Introduction to Programming, using Scheme

1
Introduction to Programming,using Scheme

• a.k.a. Bugs, and How to Learn From Them 101
• Dinoj Surendran (dinoj_at_cs, Eckhart basement, Room
  2a)

2
Basic Questions

• What is programming?
• Writing down an explicit set of instructions that
  a machine can follow, usually with a task in
  mind.
• What is Scheme?
• A functional programming language based on Lisp.
• How are my grades calculated?
• Homework 60, Midterm 20, Final 20.
• 16 homeworks at 4 each.
• Extra credit for challenge problems.
• Whats the course webpage?
• http//www.cs.uchicago.edu/dinoj/2002summer115.ht
  ml
• What are my Office Hours?
• Tuesdays and Thursdays 1300 1400. I am always
  accessible by email or via the class mailing
  list.

3
More Basic Questions

• What text are we using? Where do I get it?
• Structure and Interpretation of Computer
  Programs, Abelson and Sussman2. The book is
  online, see class webpage.
• Can I ask my friends for help with my homework?
• No. You can discuss all you want about general
  concepts, but no more.
• Homework suspected to be the product of
  collaboration receives no credit. Two incidents
  of this ?trouble.
• How much homework will there be?
• Lots. Check the class webpage an hour after
  class. It is due by 9pm of the day of the next
  class, and returned to you at the class after
  that.
• What is the late homework policy?
• 20 if handed late, but still on the deadline
  day, and 50 off if handed in the day after that.
  Excuses for not doing it in time please tell me
  24 hours in advance of the deadline.
• What if I cant finish my homework in time?
• Hand it in anyway for partial credit. A short
  note saying detailing the bug would be good.

4
Computer Science

• A misnomer by the same token, Biology should be
  called Microscope Science or Astronomy Telescope
  Science
• We study computation, and computers just happen
  to be the tools we use.
• The purpose of computing is insight, not numbers.
  -- R. Hamming
• Computer scientists study vision, languages,
  mathematics, hearing, kinematics, neuroscience,
  physics, etc in addition to compilers, operating
  systems and the internet
• Programming is a basic skill, just as calculus is
  a basic skill for mathematicians. Mathematicians
  dont solve calculus problems all the time, but
  can do so when they have to.

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Programming Errors

• As soon as we started programming, we found to
  our surprise that it wasn't as easy to get
  programs right as we had thought. Debugging had
  to be discovered. I can remember the exact
  instant when I realized that a large part of my
  life from then on was going to be spent in
  finding mistakes in my own programs. -- Maurice
  Wilkes, 1949
• There are two ways to write error-free programs
  only the third works. -- Alan J. Perlis
• I really hate this damned machineI wish that
  they would sell it.It never does quite what I
  wantBut only what I tell it. -- A Programmer's
  Lament

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Programming Erring Learning

• The road to wisdom?Well its plain and simple to
  expressErr and err and err again, but less and
  less and less. -- Piet Hein
• I, myself, have had many failures and I've
  learned that if you are not failing a lot, you
  are probably not being as creative as you could
  be -you aren't stretching your imagination. --
  J. Backus
• Learning is never done without errors and defeat.
  -- Lenin

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Programming Avoiding Errors

• The most important single aspect of software
  development is to be clear about what you are
  trying to build.
  -- Bjarne Stroustrup
• ...well over half of the time you spend working
  on a project (on the order of 70 percent) is
  spent thinking, and no tool, no matter how
  advanced, can think for you. Consequently, even
  if a tool did everything except the thinking for
  you -- if it wrote 100 percent of the code, wrote
  100 percent of the documentation, -- the best
  you could hope for would be a 30 percent
  improvement in productivity. In order to do
  better than that, you have to change the way you
  think. -- Fred Brook paraphrased

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Programming Avoiding Errors II

• Haste is of the devil. Slowness is of God.
  -- H L Mencken
• You're bound to be unhappy if you optimize
  everything. -- Donald Knuth
• Programming can be fun, so can cryptography
  however they should not be combined. --
  Kreitzberg and Shneiderman
• Programs must be written for people to read, and
  only incidentally for machines to execute. --
  SICP

