6.001 FT04 - recitation 11

Tagged Data

variable

(define *variable-tag* 'variable)

(define (make-variable vname)
  (list *variable-tag* vname))

(define (variable? x)
  (tagged-list? x *variable-tag*))

(define (varname var)
  (if (variable? var)
      (cadr var)
      (error "not a variable: " var)))

(define (variable=? v1 v2)
  (eq? (varname v1) (varname v2)))


constant-add

(define (constant-add c1 c2)
  (make-constant (+ (constval c1) (constval v2))))

poly-add

(define (poly-add p1 p2)
  (define (add-terms t1 t2)
    (cond ((null? t1)
	   t2)
	  ((null? t2)
	   t1)
	  (else
	   (cons (add (car t1)
		      (car t2))
		 (add-terms (cdr t1) (cdr t2))))))

  (if (and (poly? p1) (poly? p2))
      (if (variable=? (poly-get-var p1)
		      (poly-get-var p2))
	  (make-poly
	   (poly-get-var p1)
	   (add-terms (poly-get-terms p1) (pol-get-terms p2)))
	  (make-poly
	   (poly-get-var p1)
	   (cons (add (car (poly-get-terms p1))
		      p2)
		 (cdr (poly-get-terms p1)))))
      (error "not given two polys")))

basic add procedure

Hard to do without promotion, see below.


promotion

(define (var->poly var)
  (make-poly var (list 0 1)))

(define (const->poly var const)
  (make-poly var (list const)))

(define (->poly var exp)
  (cond ((constant? exp)
	 (const->poly var exp))
	((variable? exp)
	 (var->poly exp))
	((poly? exp)
	 exp)
	(else
	 (error "unknown exp" exp))))

(define (add e1 e2)
  (if (and (constant? e1)
	   (constant? e2))
      (constant-add e1 e2)
      (let ((var (find-var e1 e2)))
	(poly-add (->poly var e1)
		  (->poly var e2))))