Extended Introduction to Computer Science

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Extended Introduction to Computer Science
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Administration

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• Book Structure and Interpretation of Computer
  Programs by Abelson Sussman
• Web http//www.cs.tau.ac.il/scheme

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Course Structure

• Three Elements
• Lectures (??????)
• Recitations (???????)
• Homework (?????? ???)
• Final Grade Homework MidTerm Exam Final Exam

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This Course
Is NOT a programming course It is an extended
introduction to COMPUTER SCIENCE
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Computer Science
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Geometry
Giha Earth
Metra Measure
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Declarative Knowledge
What is true
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Imperative Knowledge
How to

• To find an approximation of x
• Make a guess G
• Improve the guess by averaging G and x/G
• Keep improving the guess until it is good enough

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How to knowledge
Process series of specific, mechanical steps
for deducing information, based on simpler data
and set of operations
Procedure particular way of describing the
steps a process will evolve through

• Need a language for description
• vocabulary
• rules for connecting elements syntax
• rules for assigning meaning to constructs
  semantics

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Designing Programs

• Controlling Complexity
• Black Box Abstraction
• Conventional Interfaces
• Meta-linguistic Abstraction

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Scheme

• We will study LISP LISt Processing
• Invented in 1959 by John McCarthy
• Scheme is a dialect of LISP invented by Gerry
  Sussman and Guy Steele

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The Scheme Interpreter

• The Read/Evaluate/Print Loop
• Read an expression
• Compute its value
• Print the result
• Repeat the above
• The Environment

Name Value
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Designing Programs

• Controlling Complexity
• Problem Decomposition
• Black Box Abstraction
• Implementation vs. Interface
• Modularity

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Language Elements
Syntax Semantics
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Computing in Scheme
gt 23
23
gt ( 3 17 5)
25
gt ( 3 ( 5 6) 8 2)
23
score
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gt (define score 23)
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Computing in Scheme
gt score
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gt (define total 25)
23
score
25
total
gt ( 100 (/ score total))
92
92
percentage
gt (define percentage ( 100 (/ score total))
gt
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Evaluation of Expressions
The value of a numeral number The value of a
built-in operator machine instructions to
execute The value of any name the associated
value in the environment

• To Evaluate a combination (as opposed to special
  form)
• Evaluate all of the sub-expressions in some order
• Apply the procedure that is the value of the
  leftmost sub-expression to the arguments (the
  values of the other sub-expressions)

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Using Evaluation Rules
gt (define score 23)
gt ( ( 5 6 ) (- score ( 2 3 2 )))
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Abstraction Compound Procedures

• How does one describe procedures?
• (lambda (x) ( x x))

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Lambda

• The use of the word lambda is taken from lambda
  calculus.
• Introduced in the Discrete Math course.
• Useful notation for functions.

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Evaluation of An Expression
To Apply a compound procedure (to a list of
arguments) Evaluate the body of the
procedure with the formal parameters replaced by
the corresponding actual values
gt ((lambda(x)( x x)) 5)
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Evaluation of An Expression
To Apply a compound procedure (to a list of
arguments) Evaluate the body of the
procedure with the formal parameters replaced by
the corresponding actual values
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Using Abstractions
gt (define square (lambda(x)( x x)))
Environment Table
gt (square 3)
square
Proc (x)( x x)
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gt ( (square 3) (square 4))
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Yet More Abstractions
gt (define sum-of-two-squares
(lambda(x y)( (square x) (square y))))
gt (sum-of-two-squares 3 4)
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gt (define f (lambda(a)
(sum-of-two-squares ( a 3) ( a 3))))
Try it outcompute (f 3) on your own
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Evaluation of An Expression (reminder)
The Substitution model
? reduction in lambda calculus
To Apply a compound procedure (to a list of
arguments) Evaluate the body of the
procedure with the formal parameters substituted
by the corresponding actual values
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Lets not norget The Environment
gt (define x 8)
gt ( x 1)
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gt (define x 5)
gt ( x 1)
The value of ( x 1) depends on the environment!
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Using the substitution model
(define square (lambda (x) ( x x)))(define
average (lambda (x y) (/ ( x y) 2))) (average 5
(square 3))(average 5 ( 3 3))(average 5
9) first evaluate operands, then substitute
(/ ( 5 9) 2)(/ 14 2) if operator is a
primitive procedure, 7 replace by result of
operation

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Booleans
Two distinguished values denoted by the constants
t and f
The type of these values is boolean
gt (lt 2 3)
t
gt (lt 4 3)
f
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Values and types
In scheme almost every expression has a value
Examples

• The value of 23 is 23
• The value of is a primitive procedure for
  addition
• The value of (lambda (x) ( x x)) is the compound
  procedure proc (x) ( x x)

Values have types. For example

• The type of 23 is numeral
• The type of is a primitive procedure
• The type of proc (x) ( x x) is a compound
  procedure
• The type of (gt x 1) is a boolean (or logical)

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No Value?

• In scheme almost every expression has a value
• Why almost?
• Example what is the value of the expression
• (define x 8)
• In scheme, the value of a define expression is
  undefined . This means implementation-dependent
  
• Dr. Scheme does not return (print) any value
  for a define expression.
• Other interpreters may act differently.

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More examples
gt (define x 8)
gt (define x ( x 2))
gt x
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gt (define x y)
reference to undefined identifier y
gt (define -)
gt ( 2 2)
0
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The IF special form
(if (lt 2 3) 2 3) gt 2 (if (lt 2 3) 2 (/ 1 0))
gt
ERROR
2

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IF is a special form

• In a general form, we first evaluate all
  arguments and then apply the function
• (if ltpredicategt ltconsequentgt ltalternativegt) is
  different
• ltpredicategt determines whether we evaluate
  ltconsequentgt or ltalternativegt.
• We evaluate only one of them !

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Syntactic Sugar for naming procedures

Instead of writing
(define square (lambda (x) ( x x))
We can write
(define (square x) ( x x))

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Some examples
(define twice
) (twice 2) gt 4 (twice 3) gt 6
(lambda (x) ( 2 x))
Using syntactic sugar (define (twice x) ( 2
x))
(define second
) (second 2 15 3) gt 15 (second 34 -5 16) gt -5
(lambda (x y z) y)
Using syntactic sugar (define (second x y z) y)
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Summary

• Computer science formalizes the computational
  process
• Programming languages are a way to describe this
  process
• Syntax
• Sematics
• Scheme is a programming language whose syntax is
  structured around compound expressions
• We model the semantics of the scheme via the
  substitution model, the mathematical equivalent
  of lambda calculus