[r2004-07-11 00:24:29 by beppe] A page of exercises

Original author: beppe
Date: 2004-07-11 00:24:29+00:00

web/tutorial/exercises.xml

+<?xml version="1.0" encoding="ISO-8859-1" standalone="yes"?>
+<page name="tutorial_exercises">
+
+<title>Exercises</title>
+<left>
+<boxes-toc/>
+<p>
+You can cut and paste the code on this page and 
+test it on the <a href="cgi-bin/cduce">online interpreter</a>.
+</p>
+</left>
+
+<box title="Tree navigation" link="intro">
+
+<section title="XPath expressions">
+<p>Write a function that implements <code>//t</code> without 
+using references types and <code>xtransform</code></p>
+<ol>
+   <li>Give a non tail-recursive version</li>
+   <li>Give a tail-recursive version</li>
+</ol>
+</section>
+</box>
+
+
+<box title="Patterns" link="pat">
+<section title="Sort (by Artur Miguel Diaz: http://ctp.di.fct.unl.pt/~amd)">
+<p>
+Write a non recursive function of type <code> Int -> Latin1</code> which given a non-negative number produces all its digits in the order.
+</p>
+<p>
+The function is given below nearly completely programmed. Define the patterns that allows to produce the result.</p>
+
+<sample> <![CDATA[
+let sortAlg (n :Int):Latin1 =
+     match string_of n with
+         %%PATTERN%% -> %%RESULT%%
+;;
+]]> </sample>
+
+<p>Example:</p>
+
+<sample> <![CDATA[
+fact 200 =
+788657867364790503552363213932185062295135977687173263294742533
+244359449963403342920304284011984623904177212138919638830257642
+790242637105061926624952829931113462857270763317237396988943922
+445621451664240254033291864131227428294853277524242407573903240
+321257405579568660226031904170324062351700858796178922222789623
+703897374720000000000000000000000000000000000000000000000000
+
+sortAlg (fact 200) =
+"00000000000000000000000000000000000000000000000000000000000000
+000000000000001111111111111111111111111122222222222222222222222
+222222222222222222222222222222233333333333333333333333333333333
+333333333444444444444444444444444444444444445555555555555555555
+555555666666666666666666666666666667777777777777777777777777777
+7777777888888888888888888888889999999999999999999999999999999"
+]]> </sample>
+
+</section>
+</box>
+
+
+<box title="Solutions" link="intro">
+
+<section title="Tree navigation">
+<sample><![CDATA[
+type t =   %%specify here a type to test%%
+
+fun ( x :[Any*]):[t*] =
+  let f( x :[Any*]):[t*]) = ...
+]]></sample>
+<p>Note here that the recursive function <code>f</code> is wrapped by a second anonymous function so that it does not expose the recursion variable.</p>
+<sample><![CDATA[
+fun (e : [Any*]):[ T*] =
+  let f( accu :[T*] , x :[Any*]):[T*] =
+     match x with
+        [ h&T&<_>(k&[Any*]) ;t] ->  f( accu@[h], k@t)
+      | [ <_>(k&[Any*]) ;t] ->  f( accu, k@t)
+      | [ h&T ;t] ->  f( accu@[h], t)
+      | [ _ ;t] ->  f( accu, t)
+      | [] -> accu
+   in f ([], e);;
+]]></sample>
+<p>Note that this implementation may generate empty branch warnings in particular</p>
+<ul>
+<li>for the first branch if <code>T&amp;&lt;_>(k&amp;[Any*])</code> is <code>Empty</code></li>
+<li>for the second branch if <code>&lt;_>(k&amp;[Any*])</code> is smaller than <code>T&amp;&lt;_>(k&amp;[Any*])</code></li>
+<li>for the first branch if <code>t</code> is smaller than <code>&lt;_>(k&amp;[Any*])</code></li>
+</ul>
+</section>
+
+<section title="Patterns">
+<sample> <![CDATA[
+let sortAlg (n :Int):Latin1 =
+    match string_of n with
+        [ (s0::'0' | s1::'1' | s2::'2' | s3::'3' | s4::'4' |
+           s5::'5' | s6::'6' | s7::'7' | s8::'8' | s9::'9')+ ] ->
+                s0 @ s1 @ s2 @ s3 @ s4 @ s5 @ s6 @ s7 @ s8 @ s9
+        | _ -> raise "Invalid argument for sortAlg."
+;;
+]]> </sample>
+</section>
+</box>
+</page>