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General Advice

• I hear and I forget I see and I remember I do
  and I understand. -- Anonymous Chinese Proverb
• He who asks is a fool for five minutes he who
  does not ask remains a fool forever. -- ACP
• Never hesitate to ask a lesser person. --
  Confucius
• The first step in fixing a broken program is
  getting it to fail repeatedly (on the simplest
  example possible). -- T. Duff
• To arrive at the simple is difficult. -- R.
  Elisha

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Now (finally!) to Scheme

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Expressions

• Everything in Scheme is an expression, and has a
  value. For example, these are primitives, and are
  their own value
• 5
• \c
• babalas
• braai
• 4.122
• 32i
• t, f
• The value is sometimes undefined, like (/ 1 0)

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Combinations

• These are more complicated expressions
• ( 4 1 49)
• ( sqrt ( 2 8) )
• ( string-append the doh of Homer)
• ( (/ 18 3) (- 8 2) )
• ( 33i 44i )
• These evaluate to 54, 4, the doh ofHomer, t
  and 024i respectively.
• Note the prefix notation! Everything is of the
  form (function arg1 argn)

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More fun with prefix notation

• Evaluate ( (/ 4 1) (- 4 2 9) ( (/ 6 3) (sqrt
  9)))
• evaluate each argument separately
• (/ 4 1) ? 4/1 4
• (- 4 2 9) ? 4-2-9 -7
• ( (/ 6 3) (sqrt 9) ) ? ( 2 3) ? 5
• then put them together
• ( 4 7 5) ? -140

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How Expressions are Evaluated

• To evaluate (operator arg1 arg2 argn)
• Evaluate all arguments (RECURSIVE!)
• Apply operator to the value of each argument
• e.g.( ( (- 5 3) (sqrt 9)) (/ ( 20 2) ( 3
  2)))
• ( ( 2 3 ) (/ 10
  5)
• ( 6
  2 )
• 8

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Functions

• Programming languages like C, Java make a huge
  distinction between functions and data. Not
  Scheme. Think of them as pipes and balls,
  both of which are objects.
• (lambda (x) ( x 2)) defines a function that
  doubles its argument
• (lambda (x y z) ( x y z) ) defines a function
  that takes three arguments and returns their sum.
• (lambda () 0) defines a function that takes no
  arguments and returns zero.
• (lamba (x) 0) defines a function taking one
  argument and returning zero.
• How to use functions place them at the start of
  a compound expression with the correct number of
  arguments, e.g.
• ( (lambda (x) ( x 2)) 3 ) ? 6
• ( (lambda (x y z) ( x y z)) 100 28 4) ? 132

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Parentheses

• We are used to using parentheses just to make
  expressions clearer. In Scheme, they have a
  specific meaning
• What is inside me is a function and its
  arguments, and Im going to apply the function to
  the arguments, and return the result.
• Therefore, expressions like (5) or (foo 3) are
  meaningless since 5 and foo are not procedures.
• Similarly, ( 3 4) is meaningful, (( 3 4)) is
  not.

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Data Abstraction

• Make it, name it, forget about it, use it
• e.g. Incrementer
• -- make it (lambda (x) ( x 1))
• -- name it (define inc (lambda (x) ( x
  1)))
• -- forget about it you no longer need to
  remember how inc was implemented, just know what
  it does
• -- use it (inc 312) ? 313
• both data and functions can be abstracted, e.g.
  (define quayle-iq 50) means that you can say
  (inc quayle-iq) and receive 51

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Why is Data Abstraction a Good Thing?

• Dont need to know how something is implemented
  in order to use it imagine a world where you
  needed to know how your car worked to get your
  drivers license
• (it would be a world with a lot of illegal
  drivers).
• Can change the implementation of something
  without changing the way it is used your car
  engine can be replaced with a new one without you
  having to change the way you drive your car.
• Code reuse you dont have to implement
  everything from scratch if you know you need
  new brakes, and know the specs used by your car,
  you can get them from someone else without having
  to make them yourself.

