Date: Wed, 07 November 2001 3:35 PM (CST) --- Temperature 71 degrees
   From: Mark Jacobson <jacobson@math-cs.cns.uni.edu>
     To: 810-080-01@uni.edu, 810-080-02@uni.edu
Subject: URL for lab stuff...

Hi discrete students,

See the http://www.cns.uni.edu/~jacobson/080/lab080.html

and the http://www.cns.uni.edu/~jacobson/c080.html

   page that links to it.

   We will do some different computer things on Friday, but the
more you look over your September 10th handout and the other resources
that are available from the

                     http://www.cns.uni.edu/~jacobson/080/lab080.html,

                                lab class, the better off you will be.

    The two pages of your textbook to study to review today's class
are:

    Page 223 Definition 5.3 and Definition 5.4

             Get the terms function, mapping, image, preimage,
             domain, codomain, and range down.

    Page 251 Definition 5.18 for composition of functions.

             If f:A -------> B and g:B ------> C, we define the
             composite function, which is denoted
                                                  g o f:A -----> C,
             by (g o f)(a) = g(f(a)),
                                     for each a elementOf A.

    The C++ program that we looked at today had a while loop and
it looks like this:

[jacobson@cowboy ~]$  more f.cpp

#include <iostream.h>

void main()
{
   int n;
   while (cin >> n)
   {
      cout << n*n << endl;
   }
}

[jacobson@cowboy ~]$ g++ f.cpp -o f.exe

[jacobson@cowboy ~]$ ls -l f.cpp
-rw-r--r--    1 jacobson cns_fac       107 Nov  7 11:47 f.cpp

[jacobson@cowboy ~]$ ls -l f.exe
-rwxr-xr-x    1 jacobson cns_fac     12966 Nov  7 14:49 f.exe

Notice that the function g++ mapped the C++ program f.cpp to the
                           machine language program f.exe, which
                           is in a file of size 12,966 bytes!!!!

                           f.cpp size =    107 bytes    source code
                           f.exe size = 12,966 bytes    object code

  f.cpp ---------------------------> f.exe
                g++
                    compiler function

  Compilers are just functions that map from the domain of C++ or
or Pascal or Ada or Java or Lisp or Visual Basic to the language of the
machine you are compiling for.

  f.cpp ---------------------------> f.exe
                g++
  source                             object
  code                               code
  C++                                machine language
  programs                           programs (Intel Pentium or
  domain                                       Sun workstation or
                                               whatever processor
                                               machine language)
                                          2
[jacobson@math-cs ~]$ ./f.exe     f(x) = x     f(2) = 4  f(4) = 16
2                                                        f(6) = 36
4
4
16
6
36
[jacobson@math-cs ~]$ ./f.exe | ./f.exe   Composition of functions using
2                                         the Unix pipe symbol (same for
16                                        Windows and DOS too)
4
256                                       f o f(6) = f(f(6)) = f(36)
6                                                            = 36 * 36
1296                                                         = 1296
[jacobson@math-cs ~]$
[jacobson@math-cs ~]$ ./f.exe < A.dat    <-- INPUT REDIRECTION - SEE HANDOUT.
1
4
9
16
25
36
49
64
81
100
[jacobson@math-cs ~]$ more A.dat    THIS IS THE DOMAIN set A.dat is set A
1                                               A = {1,2,3,4,5,6,7,8,9,10}
2
3
4
5
6
7
8
9
10

  See you on Friday, in the Wright 112 lab.

  Mark