a1, y :: a2) xys
+  in
+  unzip_tr' ([], []) (reverse_tr l);;
+
+(**/**)
+let test_unzip_tr () =
+  assert (unzip_tr [] = ([], []));
+  assert (unzip_tr [(1, 'a')] = ([1], ['a']));
+  assert (unzip_tr [(1, 'a'); (2, 'b')] = ([1; 2], ['a'; 'b']))
+(**/**)
+
+(** [dedup l] takes in a list [l] and collapses consecutive duplicated
+  * elements into a single element; non tail recursive *)
+let rec dedup l =
+  match l with
+  | [] -> []
+  | [x] -> l
+  | x :: y :: zs ->
+    if x = y then dedup (x :: zs)
+    else x :: dedup (y :: zs);;
+
+(**/**)
+let test_dedup () =
+  assert (dedup [] = []);
+  assert (dedup [1] = [1]);
+  assert (dedup [1; 2] = [1; 2]);
+  assert (dedup [1; 1; 2; 2; 2; 1; 3; 3; 2] = [1; 2; 1; 3; 2])
+(**/**)
+
+(** [dedup l] takes in a list [l] and collapses consecutive duplicated
+  * elements into a single element; tail recursive *)
+let dedup_tr l =
+  let rec dedup' acc l =
+    match l with
+    | [] -> acc
+    | [x] -> l
+    | x :: y :: zs ->
+      if x = y then dedup' (x :: acc) (x :: zs)
+      else x :: dedup' (x :: acc) (y :: zs)
+  in
+  dedup' [] l;;
+
+(**/**)
+let test_dedup_tr () =
+  assert (dedup_tr [] = []);
+  assert (dedup_tr [1] = [1]);
+  assert (dedup_tr [1; 2] = [1; 2]);
+  assert (dedup_tr [1; 1; 2; 2; 2; 1; 3; 3; 2] = [1; 2; 1; 3; 2])
+(**/**)
+
+(**/**)
+let run_all_tests () =
+  test_reverse();
+  test_reverse_tr();
+  test_zip();
+  test_zip_tr();
+  test_unzip();
+  test_unzip_tr();
+  test_dedup();
+  test_dedup_tr();
+(**/**)

lecture02/html/Length.html

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+<!DOCTYPE html>
+<html>
+<head>
+<link rel="stylesheet" href="style.css" type="text/css">
+<meta content="text/html; charset=UTF-8" http-equiv="Content-Type">
+<meta name="viewport" content="width=device-width, initial-scale=1">
+<link rel="Start" href="index.html">
+<link rel="Up" href="index.html">
+<link title="Index of values" rel=Appendix href="index_values.html">
+<link title="Index of modules" rel=Appendix href="index_modules.html">
+<link title="Length" rel="Chapter" href="Length.html"><title>Length</title>
+</head>
+<body>
+<div class="navbar">&nbsp;<a class="up" href="index.html" title="Index">Up</a>
+&nbsp;</div>
+<h1>Module <a href="type_Length.html">Length</a></h1>
+
+<pre><span id="MODULELength"><span class="keyword">module</span> Length</span>: <code class="code">sig</code> <a href="Length.html">..</a> <code class="code">end</code></pre><div class="info module top">
+<div class="info-desc">
+<p>returns the number of elements in the list <code class="code">l</code> - non tail recursive</p>
+</div>
+</div>
+<hr width="100%">
+
+<pre><span id="VALlength"><span class="keyword">val</span> length</span> : <code class="type">'a list -&gt; int</code></pre>
+<pre><span id="VALtest_length"><span class="keyword">val</span> test_length</span> : <code class="type">unit -&gt; unit</code></pre>
+<pre><span id="VALlength_tr"><span class="keyword">val</span> length_tr</span> : <code class="type">'a list -&gt; int</code></pre><div class="info ">
+<div class="info-desc">
+<p>returns the number of elements in the list <code class="code">l</code> - tail recursive</p>
+</div>
+</div>
+
+<pre><span id="VALtest_length_tr"><span class="keyword">val</span> test_length_tr</span> : <code class="type">unit -&gt; unit</code></pre></body></html>

