Comp210 Lecture

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Welcome to Comp210!

Admnistrivia

The Comp210 home page and what you can find there
General course info = the handout. The key points:
1. Who -- the staff
2. What -- the assignments, etc.
  1. Once a week homework plust 3 exams.
  2. Working in pairs.
  3. Electronically dropping off homework
3. Where - the labs
  1. Sign up for a lab.
  2. Go to your preferred lab this week
4. How - the Honor System

What is Computing?

What do computers do anyway?
1. What does it mean to "compute" something?
2. What are we saying about the specifics of what a computer does?
3. How does one accomplish the task of "general purpose" computing?
4. The difference between
  1. Universal = can do everything.
  2. Abstract = does the "essence" of things. Needs "concrete", specific inputs to do anything in particular.
5. Does a computer perform universal tasks (does everything possible) or does it do "abstract" tasks?
What is a "program"?
1. Specific tasks vs. abstract tasks
2. How do we represent abstract tasks?
  1. What is "mathematics"?
  2. What is a mathematical "function"?
  3. The relationship between tasks and functions.
3. Programs can be represented by functions.

Programming with Functions

There are lots of examples of functions:

[get examples from class]
Note that arithmetic's notation wasn't always the clearest: you've been taught "y=x+1" is a function; what is the input? What is the output? (Is "x=y+1" the same function? What about "m=n+1"?) Really, "add1" might be a better name for the function, and we could write "let add1(n) = n+1".
The Academy Awards (takes in a list of movies, and returns (ahem) the best one. Note that the Academy is what performs the computation.
The registrar has a function from student to library-fine. (Well, okay, at-which-time is also an implicit input to the function.)
A web-search-engine is a function, taking in keywords, return a web-page (with links to other pages).

So functions aren't always about numbers. That said, today we'll only use functions on numbers. (We'll start enriching our world starting next time.)

Examples of computing, and generalizing to programs:

A pizza costs $12, and has eight slices.
If you eat 2 pieces, you owe $12*(2/8) = $3.
If you eat 1 pieces, you owe $12*(1/8) = $1.50
If you eat 8 pieces, you owe $12*(8/8) = $12.00
Of course, we learn to abstract out the parts of the calcuation in common, and express it as a more general rule:
owes(p) = $12*(p/8). owes(p) does not represent the calculation of any particular amount of money owed, but instead is the abstraction of all such calculations.
A different formula, that you once memorized in school (since it's not so obvious, if you're not taught it).
A disc of radius 6" has an area of 36pi sq. in.
In general: dough-area(r) = pi*r^2.
Consider the folks who make the pizza. For a given diameter, how much of the pizza is covered with toppings? Note that there is a 1-inch border, which is crust-only.
A pizza of diameter 14" has a radius of 7", of which 1" is crust, so the toppings cover a disc of radius 6": Draw picture.
pizza-topping-area(14) = dough-area(6) = 36pi.

In general: pizza-topping-area(d) = dough-area( d/2 - 1).
Does this rule make sense? Let's try some more tests:
pizza-topping-area(8) = dough-area(8/2 - 1) = dough-area(3).
pizza-topping-area(2) = dough-area(2/2 - 1) = dough-area(0).

Finally, a question: we could instead have written
pizza-topping-area(d) = pi (d/2 - 1)^2, or even
pizza-topping-area(d) = pi/4*d^2 - pi*d + pi.
Do we have a preference? Yes! The first version reflects how we think about the problem, while the second makes the reader scratch their head and wonder if it's really correct.

The First Law of Programming: Your code should reflect the way you think about a problem.

The code in a program is an expression of how you conceptualize the problem. Programming is a very personal process since it depends on the individual programmer's view of the world.

Code that reflects a natural way of looking at the problem is both easier to understand, easier to maintain, and more likely to be correct.

Summary:

computing as asbstractions
abstractions as functions;
as algebra, substitute equal expressions until value reached
single point of control
First law of programming