78 lines
No EOL
2.7 KiB
Scheme
78 lines
No EOL
2.7 KiB
Scheme
#lang sicp
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(define (variable? x) (symbol? x))
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(define (same-variable? v1 v2)
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(and (variable? v1) (variable? v2) (eq? v1 v2)))
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(define (=number? exp num) (and (number? exp) (= exp num)))
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(define (make-sum a1 a2)
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(cond ((=number? a1 0) a2)
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((=number? a2 0) a1)
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((and (number? a1) (number? a2))
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(+ a1 a2))
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(else (list '+ a1 a2))))
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(define (make-product m1 m2)
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(cond ((or (=number? m1 0) (=number? m2 0)) 0)
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((=number? m1 1) m2)
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((=number? m2 1) m1)
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((and (number? m1) (number? m2)) (* m1 m2))
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(else (list '* m1 m2))))
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(define (sum? x) (and (pair? x) (eq? (car x) '+)))
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(define (addend s) (cadr s))
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(define (augend s) (caddr s))
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(define (product? x) (and (pair? x) (eq? (car x) '*)))
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(define (multiplier p) (cadr p))
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(define (multiplicand p) (caddr p))
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; for the purposes of our exponentiation exercise, we need to determine whether
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; the exponent is constant so that we can apply the rule correctly
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(define (constant? x var)
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(or (number? x)
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(and (variable? x) (not (same-variable? x var)))
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(and (sum? x)
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(constant? (addend x) var)
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(constant? (augend x) var))
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(and (product? x)
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(constant? (multiplier x) var)
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(constant? (multiplicand x) var))
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(and (exponentiation? x)
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(constant? (base x) var)
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(constant? (exponent x) var))))
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(define (make-exponentiation b e)
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(cond ((=number? e 0) 1)
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((=number? e 1) b)
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((=number? b 0) 0)
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((and (number? b) (number? e)) (expt b e))
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(else (list '** b e))))
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(define (exponentiation? x) (and (pair? x) (eq? (car x) '**)))
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(define (base e) (cadr e))
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(define (exponent e) (caddr e))
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(define (deriv exp var)
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(cond ((number? exp) 0)
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((variable? exp) (if (same-variable? exp var) 1 0))
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((sum? exp) (make-sum (deriv (addend exp) var)
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(deriv (augend exp) var)))
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((product? exp)
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(make-sum
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(make-product (multiplier exp)
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(deriv (multiplicand exp) var))
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(make-product (deriv (multiplier exp) var)
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(multiplicand exp))))
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((exponentiation? exp)
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(if (constant? (exponent exp) var)
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(make-product (make-product (exponent exp)
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(make-exponentiation (base exp)
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(make-sum
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(exponent exp)
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-1)))
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(deriv (base exp) var))
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(error "non-constant exponents not yet supported: DERIV" exp)))
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(else
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(error "unknown expression type: DERIV" exp)))) |