CS1: Introduction to Computation

1
CS1Introduction to Computation

• Day 2 October 2, 2002
• Substitution Model

Add cards (and questions) AFTER class.
2
Precision

• Human (natural) Language is imprecise
• Full of ambiguity
• Computer languages must be precise
• Only one meaning
• No ambiguity

3
Last Time

• Saw how to form Scheme expressions

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Today

• Define their meaning
• By developing a precise model for interpreting
  them
• Model Substitution Model

5
Admin 1

• We do post slides after class
• see course schedule online
• Will try to post preliminary slides before class
• Same place
• Probably by 11am (prob. with a few errors)
• No promise
• Put Scheme code on handout
• Usually back of Big Idea handout
• (More admin at end of class)

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Scheme Combinations

• Scheme combination
• (fun op1 op2 op3 )
• Delimited by parentheses
• First element is the Operator
• Rest are Operands

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Scheme Combinations

• ( 2 3)
• (- 4 1)
• ( 2 3 4)
• (abs -7)
• (abs ( (- x1 x2) (- y1 y2)))

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Meaning?

• What does a Scheme expression mean?
• How do we know what value will be calculated by
  an expression?
• (abs ( (- x1 x2) (- y1 y2)))

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Substitution Model

• To evaluate a Scheme expression
• Evaluate its operands
• Evaluate the operator
• Apply the operator to the evaluated operands
• (fun op1 op2 op3 )

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Example Expression Eval

• Example ( 3 ( 4 5) )

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Example Expression Eval

• Example ( 3 ( 4 5))
• Evaluate 3
• Evaluate ( 4 5)
• Evaluate 4
• Evaluate 5
• Evaluate
• Apply to 4, 5 ? 20
• Evaluate
• Apply to 3, 20 ? 23

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Another Example

• ( 3 (- 4 ( 5 (expt 2 2))))
• Evaluate 3
• Evaluate (- 4 ( 5 (expt 2 2)))
• Evaluate 4
• Evaluate ( 5 (expt 2 2))
• Evaluate 5
• Evaluate (expt 2 2)
• Evaluate 2
• Evaluate 2
• Apply expt to 2,2 ? 4
• Apply to 5,4 ? 20
• Apply to 4, 20 ? -16
• Apply to 3, -16 ? -13

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Evaluation with Variables

• An assignment provides an association between a
  variable and its value
• (define X 3)
• To evaluate a variable
• Lookup the value associated with the variable
• And replace the variable with the value

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Variable Evaluation Example

• (define X 3)
• Evaluate X
• Lookup value of X
• X has value 3
• Result 3

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Simple Expression Evaluation

• Scheme Assignment and Evaluation
• (define X 3)
• (define Y 4)
• Evaluate ( X Y)
• Evaluate X ? 3
• Evaluate Y ? 4
• Apply to 3,4 ? 7

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Special Forms

• N.B. There are a few special forms which do not
  evaluate in quite the same way as weve
  described.
• define is one of them
• (define X 3)
• We do not evaluate X before applying define to X
  and 3
• We simply
• Evaluate the second argument (3)
• Make an association for it to the first argument
  (X)

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Lambda

• Lambda is also a special form
• Result of a lambda is always a function
• (an operator)
• We do not evaluate its contents
• Dont even treat them the same

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Scheme Functional Definition

• A(r) pi r2
• (define A (lambda (r) ( pi (expt r 2))))

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Evaluate a function call

• To Evaluate a function call
• Evaluate the arguments
• Apply the function
• To Apply a function call
• Replace the function argument variable with the
  value given in the call everywhere it occurs
• Evaluate the resulting expression

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Informally

• (define f
• (lambda (x)
• ( x 1)))
• What does this function do?
• (f 2)
• Substitute 2 for x
• (f 2)
• ( 2 1)
• 3

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Evaluate a function call

• (define f
• (lambda (x)
• ( x 1)))
• Evaluate (f 2)
• Evaluate 2
• Evaluate f ? (lambda (x) ( x 1))
• Apply (lambda (x) ( x 1)) to 2
• Substitute 2 for x in the expression ( x 1) ?
  ( 2 1)
• Evaluate ( 2 1) ? 3

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Evaluate Function Call

• (define f (lambda (x y)
• ( ( 3 x) ( -4 y) 2))))
• Evaluate (f 3 2)
• Evaluate 3
• Evaluate 2
• Evaluate f ? (lambda (x y) ( ( 3 x) ( -4 y)
  2))
• Apply f to 3 2
• Substitute 3 for x, 2 for y
• ( ( 3 3) ( -4 2) 2))
• Evaluate . 3

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Syntactic Sugar

• Equivalent expressions
• (define f (lambda (x) ( x 1))
• (define (f x) ( x 1))
• Simply an alternate syntax
• Allows us not to write lambda
• Maybe more natural for some
• Means the same thing