lecture02/html/index.html

@@ -0,0 +1,27 @@
+<!DOCTYPE html>
+<html>
+<head>
+<link rel="stylesheet" href="style.css" type="text/css">
+<meta content="text/html; charset=UTF-8" http-equiv="Content-Type">
+<meta name="viewport" content="width=device-width, initial-scale=1">
+<link rel="Start" href="index.html">
+<link title="Index of values" rel=Appendix href="index_values.html">
+<link title="Index of modules" rel=Appendix href="index_modules.html">
+<link title="Length" rel="Chapter" href="Length.html"><title></title>
+</head>
+<body>
+<div class = "index-list">
+<ul class="indexlist">
+<li><a href="index_values.html">Index of values</a></li>
+<li><a href="index_modules.html">Index of modules</a></li>
+</ul>
+</div>
+
+<table class="indextable module-list">
+<tr><td class="module"><a href="Length.html">Length</a></td><td><div class="info">
+ returns the number of elements in the list <code class="code">l</code> - non tail recursive
+</div>
+</td></tr>
+</table>
+</body>
+</html>

lecture02/html/index_attributes.html

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+<html>
+<head>
+<link rel="stylesheet" href="style.css" type="text/css">
+<meta content="text/html; charset=UTF-8" http-equiv="Content-Type">
+<meta name="viewport" content="width=device-width, initial-scale=1">
+<link rel="Start" href="index.html">
+<link title="Index of values" rel=Appendix href="index_values.html">
+<link title="Index of modules" rel=Appendix href="index_modules.html">
+<link title="Length" rel="Chapter" href="Length.html"><title>Index of class attributes</title>
+</head>
+<body>
+<div class="navbar">&nbsp;<a class="up" href="index.html" title="Index">Up</a>
+&nbsp;</div>
+<h1>Index of class attributes</h1>
+<table>
+</table>
+</body>
+</html>

lecture02/html/index_class_types.html

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+<html>
+<head>
+<link rel="stylesheet" href="style.css" type="text/css">
+<meta content="text/html; charset=UTF-8" http-equiv="Content-Type">
+<meta name="viewport" content="width=device-width, initial-scale=1">
+<link rel="Start" href="index.html">
+<link title="Index of values" rel=Appendix href="index_values.html">
+<link title="Index of modules" rel=Appendix href="index_modules.html">
+<link title="Length" rel="Chapter" href="Length.html"><title>Index of class types</title>
+</head>
+<body>
+<div class="navbar">&nbsp;<a class="up" href="index.html" title="Index">Up</a>
+&nbsp;</div>
+<h1>Index of class types</h1>
+<table>
+</table>
+</body>
+</html>

lecture02/html/index_classes.html

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+<html>
+<head>
+<link rel="stylesheet" href="style.css" type="text/css">
+<meta content="text/html; charset=UTF-8" http-equiv="Content-Type">
+<meta name="viewport" content="width=device-width, initial-scale=1">
+<link rel="Start" href="index.html">
+<link title="Index of values" rel=Appendix href="index_values.html">
+<link title="Index of modules" rel=Appendix href="index_modules.html">
+<link title="Length" rel="Chapter" href="Length.html"><title>Index of classes</title>
+</head>
+<body>
+<div class="navbar">&nbsp;<a class="up" href="index.html" title="Index">Up</a>
+&nbsp;</div>
+<h1>Index of classes</h1>
+<table>
+</table>
+</body>
+</html>

lecture02/html/index_exceptions.html

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+<html>
+<head>
+<link rel="stylesheet" href="style.css" type="text/css">
+<meta content="text/html; charset=UTF-8" http-equiv="Content-Type">
+<meta name="viewport" content="width=device-width, initial-scale=1">
+<link rel="Start" href="index.html">
+<link title="Index of values" rel=Appendix href="index_values.html">
+<link title="Index of modules" rel=Appendix href="index_modules.html">
+<link title="Length" rel="Chapter" href="Length.html"><title>Index of exceptions</title>
+</head>
+<body>
+<div class="navbar">&nbsp;<a class="up" href="index.html" title="Index">Up</a>
+&nbsp;</div>
+<h1>Index of exceptions</h1>
+<table>
+</table>
+</body>
+</html>

