MASSACHVSETTS INSTITVTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.001--Structure and Interpretation of Computer Programs
Fall Semester, 1998

Lecture Notes, September 9

Scheme Basics

Language Components

Primitives
Means of combination
- procedure application
- compound data structures
Means of abstraction
- naming
- procedures
- data abstractions

Rules for Scheme

1.: (Almost) Every expression has a value (which is returned when the expression is evaluated).
2.: Every value has a type.

Rules for Evaluation

1.

If expression is self-evaluating, return value.

2.

If a name, return value associated with that name in the environment.

3.

If a special form, do something special.

4.

If a combination, then

(a): Evaluate all of the subexpressions of the combination (in any order).
(b): Apply the operator to the values of the operands (the arguments) and return the result.

Rules for Application

1.: If procedure is primitive (built-in), just do it.
2.: If procedure is a compound procedure, then evaluate the body of the procedure with each formal parameter replaced by the corresponding actual argument value.

Taxonomy of Expressions

Primitive Expressions
- Constants (self-evaluating)
  - Numerals, e.g. 7 == Sch-Num 7
  - Strings, e.g. "hello" == Sch-String hello
  - Booleans, e.g. #f #t == Sch-Bools
- Names
  - e.g. + == primitive procedure
  - e.g. x == variable created by define or procedure application
Compound Expressions
- Combinations: (<operator> <operand> <operand> ...)
- Special Forms
  - define: (define <name> <exp>)
  - lambda: (lambda (<formal1> <formal2> ...) <body>)
  - if: (if <predicate> <consequent> <alternative>)
  - ... more to come! ...

Approximations for Square Root

(define try
  (lambda (guess x)
    (if (good-enuf? guess x)
        guess
        (try (improve guess x) x))))

(define improve
  (lambda (guess x)
    (average guess (/ x guess))))

(define average
  (lambda (a b)
    (/ (+ a b) 2)))

(define good-enuf?
  (lambda (guess x)
    (< (abs (- (square guess) x)) 0.001)))

(define sqrt
  (lambda (x) (try 1 x)))

About this document ...

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Duane Boning
1998-09-10