/
differentiation.scm
executable file
·46 lines (35 loc) · 1.28 KB
/
differentiation.scm
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(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))))
(else
(error "unknown expression type: DERIV" exp))))
(define variable? symbol?)
(define (same-variable? v1 v2)
(and (variable? v1) (variable? v2) (eq? v1 v2)))
(define (sum? x) (and (pair? x) (eq? (car x) '+)))
(define addend cadr)
(define augend caddr)
(define (product? x) (and (pair? x) (eq? (car x) '*)))
(define multiplier cadr)
(define multiplicand caddr)
(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 (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 (=number? exp num) (and (number? exp) (= exp num)))