lecture02/html/index_extensions.html

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+<html>
+<head>
+<link rel="stylesheet" href="style.css" type="text/css">
+<meta content="text/html; charset=UTF-8" http-equiv="Content-Type">
+<meta name="viewport" content="width=device-width, initial-scale=1">
+<link rel="Start" href="index.html">
+<link title="Index of values" rel=Appendix href="index_values.html">
+<link title="Index of modules" rel=Appendix href="index_modules.html">
+<link title="Length" rel="Chapter" href="Length.html"><title>Index of extensions</title>
+</head>
+<body>
+<div class="navbar">&nbsp;<a class="up" href="index.html" title="Index">Up</a>
+&nbsp;</div>
+<h1>Index of extensions</h1>
+<table>
+</table>
+</body>
+</html>

lecture02/html/index_methods.html

@@ -0,0 +1,18 @@
+<html>
+<head>
+<link rel="stylesheet" href="style.css" type="text/css">
+<meta content="text/html; charset=UTF-8" http-equiv="Content-Type">
+<meta name="viewport" content="width=device-width, initial-scale=1">
+<link rel="Start" href="index.html">
+<link title="Index of values" rel=Appendix href="index_values.html">
+<link title="Index of modules" rel=Appendix href="index_modules.html">
+<link title="Length" rel="Chapter" href="Length.html"><title>Index of class methods</title>
+</head>
+<body>
+<div class="navbar">&nbsp;<a class="up" href="index.html" title="Index">Up</a>
+&nbsp;</div>
+<h1>Index of class methods</h1>
+<table>
+</table>
+</body>
+</html>

lecture02/html/index_module_types.html

@@ -0,0 +1,18 @@
+<html>
+<head>
+<link rel="stylesheet" href="style.css" type="text/css">
+<meta content="text/html; charset=UTF-8" http-equiv="Content-Type">
+<meta name="viewport" content="width=device-width, initial-scale=1">
+<link rel="Start" href="index.html">
+<link title="Index of values" rel=Appendix href="index_values.html">
+<link title="Index of modules" rel=Appendix href="index_modules.html">
+<link title="Length" rel="Chapter" href="Length.html"><title>Index of module types</title>
+</head>
+<body>
+<div class="navbar">&nbsp;<a class="up" href="index.html" title="Index">Up</a>
+&nbsp;</div>
+<h1>Index of module types</h1>
+<table>
+</table>
+</body>
+</html>

lecture02/html/index_modules.html

@@ -0,0 +1,24 @@
+<html>
+<head>
+<link rel="stylesheet" href="style.css" type="text/css">
+<meta content="text/html; charset=UTF-8" http-equiv="Content-Type">
+<meta name="viewport" content="width=device-width, initial-scale=1">
+<link rel="Start" href="index.html">
+<link title="Index of values" rel=Appendix href="index_values.html">
+<link title="Index of modules" rel=Appendix href="index_modules.html">
+<link title="Length" rel="Chapter" href="Length.html"><title>Index of modules</title>
+</head>
+<body>
+<div class="navbar">&nbsp;<a class="up" href="index.html" title="Index">Up</a>
+&nbsp;</div>
+<h1>Index of modules</h1>
+<table>
+<tr><td align="left"><div>L</div></td></tr>
+<tr><td><a href="Length.html">Length</a> </td>
+<td><div class="info">
+ returns the number of elements in the list <code class="code">l</code> - non tail recursive
+</div>
+</td></tr>
+</table>
+</body>
+</html>

lecture02/html/index_types.html

@@ -0,0 +1,18 @@
+<html>
+<head>
+<link rel="stylesheet" href="style.css" type="text/css">
+<meta content="text/html; charset=UTF-8" http-equiv="Content-Type">
+<meta name="viewport" content="width=device-width, initial-scale=1">
+<link rel="Start" href="index.html">
+<link title="Index of values" rel=Appendix href="index_values.html">
+<link title="Index of modules" rel=Appendix href="index_modules.html">
+<link title="Length" rel="Chapter" href="Length.html"><title>Index of types</title>
+</head>
+<body>
+<div class="navbar">&nbsp;<a class="up" href="index.html" title="Index">Up</a>
+&nbsp;</div>
+<h1>Index of types</h1>
+<table>
+</table>
+</body>
+</html>

