MIT 6.001                                       Fall, 1997
Instructor: A. Meyer                            T.A.: A Chefter

        Recitation #7, Problems Done in Recitation, Fri., 10/3/97

Today, for simplicity, we'll consider abstract expressions w/o the Product
case included in lecture.

To work with abstract expressions we need contructors MAKE-CONTANT,
MAKE-VARIABLE, and MAKE-SUM, which contruct a corresponding expression
given a contant, a variable, or an addend and an augend. We also need
selectors VARIABLE-NAME, CONTANT-VALUE, ADDEND, and AUGEND.  We require
only that the contructors and selectors obey the rules:

(contant-value (make-contant c))  => c
(variable-name (make-variable v)) => v
(addend (make-sum e1 e2))         => e1
(augend (make-sum e1 e2))         => e2


Exercise 1.  Implement the constructors and selectors.

Now, we are going to define "observers" CONTANT?, VARIABLE?, and SUM?
satisfying the following Contract:

                          contract for CONSTANT?
(contant? (make-contant c))   => #t
(contant? (make-variable v))  => #f
(contant? (make-sum e1 e2))   => #f

                          contract for VARIABLE?
(variable? (make-variable v)) => #t
(variable? (make-constant c)) => #f
(varaible? (make-sum e1 e2))  => #f

                            contract for SUM?
(sum? (make-sum e1 e2))  => #t
(sum? (make-variable v)) => #f
(sum? (make-contant c))  => #f


Exercise 2. implement the observers.

-----------------------------------------------------

SOLUTION 1:

              A Simple Implementation of Expressions

(define (make-contant num) num)
(define (make-variable sym) sym)
(define (make-sum exp1 exp2) (list 'sum exp1 exp2))

(define (contant-value cont) cont)
(define (variable-name var) var)
(define addend cadr)
(define augend caddr)


SOLUTION 2:

(define constant? number?)

(define variable? symbol?)

(define (sum? exp)
  (and (pair? exp) 
       (eq? (car exp) 'sum)))