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Example 1.1

• A function that returns the circumference of a
  circle, when given its radius
• (define pi 3.14159)
• (define circum
• (lambda (r) ( 2 r pi))
• )
• Alternatively (define (circum x) ( 2 x pi) )
• Note how name of parameter (x or r) is irrelevant
• Usage (circum 5) ? 31.4159

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Example 1.2

• Function which greets when you give it a name
• (define hello (lambda (name)
  (string-append hello name you slimy
  worm) ) )
• (define (hello name) (string-append hello
  name you slimy worm) )
• Usage (hello don) ? hello don you slimy worm

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Example 1.3

• (define (piggy x) ( 2 x) )
• (define (gonzo x y) (- x y) )
• (define (bunsen x y) (/ x y) )
• (define (kermit x y)
• (bunsen (piggy x) (gonzo x y) ) )
• Usage (gonzo 100 2) ? 98
• (bunsen 100 0) ? aaargh!!
• (piggy (bunsen 6 2)) ? (piggy 3) ? 6
• (kermit 5 2) ? (bunsen (piggy 5) (gonzo 5 2) )
  ? (bunsen 10 3) ? 10/3

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The Substitution Model

• How expressions are evaluated
• If the expression is a primitive, it is its own
  value
• If it is a compound expression -- not a special
  form -- like (function arg1 argn), then
• Evaluate function, arg1, argn
• Apply function to arguments, by replacing the
  parameters in the body of the function definition
  with the arguments, and then evaluating this

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Example 1.4(Substitution Model)

• (define piggy (lambda (x) ( 2 x)) )
• (define gonzo (lambda (x y) (- x y)) )
• Evaluate (piggy (gonzo 3 5))
• -- evaluate piggy (lambda (x) ( 2 x))
• -- evaluate (gonzo 3 5)
• -- evaluate gonzo (lambda (x y) (- x y) )
• -- evaluate 3 5 these are primitives so are
  themselves.
• -- apply (lambda (x y) (- x y)) to 3 5
  eval (- 3 5) ? -2
• -- (gonzo 3 5) has been evaluated to get 2
• -- apply (lambda (x) ( 2 x)) to 2 eval ( 2
  2) ? -4

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Substitution Model fine print

• This is an idealized version of how things work
• EXCEPTION If the function is AND or OR, and the
  first argument evaluates to f or t
  respectively, the second argument is not
  evaluated.
• Therefore (or ( 2 2) (/ 1 0) ) will not produce
  an error since (/ 1 0) will not be evaluated
• Suppose we defined our own OR function
• (define myor (lambda (x y) (or x y)) )
• (define (myor x y) (or x y) )
• (myor ( 2 2) (/ 1 0))will produce an error. WHY?

25
Conditional Statements

• The general form of a conditional
• (cond (ltp1gt lte1gt)
• (ltp2gt lte2gt)
• ...
• (ltpngt ltengt)
• )
• For example, this function returns the max of a,b
• (lambda (a b)
• (cond ( (gt a b) a)
• ( (lt a b) b)
• ( ( a b) a)
• )
• )

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Conditional Statements (else)

• For convenience, the last condition can be
  else, which covers every other condition
• (lambda (a b)
• (cond ((gt a b) a)
• ( else b)
• )
• )

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Conditional Statements (if)

• A common occurrence is that there are only two
  conditions
• (if condition dothis dothat)
• For example
• (lambda (a b) (if (gt a b) a b) )
• (lambda (x) ( (if (gt x 0) -) x) )
• implement the MAX and ABS function

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Example 1.5

• The IF statement can be replaced by the COND
  statement.
• (define (myif condition dothis dothat)
• (cond
• (condition dothis)
• (else dothat)
• )
• )

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Example 1.5

• Consider the following function to return (sin
  x)/x
• (define (lambda x)
• (myif ( x 0)
• 1
• (/ (sin x) x)
• )
• )
• This crashes when given the input x0.
• The same function, with MYIF replaced by IF, does
  not crash. WHY?
• Moral IF can be replaced by COND, but only
  internally.

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Example 1.6

• Define a procedure that displays the roots of
  ax2bxc 0. If there are no roots, it displays
  no roots. You can assume a is nonzero.
• Solution
• calculate b2-4ac
• If this is negative, display no roots
• Otherwise, display (-b /- sqrt(b2-4ac) ) / 2a

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Example 1.6

• (define (discrim a b c) (- ( b b) ( 4 a c) ) )
• (define (solvequadratic a b c) assumes a
  nonzero
• (if (lt (discrim a b c) 0)
• (begin (display no roots) (newline) )
• (begin
• (display (/ ( (- b) (sqrt (discrim a b
  c))) ( 2 a))) (newline)
• (display (/ (- (- b) (sqrt (discrim a b
  c))) ( 2 a))) (newline)
• )
• )
• )