lecture02/html/index_values.html

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+<html>
+<head>
+<link rel="stylesheet" href="style.css" type="text/css">
+<meta content="text/html; charset=UTF-8" http-equiv="Content-Type">
+<meta name="viewport" content="width=device-width, initial-scale=1">
+<link rel="Start" href="index.html">
+<link title="Index of values" rel=Appendix href="index_values.html">
+<link title="Index of modules" rel=Appendix href="index_modules.html">
+<link title="Length" rel="Chapter" href="Length.html"><title>Index of values</title>
+</head>
+<body>
+<div class="navbar">&nbsp;<a class="up" href="index.html" title="Index">Up</a>
+&nbsp;</div>
+<h1>Index of values</h1>
+<table>
+<tr><td align="left"><div>L</div></td></tr>
+<tr><td><a href="Length.html#VALlength">length</a> [<a href="Length.html">Length</a>]</td>
+<td></td></tr>
+<tr><td><a href="Length.html#VALlength_tr">length_tr</a> [<a href="Length.html">Length</a>]</td>
+<td><div class="info">
+ returns the number of elements in the list <code class="code">l</code> - tail recursive
+</div>
+</td></tr>
+<tr><td align="left"><div>T</div></td></tr>
+<tr><td><a href="Length.html#VALtest_length">test_length</a> [<a href="Length.html">Length</a>]</td>
+<td></td></tr>
+<tr><td><a href="Length.html#VALtest_length_tr">test_length_tr</a> [<a href="Length.html">Length</a>]</td>
+<td></td></tr>
+</table>
+</body>
+</html>

lecture02/html/style.css

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+.keyword { font-weight : bold ; color : Red }
+.keywordsign { color : #C04600 }
+.comment { color : Green }
+.constructor { color : Blue }
+.type { color : #5C6585 }
+.string { color : Maroon }
+.warning { color : Red ; font-weight : bold }
+.info { margin-left : 3em; margin-right: 3em }
+.param_info { margin-top: 4px; margin-left : 3em; margin-right : 3em }
+.code { color : #465F91 ; }
+.typetable { border-style : hidden }
+.paramstable { border-style : hidden ; padding: 5pt 5pt}
+tr { background-color : White }
+td.typefieldcomment { background-color : #FFFFFF ; font-size: smaller ;}
+div.sig_block {margin-left: 2em}
+*:target { background: yellow; }
+body {font: 13px sans-serif; color: black; text-align: left; padding: 5px; margin: 0}
+h1 { font-size : 20pt ; text-align: center; }
+h2 { font-size : 20pt ; text-align: center; }
+h3 { font-size : 20pt ; border: 1px solid #000000; margin-top: 5px; margin-bottom: 2px;text-align: center; background-color: #90BDFF ;padding: 2px; }
+h4 { font-size : 20pt ; border: 1px solid #000000; margin-top: 5px; margin-bottom: 2px;text-align: center; background-color: #90DDFF ;padding: 2px; }
+h5 { font-size : 20pt ; border: 1px solid #000000; margin-top: 5px; margin-bottom: 2px;text-align: center; background-color: #90EDFF ;padding: 2px; }
+h6 { font-size : 20pt ; border: 1px solid #000000; margin-top: 5px; margin-bottom: 2px;text-align: center; background-color: #90FDFF ;padding: 2px; }
+div.h7 { font-size : 20pt ; border: 1px solid #000000; margin-top: 5px; margin-bottom: 2px;text-align: center; background-color: #90BDFF ; padding: 2px; }
+div.h8 { font-size : 20pt ; border: 1px solid #000000; margin-top: 5px; margin-bottom: 2px;text-align: center; background-color: #E0FFFF ; padding: 2px; }
+div.h9 { font-size : 20pt ; border: 1px solid #000000; margin-top: 5px; margin-bottom: 2px;text-align: center; background-color: #F0FFFF ; padding: 2px; }
+div.h10 { font-size : 20pt ; border: 1px solid #000000; margin-top: 5px; margin-bottom: 2px;text-align: center; background-color: #FFFFFF ; padding: 2px; }
+a {color: #416DFF; text-decoration: none}
+a:hover {background-color: #ddd; text-decoration: underline}
+pre { margin-bottom: 4px; font-family: monospace; }
+pre.verbatim, pre.codepre { }
+.indextable {border: 1px #ddd solid; border-collapse: collapse}
+.indextable td, .indextable th {border: 1px #ddd solid; min-width: 80px}
+.indextable td.module {background-color: #eee ;  padding-left: 2px; padding-right: 2px}
+.indextable td.module a {color: #4E6272; text-decoration: none; display: block; width: 100%}
+.indextable td.module a:hover {text-decoration: underline; background-color: transparent}
+.deprecated {color: #888; font-style: italic}
+.indextable tr td div.info { margin-left: 2px; margin-right: 2px }
+ul.indexlist { margin-left: 0; padding-left: 0;}
+ul.indexlist li { list-style-type: none ; margin-left: 0; padding-left: 0; }
+ul.info-attributes {list-style: none; margin: 0; padding: 0; }
+div.info > p:first-child { margin-top:0; }
+div.info-desc > p:first-child { margin-top:0; margin-bottom:0; }