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Evaluating define

• To evaluate (define (f x) ( x 1))
• Desugar it into lambda form
• (define f (lambda (x) ( x 1))
• Evaluate like any define
• Create an association between the name f and the
  function (lambda (x) ( x 1))

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Example

• (define sq (lambda (x) ( x x))
• (define d (lambda (x y) ( (sq x) (sq y))))
• Evaluate (d 3 4)
• Evaluate 3?3
• Evaluate 4?4
• Evaluate d?(lambda (x y) ( (sq x) (sq y)))
• Apply (lambda (x y) ) to 3 4

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Example

• Apply (lambda (x y) ( (sq x) (sq y))) to 3 4
• Substitute 3 for x, 4 for y in ( (sq x) (sq y))
• Evaluate ( (sq 3) (sq 4))
• Evaluate (sq 3)
• Evaluate 3?3
• Evaluate sq?(lambda (x) ( x x))
• Apply (lambda (x) ( x x)) to 3
• Substitute 3 for x in ( x x)
• Evaluate ( 3 3)
• Evaluate 3?3
• Evaluate 3?3
• Apply to 3 3 ? 9

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Example

• Apply (lambda (x y) ( (sq x) (sq y))) to 3 4
• Substitute 3 for x, 4 for y in ( (sq x) (sq y))
• Evaluate ( (sq 3) (sq 4))
• Evaluate (sq 3)?many steps, previous slide?9
• Evalute (sq 4)
• Evaluate 4?4
• Evaluate sq?(lambda (x) ( x x))
• Apply (lambda (x) ( x x)) to 4
• Substitute 4 for x in ( x x)
• Evaluate ( 4 4)
• Evaluate 4?4
• Evaluate 4?4
• Apply to 4 4 ? 16

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Example

• Apply (lambda (x y) ( (sq x) (sq y))) to 3 4
• Substitute 3 for x, 4 for y in ( (sq x) (sq y))
• Evaluate ( (sq 3) (sq 4))
• Evaluate (sq 3)?many steps, 2 slides back?9
• Evaluate (sq 4)?many steps, previous slide?16
• Apply to 9 and 16 ?25
• which is final result
• (d 3 4) ? 25

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Substitution Model

• Given precise model for evaluation
• Can carry out mechanically
• By you
• By the computer
• Will be basis of our understanding for first half
  of course (until midterm)
• will expand and revise later

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Use the Model

• The model is simple
• Yes, it is tedious to evaluate all those steps
• But, thats how the machine works
• You can understand anything by applying the model
  carefully
• Dont skip steps

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Uncertainty / Unknown

• To be a good Scientist / Student
• Must be comfortable with the unknown
• comfortable with what you dont know
• Dont be too quick to latch on to an answer
• You may grab the wrong one
• Be open to a better (the right) answer

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Quote

• To stay young requires unceasing cultivation of
  the ability to unlearn old falsehoods.
• Notebooks of Lazarus Long

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Big Ideas

• Computer languages must be precise
• Define their meaning with a model
• Current model substitution model
• Can use it to understand the meaning of any
  Scheme expression

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Admin Wrapup
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Unix Tutorial Section

• Tonight!
• At 10pm
• In Jorgensen 74
• By Jason Mitchell
• ls, cd, mkdir, cat, more, rm, xterm, exit,
  scheme, .
• (if any of these are foreign to yougo!)

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Recitations

• Start Tomorrow
• Bring your questions!
• Two recitations at every time slot
• One is advanced
• Other is beginner
• Choose which one based on your comfort level

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Advanced vs. Beginner

• Beginner
• Dont feel inhibited asking any question because
  its too basic
• What is an operator?
• Advanced
• Dont feel inhibited (geeky) for asking a
  question because its too advanced
• Why havent you told us about types?

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Sections

• Beginner
• Thurs. 4pm Broad 100
• Fri. 1pm Beckman 115
• Fri. 2pm Beckman 115

• Advanced
• Thurs. 4pm Jorgensen 74
• Fri. 1pm Broad 100
• Fri. 2pm Broad 100

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UGCS Accounts

• Signup for your UGCS accounts
• card access being handled as part of that
• (not the way I told you on Monday)
• Necessary to create your cs1man account
• (probably wont be ready for submits until Monday)

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Jorgensen Access

• Only need cards after 530pm
• If card not work
• Phones by first floor doors
• Call UGCS Lab 2028
• (Call Security 4702)

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Lab Sections

• Now posted on the web
• Linked from CS1 home page on UGCS
• Not fillout form Monday?
• Mail ben_at_ugcs.caltech.edu with 4 preferences
• Start Sunday
• Some of you will have lab sections before next
  lecture
• Lab is staffed the rest of this week
• through Friday midnight
• Except 68pm

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ACM Programming Contest

• Team Practice
• Tues 830-1030pm
• Oct. 8th first meeting
• Jorgensen 154
• Mail ben_at_ugcs