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Extended Introduction to Computer Science

Extended Introduction to Computer Science. Administration. סגל הקורס: מרצים: ד"ר דניאל דויטש, איל כהן מתרגלת:לבנת ג'רבי בודק: ינון פלד Book: Structure and Interpretation of Computer Programs – by Abelson & Sussman Web: http://www.cs.tau.ac.il/~scheme. Course Structure. Three Elements

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Extended Introduction to Computer Science

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  1. Extended Introduction to Computer Science

  2. Administration • סגל הקורס: • מרצים: ד"ר דניאל דויטש, איל כהן • מתרגלת:לבנת ג'רבי • בודק:ינון פלד • Book: Structure and Interpretation of Computer Programs – by Abelson & Sussman • Web: http://www.cs.tau.ac.il/~scheme

  3. Course Structure • Three Elements • Lectures (הרצאות) • Recitations (תרגולים) • Homework (תרגילי בית) • Final Grade = Homework (30%) + Final Exam (70%) חובה להגיש ולקבל ציון עובר עבור לפחות 80% מהתרגילים!!

  4. This Course… Is NOT a programming course It is an extended introduction to COMPUTER SCIENCE…

  5. Declarative Knowledge “What is true”

  6. An algorithm due to: [Heron of Alexandria] 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

  7. 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 X/G = 2 G = ½ (1+ 2) = 1.5 X/G = 4/3 G = ½ (3/2 + 4/3) = 17/12 = 1.416666 X/G = 24/17 G = ½ (17/12 + 24/17) = 577/408 = 1.4142156

  8. Scheme “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

  9. Designing Programs • Controlling Complexity • Black Box Abstraction • Conventional Interfaces • Meta-linguistic Abstraction

  10. Expressions Data or procedures Syntax Semantics 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

  11. The Scheme Interpreter • The Read/Evaluate/Print Loop • Read an expression • Compute its value • Print the result • Repeat the above • The Environment Name Value

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

  13. Language Elements Syntax Semantics

  14. Expression whose value is a procedure Closing parenthesis Environment Table Other expressions Name Value Opening parenthesis Computing in Scheme ==> 23 23 ==> (+ 3 17 5) 25 ==> (+ 3 (* 5 6) 8 2) score 23 43 ==> (define score 23)

  15. Environment Table Name Value Computing in Scheme ==> score 23 ==> (define total 25) score 23 total 25 ==> (* 100 (/ score total)) 92 percentage 92 ==> (define percentage (* 100 (/ score total)) ==>

  16. 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)

  17. Special Form (second sub-expression is not evaluated) * + 5 6 - 23 * 2 3 2 11 12 11 121 Using Evaluation Rules ==> (define score 23) ==> (* (+ 5 6 ) (- score (* 2 3 2 )))

  18. formal parameters body To process multiply it by itself something • Special form – creates a “procedure object” and returns it as a “value” Proc (x) (* x x) Internal representation Abstraction – Compound Procedures • How does one describe procedures? • (lambda (x) (* x x))

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

  20. Proc(x)(* x x) 5 (* 5 5) 25 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 ==> ((lambda(x)(* x x)) 5)

  21. The value of a numeral: number The value of a built-in operator: machine instructions to execute The value of any name: the associated object in the environment • To Evaluate a combination: (other than special form) • Evaluate all of the sub-expressions in any order • Apply the procedure that is the value of the leftmost sub-expression to the arguments (the values of the other sub-expressions) 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

  22. (* 3 3) (* 4 4) + 9 16 25 Using Abstractions ==> (define square (lambda(x)(* x x))) Environment Table ==> (square 3) square Proc (x)(* x x) 9 ==> (+ (square 3) (square 4))

  23. Yet More Abstractions ==> (define sum-of-two-squares (lambda(x y)(+ (square x) (square y)))) ==> (sum-of-two-squares 3 4) 25 ==> (define f (lambda(a) (sum-of-two-squares (+ a 3) (* a 3)))) Try it out…compute (f 3) on your own

  24. The value of a numeral: number The value of a built-in operator: machine instructions to execute The value of any name: the associated object in the environment • To Evaluate a combination: (other than special form) • Evaluate all of the sub-expressions in any order • Apply the procedure that is the value of the leftmost sub-expression to the arguments (the values of the other sub-expressions) Evaluation of An Expression (reminder)  reduction in lambda calculus The Substitution model 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

  25. Lets not forget The Environment ==> (define x 8) ==> (+ x 1) 9 ==> (define x 5) ==> (+ x 1) The value of (+ x 1) depends on the environment! 6

  26. 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

  27. Booleans Two distinguished values denoted by the constants #t and #f The type of these values is boolean ==> (< 2 3) #t ==> (< 4 3) #f

  28. 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) Valueshavetypes. For example: • The type of 23is numeral • The type of + is a primitive procedure • The type of proc (x) (* x x) is a compound procedure • The type of (> x 1) is a boolean (or logical)

  29. 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.

  30. Environment Table x 8 + #<-> Name Value 16 More examples ==> (define x 8) ==> (define x (* x 2)) ==> x 16 ==> (define x y) reference to undefined identifier: y ==> (define + -) ==> (+ 2 2) 0

  31. (if <predicate> <consequent> <alternative>) • If the value of <predicate> is #t, • Evaluate <consequent> and return it • Otherwise • Evaluate <alternative> and return it The IF special form (if (< 2 3) 2 3) ==> 2 (if (< 2 3) 2 (/ 1 0)) ==> ERROR 2

  32. IF is a special form • In a general form, we first evaluate all arguments and then apply the function • (if <predicate> <consequent> <alternative>) is different: • <predicate> determines whether we evaluate <consequent> or <alternative>. • We evaluate only one of them !

  33. Syntactic Sugar for naming procedures Instead of writing: (define square (lambda (x) (* x x)) We can write: (define (square x) (* x x))

  34. Some examples: (define twice ) (twice 2) ==> 4 (twice 3) ==> 6 (lambda (x) (* 2 x)) Using “syntactic sugar”: (define (twice x) (* 2 x)) (define second ) (second 2 15 3) ==> 15 (second 34 -5 16) ==> -5 (lambda (x y z) y) Using “syntactic sugar”: (define (second x y z) y)

  35. 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

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