2.56.tex

\documentclass[a4paper,12pt]{article}
\usepackage{listings}
\lstset{language=Lisp}

\begin{document}
\begin{lstlisting}
(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-sub (exponent exp) 1))
                        (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 (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 (=number? exp num)
  (and (number? exp) (= exp num)))
 
(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 (sum? x)
  (and (pair? x) (eq? (car x) '+)))

(define (addend s) (car (cdr s)))
(define (augend s) (car (cdr (cdr s))))

(define (product? x)
  (and (pair? x) (eq? (car x) '*)))

(define (multiplier p) (car (cdr p)))
(define (multiplicand p) (car (cdr (cdr p))))

(define (make-sub a1 a2)
  (make-sum a1 (make-product -1 a2)))

(define (make-exponentiation base exponent)
  (cond ((=number? exponent 0) 1)
        ((=number? exponent 1) base)
        (else (list '** base exponent))))

(define (exponentiation? x)
  (and (pair? x) (eq? (car x) '**)))

(define (base e) (car (cdr e)))
(define (exponent e) (car (cdr (cdr e))))
\end{lstlisting}
\end{document}