lecture02/html/type_Length.html

@@ -0,0 +1,11 @@
+<html><head>
+<link rel="stylesheet" href="style.css" type="text/css">
+<meta content="text/html; charset=UTF-8" http-equiv="Content-Type">
+<meta name="viewport" content="width=device-width, initial-scale=1">
+<link rel="Start" href="index.html">
+<link title="Index of values" rel=Appendix href="index_values.html">
+<link title="Index of modules" rel=Appendix href="index_modules.html">
+<link title="Length" rel="Chapter" href="Length.html"><title>Length</title>
+</head>
+<body>
+<code class="code"><span class="keyword">sig</span>&nbsp;<span class="keyword">end</span></code></body></html>

lecture02/lists.ml

@@ -0,0 +1,187 @@
+(*
+  if everything is fine, test functions
+  will return the unit value
+*)
+
+(** [length l] returns the number of elements in the list [l]; non tail recursive *)
+let rec length l =
+  match l with
+  | [] -> 0
+  | x :: xs -> 1 + length xs;;
+
+(**/**)
+let test_length () =
+  assert (length [] = 0);
+  assert (length [2] = 1);
+  assert (length [5; 7; 8;] = 3)
+(**/**)
+
+(** [length_tr l] returns the number of elements in the list [l]; tail recursive *)
+let length_tr l =
+  let rec lenth_tr' acc l =
+    match l with
+    | [] -> acc
+    | _ :: xs -> lenth_tr' (acc + 1) xs
+  in
+  lenth_tr' 0 l;;
+
+(**/**)
+let test_length_tr () =
+  assert (length_tr [] = 0);
+  assert (length_tr [2] = 1);
+  assert (length_tr [5; 7; 8;] = 3)
+(**/**)
+
+(** [reverse l] returns the reverse order of list [l]; non tail recursive *)
+let rec reverse l =
+  match l with
+  | [] -> []
+  | x :: xs -> reverse xs @ [x];;
+
+(**/**)
+let test_reverse () =
+  assert (reverse [] = []);
+  assert (reverse [1] = [1]);
+  assert (reverse [1; 2] = [2; 1])
+(**/**)
+
+(** [reverse_tr l] returns the reverse order of list [l]; tail recursive *)
+let reverse_tr l =
+  let rec reverse_tr' acc l =
+    match l with
+    | [] -> acc
+    | x :: xs -> reverse_tr' (x :: acc) xs
+  in
+  reverse_tr' [] l;;
+
+(**/**)
+let test_reverse_tr () =
+  assert (reverse_tr [] = []);
+  assert (reverse_tr [1] = [1]);
+  assert (reverse_tr [1; 2] = [2; 1])
+(**/**)
+
+(* list.rev is a built in reverse function *)
+
+(** [take n l] returns a list containing the first [n] elements of [l];
+  * return [] if (n <= 0); return [l] if [l has fewer elements than [n]];
+  * non tail recursive *)
+let rec take n l =
+  if n <= 0 then []
+  else
+    match l with
+    | [] -> []
+    | x :: xs -> x :: take (n - 1) xs
+
+(**/**)
+let test_take () =
+  assert (take 0 [1; 2; 3;] = []);
+  assert (take 3 [4; 5; 6; 7; 8; 9] = [4; 5; 6]);
+  assert (take 5 [1; 2; 3] = [1; 2; 3])
+(**/**)
+
+(** [take_tr n l] returns a list containing the first [n] elements of [l];
+  * return [] if (n <= 0); return [l] if [l has fewer elements than [n]];
+  * tail recursive *)
+let take_tr n l =
+  let rec take_tr' acc n l =
+    if n <= 0 then reverse_tr(acc)
+    else
+      match l with
