Notes: Friday 25 January 2002
- Now: Problem Set
1
- 28 January: Read SICP, 1.2
- 30 January: Read GEB, Little Harmonic Labyrinth and Chapter
5
- 1 February: Read SICP, 1.3
- 4 February: Problem Set 2
Reading Guide
As you read GEB chapter 5, here are some things to think about:
- How do the Recursive Transition Networks he uses to describe
languages compare to the Backus Naur Form we saw in class? Can any
Recursive Transition Network be rewritten as in Backus Naur Form? Which
notation is more compact? Which notation is easier to understand?
- Can you translate his definition of FIBO (p. 136) into a
Scheme procedure that calculates Fibonacci numbers?
- Are Feynman diagrams a formal system? Are they a language?
Richard Feynman won the Nobel Prize in Physics in 1965 and was important
in the Manhattan Project and in the Space Shuttle Challenger
investigation. He also made important contributions to Computer Science
(a few of which we will see later in this class). In 1984, Richard
Feynman and Gerry Sussman co-taught a course at Caltech using an early
version of the Wizard Book. Here's a story about that from Feynman
Online:
In the beginning part of 1984, Feynman was teaching a course on
computing at Caltech. The course was also co-jointly taught by Gerald
Sussman from MIT. On one occasion Feynman was lecturing at the
blackboard, but this time Sussman kept coming up and correcting
him. Later that week Feynman was supposed to come over for dinner. On
the night in question, Feynman's wife Gweneth called to say that Feynman
was in the hospital and that they would not be able to come over. She
told me not to tell anyone, as she didn't want the word to get
around. Apparently Feynman in his excitement to purchase a new computer
tripped on the sidewalk curb and hit his head. This caused some internal
complications and bleeding. In a week or so, Feynman was back on his
feet and returned to class. At lunch Feynman related what had
happened. After bumping his head, he paid little or no attention to
it. He was bleeding when he entered the computer store. What was
interesting is that he gradually began to loose his sense of what was
happening around him without internally realizing it. First, he couldn't
locate his car. Then he had a very strange session with one of his
artistic models. And on another day, he told his secretary Helen Tuck
that he was going home, and proceeded to undress and lie down in his
office. He forgot that he was to give a lecture at Hughs aircraft, and
so on... Everything was just rationalized away. But you know, he said,
NO ONE told me I was going crazy. Now why not? I said, Come on. You are
always doing weird stuff. Besides there such a fine line between genius
and madness that it sometimes difficult to tell! Listen, ape, the next
time I go crazy around here, you be sure to tell me!
For more stories about Feynman, "Surely
You're Joking, Mr. Feynman!": Adventures of a Curious Character is
highly recommended summer reading.
Notes
Scheme Rules of Evaluation
(Repeated from 22 Jan notes, except expanded
Rule 4.)
Evaluation Rule 1: Primitives. If the expression is a primitive,
it is self-evaluating.
Evaluation Rule 2: Names. If the expression is a name, it
evaluates to the value associated with that name.
Evaluation Rule 3: Application. If the expression is an application:
(a) Evaluate all the subexpressions of the combination (in any order)
(b) Apply the value of the first subexpression to the values of all the other subexpressions.
Evaluation Rule 4: Special Forms. If the expression is a special
form, do something special.
Eval 4-if. If the expression is
(if Expression0 Expression1 Expression2)
evaluate Expression0. If it evaluates to #f, the value of the if
expression is the value of Expression1. Otherwise, the value of the if
expression is the value of Expression2.
Eval 4-lambda. Lambda expressions self-evaluate. (Do not do anything
until it is applied.)
Eval 4-define. If the expression is (define Name Expression)
associate the Expression with Name (for Evaluation
Rule 2).
Eval 4-begin. If the expression is (begin
Expression0 Expression1
... Expressionk ) evaluate all the
sub-expressions Expression0,
Expression1,
... ,Expressionk in order. The
value of the begin expression is the value of
Expressionk.
Application Rule 1: Primitives. If the procedure to apply is a
primitive, just do it.
Application Rule 2: Compound Procedures. If the procedure is a
compound procedure, evaluate the body of the procedure
with each formal parameter replaced by the corresponding actual argument
expression value.
Syntactic Sugar
(define (square x) (* x x))
is actually syntactic sugar (and easier way to write something that
means exactly the same thing) for:
(define square (lambda (x) (begin (* x x))))
Defining Recursive Procedures
- Be optimistic.
- Assume you can solve it.
- If you could, how would you solve a bigger problem.
- Think of the simplest version of the problem, something you can already
solve.
- This is called the base case.
- Usually something like solve for 0 or the empty list
- Combine them to solve the problem.
(define (find-closest-number-extra
goal new-number numbers)
(if (empty? numbers)
new-number ;;; No others, new-number is best
(if (< (abs (- new-number goal))
(abs (- (find-closest-number goal numbers)
goal)))
new-number
(find-closest-number goal numbers))))
(define (find-closest-number goal numbers)
(find-closest-number-extra goal
(first numbers)
(rest numbers)))
This isn't the best way of doing this — think about ways to improve
the code.
"Somehow it seems to fill my head with ideas - only I don't exactly know what they are!"
Alice, in Alice and Wonderland by Lewis Carroll after hearing The Jaberwocky.
The best book on programming for the layman is Alice in Wonderland; but that's because it's the best book on anything for the layman.
Alan Perlis, author
of SICP Forward and First Turing Award (biggest prize for Computer
Science) Winner
