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67 lines
2.1 KiB
67 lines
2.1 KiB
2 years ago
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Exercise 2.73: 2.3.2 described a
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program that performs symbolic differentiation:
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(define (deriv exp var)
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(cond ((number? exp) 0)
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((variable? exp)
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(if (same-variable? exp var) 1 0))
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((sum? exp)
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(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
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(multiplier exp)
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(deriv (multiplicand exp) var))
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(make-product
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(deriv (multiplier exp) var)
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(multiplicand exp))))
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⟨more rules can be added here⟩
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(else (error "unknown expression type:
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DERIV" exp))))
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We can regard this program as performing a dispatch on the type of the
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expression to be differentiated. In this situation the “type tag” of the
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datum is the algebraic operator symbol (such as +) and the operation
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being performed is deriv. We can transform this program into
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data-directed style by rewriting the basic derivative procedure as
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(define (deriv exp var)
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(cond ((number? exp) 0)
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((variable? exp)
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(if (same-variable? exp var)
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1
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0))
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(else ((get 'deriv (operator exp))
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(operands exp)
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var))))
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(define (operator exp) (car exp))
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(define (operands exp) (cdr exp))
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Explain what was done above. Why can’t we assimilate the predicates
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number? and variable? into the data-directed dispatch?
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Write the procedures for derivatives of sums and products, and the auxiliary
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code required to install them in the table used by the program above.
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Choose any additional differentiation rule that you like, such as the one for
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exponents (Exercise 2.56), and install it in this data-directed
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system.
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In this simple algebraic manipulator the type of an expression is the algebraic
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operator that binds it together. Suppose, however, we indexed the procedures
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in the opposite way, so that the dispatch line in deriv looked like
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((get (operator exp) 'deriv)
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(operands exp) var)
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What corresponding changes to the derivative system are required?
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