+      | [] -> acc
+      | x :: xs -> x :: take_tr' (x :: acc) (n - 1) xs
+  in
+  take_tr' [] n l;;
+
+(**/**)
+let test_take_tr () =
+  assert (take_tr 0 [1; 2; 3;] = []);
+  assert (take_tr 3 [4; 5; 6; 7; 8; 9] = [4; 5; 6]);
+  assert (take_tr 5 [1; 2; 3] = [1; 2; 3])
+(**/**)
+
+(** [every_other l] returns a list consisting of every other element of [l]
+  * starting from the first element; non tail recursive *)
+let rec every_other l =
+  match l with
+  | x :: _ :: xs -> every_other xs
+  | _ -> l;;
+
+(**/**)
+let test_every_other () =
+  assert (every_other [] = []);
+  assert (every_other [1] = []);
+  assert (every_other [1; 2] = [2]);
+  assert (every_other [1; 2; 3] = [2]);
+  assert (every_other [1; 2; 3; 4] = [2; 4])
+(**/**)
+
+(** [every_other_tr l] returns a list consisting of every other element of [l]
+  * starting from the first element; tail recursive *)
+let every_other_tr l =
+  let rec every_other_tr' acc l =
+    match l with
+    | x :: _ :: xs -> every_other_tr' (x :: acc) xs
+    | _ -> reverse_tr acc
+  in
+  every_other_tr' [] l;;
+
+(**/**)
+let test_every_other_tr () =
+  assert (every_other_tr [] = []);
+  assert (every_other_tr [1] = []);
+  assert (every_other_tr [1; 2] = [2]);
+  assert (every_other_tr [1; 2; 3] = [2]);
+  assert (every_other_tr [1; 2; 3; 4] = [2; 4])
+(**/**)
+
+(** [sum l1 l2] returns a list consisting of the sum of corresponding integers
+  * in [l1] and [l2]; non tail recursive *)
+let rec sum l1 l2 =
+  match l1, l2 with (* this is a tuple of (l1, l2) *)
+  | [], _ | _, [] -> [] (* if l1 is empty or l2 is empty, return empty *)
+  | x1 :: xs1, x2 :: xs2 ->
+    (x1 + x2) :: sum xs1 xs2;;
+
+(**/**)
+let test_sum () =
+  assert (sum [] [] = []);
+  assert (sum [1] [] = []);
+  assert (sum [] [1] = []);
+  assert (sum [7] [8] = [15]);
+  assert (sum [7; 3] [8; 8] = [15; 11]);
+  assert (sum [7] [8; 8] = [15])
+(**/**)
+
+(** [sum_tr l1 l2] returns a list consisting of the sum of corresponding integers
+  * in [l1] and [l2]; tail recursive *)
+let sum_tr l1 l2 =
+  let rec sum_tr' acc l1 l2 =
+    match l1, l2 with
+    | [], _ | _, [] -> reverse_tr acc
+    | x1 :: xs1, x2 :: xs2 ->
+      sum_tr' ((x1 + x2) :: acc) xs1 xs2
+  in
+  sum_tr' [] l1 l2;;
+
+(**/**)
+let test_sum_tr () =
+  assert (sum_tr [] [] = []);
+  assert (sum_tr [1] [] = []);
+  assert (sum_tr [] [1] = []);
+  assert (sum_tr [7] [8] = [15]);
+  assert (sum_tr [7; 3] [8; 8] = [15; 11]);
+  assert (sum_tr [7] [8; 8] = [15])
+(**/**)
+
+(** [count_change amt denoms] returns the number of ways of breaking up [amt]
+  * into currencies with denominations specified by [denoms];
+  * Require: elements of [denoms] must be positive *)
+let rec count_change amt denoms =
+  if amt < 0 then 0
+  else if amt = 0 then 1
+  else
+    match denoms with
+    | [] -> 0
+    | d :: ds ->
+      count_change (amt - d) denoms + count_change amt ds;; (* use/not-use d *)