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Example 1.6

• (define (solvequadratic a b c)
• (define (discrim a b c) (- ( b b) ( 4 a c)
  ) )
• (if (lt (discrim a b c) 0)
• (begin (display no roots) (newline) )
• (begin
• (display (/ ( (- b) (sqrt (discrim a b
  c))) ( 2 a))) (newline)
• (display (/ (- (- b) (sqrt (discrim a b
  c))) ( 2 a))) (newline)
• )
• )
• )

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Example 1.6

• (define (solvequadratic a b c)
• (define discrim (- ( b b) ( 4 a c) ) )
• (if (lt discrim 0)
• (begin (display no roots) (newline) )
• (begin
• (display (/ ( (- b) (sqrt discrim)) ( 2
  a))) (newline)
• (display (/ (- (- b) (sqrt discrim)) ( 2
  a))) (newline)
• )
• )
• )

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Example 1.6

• Improved solution store intermediate variables.
  (More on the LET statement in future lectures.)
• (define (solvequadratic a b c)
• (define discrim (- ( b b) ( 4 a c) ) )
• (if (lt discrim 0)
• (begin (display "no roots") (newline) )
• (let ((denom ( 2 a))
• (part1 (/ (- b) denom) )
• (part2 (/ (sqrt discrim) denom) ))
• (begin (display (- part1 part2) )
• (newline)
• (display ( part1 part2) )
• (newline)
• ))))

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Example 1.7

• Rewrite previous example so that it deals with
  all possible cases of a, b, c.
• (define (solvegeneralquad a b c)
• (if ( a 0)
• (if ( b 0)
• (if ( c 0)
• (begin (display "any x is
  solution") (newline) )
• (begin (display "no
  solutions") (newline) )
• )
• (begin (display (/ (- c) b) )
  (newline) )
• )
• (solvequadratic a b c)
• )
• )

36
Example 1.8

• Finding square roots with Newtons Method begin
• x 1
• while x not close enough to sqrt(A)
• x ½ (x A/x)
• end
• x A/x ½(x A/x)
• 1 2/1 2 ½ (2 1) 1.5
•   1.5 2/1.5 1.3333 ½ (1.3333
  1.5) 1.4167
•   1.4167 2/1.4167 1.4118 ½
  (1.4167 1.4118) 1.4142

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Example 1.8

• Implementing a procedure like this will become
  standard to you. For now, you have to think a
  bit. The basic idea is to keep trying new
  guesses
• (define (trythis x A)
• (if (goodenough x A)
• x
• (trythis (newguess x A) A)
• )
• )
• You now need to figure out what (goodenough x A)
  and (newguess x A) should be.

38
Example 1.8

• The algorithm clearly states how we should find a
  new guess given the previous guess
• (define (newguess x A) (/ ( x (/ A x)) 2) )
• An unsophisticated way of deciding whether a
  guess x is good enough is checking if x2 A lt
  0.001
• (define (goodenough x A)
• (lt (abs (- ( x x) A)) 0.001)
• )

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Example 1.8

• We have now defined three separate parts of our
  program
• (define (trythis x A)
• (if (goodenough x A)
• x
• (trythis (newguess x A) A)))
• (define (newguess x A) (/ ( x (/ A x)) 2) )
• (define (goodenough x A) (lt (abs (- ( x x)
  A)) 0.001) )
• How do we put all this together? We need to make
  the call (trythis 1 A).

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Example 1.8

• (define (NewtonRoot A)
• (define (trythis x A)
• (if (goodenough x A)
• x
• (trythis (newguess x A) A)))
• (define (newguess x A) (/ ( x (/ A x)) 2) )
• (define (goodenough x A) (lt (abs (- ( x x)
  A)) 0.001) )
• (trythis 1.0 A)
• ) ?

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Summary

• Computer Science isnt all about programming
• Programming is all about making errors and
  learning from them. And also about thinking.
• In Scheme, every expression has a value.
• Parentheses mean (evaluate me).
• Scheme makes no distinction between functions and
  data.
• Functions are defined using lambda.
• The Substitution Model gives an idea as to how
  Scheme evaluates expressions.
• Data abstraction means naming data and functions
  and then using them via these names
• Conditional statements are implemented using if
  and cond.