jimbreen

;; SICP Exercise 2.73

;; Section 2.3.2 described a program that performs symbolic differentiation: 
;; 
;; (define (deriv exp var) 
;;   (cond ((number? exp) 0) 
;;         ((variable? exp) (if (same-variable? exp var) 1 0)) 
;;         ((sum? exp) 
;;           (make-sum (deriv (addend exp) var) 
;;                     (deriv (augend exp) var))) 

jimbreen

;; SICP Excercise 2.56

;; Show how to extend the basic differentiator to handle more kinds 
;; of expressions. For instance, implement the differentiation rule 
;;      d(u^n)             /du\
;;      ------ = nu^(n-1) | -- |
;;        dx               \dx/
;; by adding a new clause to the deriv program and defining appropriate pro- 
;; cedures exponentiation?, base, exponent, and make-exponentiation. (You 
;; may use the symbol ** to denote exponentiation.) Build in the rules that any- 

jimbreen

;; SICP
;; Exercise 2.54
;;
;; Two lists are said to be equal? if they contain equal elements 
;;arranged in the same order. For example, 

    (equal? '(this is a list) '(this is a list)) 

;; is true, but 

jimbreen

;; SICP
;; Exercise 2.41. 
;; 
;; Write a procedure to find all ordered triples of distinct positive integers i, j , and k less than 
;; or equal to a given integer n that sum to a given integer s.
;; 

(define (unique-triplets n)
  (flatmap 
    (lambda (i) 

jimbreen

;; SICP
;; Exercise 2.40. 
;; 
;; Define a procedure unique-pairs that, given an integer n, generates the sequence of pairs 
;; (i, j ) with 1 ≤ j ≤ i ≤ n. Use unique-pairs to simplify the definition of prime-sum-pairs given above.

(define (unique-pairs n)
  (flatmap 
    (lambda (i) 
      (map (lambda (j) (list i j)) 

jimbreen

;; SICP
;; Exercise 2.33. 
;; 
;; Fill in the missing expressions to complete the following definitions of some basic list- 
;; manipulation operations as accumulations: 
;; 
;; (define (map p sequence) 
;;   (accumulate (lambda (x y) <??>) nil sequence)) 
;; (define (append seq1 seq2) 
;;   (accumulate cons <??> <??>)) 

jimbreen

;; SICP
;; Exercise 2.19. 
;; 
;; Consider the change-counting program of section 1.2.2. It would be nice to be able to easily 
;; change the currency used by the program, so that we could compute the number of ways to change a British 
;; pound, for example. As the program is written, the knowledge of the currency is distributed partly into the 
;; procedure first-denomination and partly into the procedure count-change (which knows that there are 
;; five kinds of U.S. coins). It would be nicer to be able to supply a list of coins to be used for making change. 
;; 
;; We want to rewrite the procedure cc so that its second argument is a list of the values of the coins to use 

jimbreen

;; SICP
;; Exercise 2.17. 
;; 
;; Define a procedure last-pair that returns the list that contains only the last element of a 
;; given (nonempty) list: 
;; (last-pair (list 23 72 149 34)) 
;; (34) 
;; 

(define (last-pair items)

jimbreen

;; SICP
;; Exercise 1.42
;; Let f and g be two one-argument functions. The composition f 
;; after g is defined to be the function x |-> f (g (x )). Define a procedure compose 
;; that implements composition. For example, if inc is a procedure that adds 1 
;; to its argument,
;;	((compose square inc) 6) 
;;	49 

(define (inc n)

jimbreen

;; SICP 1.3
;;
;; Exercise 1.3.  Define a procedure that takes three numbers as arguments and
;; returns the sum of the squares of the two larger numbers.
;;
;; This solution is based on discussion (primarily by Jim Weirich) during the 
;; Alpha study group's weekly meeting

(define (square x) (* x x))
(define (sum-of-squares x y) (+ (square x) (square y)))