lecture02/notes02.ml

@@ -0,0 +1,135 @@
+(*
+  ***** TUPLES *****
+  has a fixed number of elements
+*)
+let x = (1, 2.1, "hello");;
+
+(*
+  this is also a tuple, but this tuple
+  is a different type to the tuple above
+*)
+let y = (1, 2.1, "hello", "goodbye");;
+
+(*
+  function with tuple argument
+
+  accepts a tuple with 3 elements of int
+*)
+let add_tuple (x, y, z) = x + y + z;;
+
+(*
+  ***** PATTERN MATCHING *****
+  where x gets deconstructed into a, b, and c
+*)
+let (a, b, c) = x;;
+
+a;;
+b;;
+c;;
+
+(*
+  ***** LISTS *****
+
+  lists are semi-colon seperated values of the same type
+  lists are a recursive data type
+*)
+let nums = [1; 2; 3];; (* this is a valid list *)
+
+(*
+  warning -
+  this is valid syntax but this is a list with a single
+  element that is a tuple of 3 ints
+*)
+let nums = [1, 2, 3];;
+(* results in - list : [(1, 2, 3)] *)
+
+(*
+  since lists are recursive data structures
+  we can add elements to the front of the list
+  as seen below
+
+  this operation is called cons
+*)
+2 :: (1 :: []);;
+2 :: 1 :: [];;
+
+(*
+  [1; 2; 3] === 1 :: 2 :: 3 :: [];;
+*)
+
+(* list of lists *)
+[[1; 2]; [3; 4]];;
+
+(* list concatonation *)
+[1; 2] @ [3; 4];;
+
+[];;
+(*
+  results in - : 'a list = []
+
+  where 'a means its a type variable
+  since lists are generic
+*)
+
+let l = [[1; 2]; [3]; []];;
+
+(*
+  pattern matching lists to extract 3
+  pattern matching must be exhaustive
+*)
+let [_; [x]; _] = l;;
+
+let data = [(1, 2, 'a'); (5, 3, 'b'); (4, 1, 'c'); (5, 0, 'd')];;
+let _ :: (_, _, x) :: _ = data;;
+x;;
+
+(*
+  recursive function
+  with pattern matching to find
+  length of list
+*)
+
+(**
+  * {length l} returns the number of elements
+  * in the list {l} - non tail recursive
+  *)
+let rec length l =
+  match l with
+  | [] -> 0
+  | x :: xs -> 1 + length xs;;
+
+(**
+  * {length_tr l} returns the number of elements
+  * in the list {l} - tail recursive
+  *)
+let length_tr l =
+  let rec aux acc l =
+    match l with
+    | [] -> acc
+    | _ :: xs -> aux (acc + 1) xs
+  in
+  aux 0 l;;
+
+(*
+  GENERATE WEB DOCUMENTATION
+
+  mkdir html
+  ocamldoc -html -d html main.ml
+
+*)
+
+(*
+  there is no void in ocaml,
+  everything has to return a value
+  all expressions have a value;
+
+  if your function has no value to
+  return, you still need to return something
+  so return the unit value
+
+  example:
+  printf is like a utility to print to the
+  console but does not need to return any value
+  so it returns the unit value
+*)
+Printf.printf "Hello, world\n";;

tinker/exponential.ml

@@ -1,20 +0,0 @@
-let fact n =
-  let rec fact' acc i =
-    if i = 0. then acc
-    else fact' (i *. acc) (i -. 1.)
-  in
-  fact' 1. n;;
-
-let pow a b =
-  let rec pow' acc i =
-    if i = 0. then acc
-    else pow' (acc *. a) (i -. 1.)
-  in
-  pow' 1. b;;
-
-let expo n x =
-  let rec expo' acc i =
-    if i = 0. then acc
-    else expo' (acc +. pow x i /. fact i) (i -. 1.)
-  in
-  expo' 1. n;;

tinker/tinker.ml

@@ -1,18 +0,0 @@
-let pow b e =
-  let rec pow' acc i =
-    if i = 0 then acc
-    else pow' (acc * b) (i - 1)
-  in
-  pow' 1 e;;
-
-let rec root n k g =
-  let next = (1. /. k) *. ((k -. 1.) *. g +. n /. float_of_int (pow g (k - 1))) in
-  if abs(next - g) < 0.00000000001 then next
-  else root n k next;;
-
-let float_pow b e =
-  let rec float_pow' acc i =
-    if i <= 0. then acc
-    else float_pow' (acc *. b) (i -. 1.)
-  in
-  float_pow' 1. e;;