/
ch23.rkt
129 lines (108 loc) · 3.02 KB
/
ch23.rkt
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#lang racket
; 2.53
; (list 'a 'b 'c)
; ; => '(a b c)
; (list (list 'george))
; ; => '((george))
; (cdr '((x1 x2) (y1 y2)))
; ; => '((y1 y2))
; (cadr '((x1 x2) (y1 y2)))
; ; => '(y1 y2)
; (pair? (car '(a short list)))
; ; => #f
; (memq 'red '((red shoes) (blue socks)))
; ; => #f
; (memq 'red '(red shoes blue socks))
; ; => '(red shoes blue socks)
; 2.54
(define (equal? lst1 lst2)
(cond [(and (empty? lst1)
(empty? lst2))
#t]
[(empty? lst1) #f]
[(empty? lst2) #f]
[else (and (eq? (car lst1)
(car lst2))
(equal? (cdr lst1)
(cdr lst2)))]))
(provide equal?)
; 2.55
; This is a bit confusing without understanding that
; 'x <=> (quote x)
; (car ''abracadabra)
; => (car (quote (quote abracadabra)))
; => (car '(quote abracadabra))
; => 'quote
; Section 2.3.2 - symbolic differentiator
(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)))
((product? exp)
(make-sum
(make-product
(multiplier exp)
(deriv (multiplicand exp) var))
(make-product
(deriv (multiplier exp) var)
(multiplicand exp))))
((exponentiation? exp)
(make-product
(exponent exp)
(make-product
(make-exponentiation
(base exp)
(make-sum -1 (exponent exp)))
(deriv (base exp) var))))
(else (error "unknown expression
type: DERIV" exp))))
(define (variable? x) (symbol? x))
(define (same-variable? v1 v2)
(and (variable? v1)
(variable? v2)
(eq? v1 v2)))
(define (=number? exp num)
(and (number? exp) (= exp num)))
(define (make-sum a1 a2)
(cond ((=number? a1 0) a2)
((=number? a2 0) a1)
((and (number? a1) (number? a2))
(+ a1 a2))
(else (list '+ a1 a2))))
(define (sum? x)
(and (pair? x) (eq? (car x) '+)))
(define (addend s) (cadr s))
(define (augend s)
(foldl make-sum 0 (cddr s)))
(define (make-product m1 m2)
(cond ((or (=number? m1 0)
(=number? m2 0))
0)
((=number? m1 1) m2)
((=number? m2 1) m1)
((and (number? m1) (number? m2))
(* m1 m2))
(else (list '* m1 m2))))
(define (product? x)
(and (pair? x) (eq? (car x) '*)))
(define (multiplier p) (cadr p))
(define (multiplicand p)
(foldl make-product 1 (cddr p)))
(define (make-exponentiation base exponent)
(cond [(and (number? base) (number? exponent))
(expt base exponent)]
[(=number? exponent 0) 1]
[(=number? exponent 1) base]
[(=number? base 0) 0]
[(=number? base 1) 1]
[else (list '** base exponent)]))
(define (exponentiation? exp)
(and (pair? exp) (eq? (car exp) '**)))
(define (base exp)
(cadr exp))
(define (exponent exp)
(caddr exp))
(provide deriv)