# [plt-scheme] Infix to prefic

Anton's nice infix macros on comp.lang.scheme made
me brush up some old code original used to have
a convenient input syntax for polynomials.
(module infix mzscheme
(require (lib "match.ss" "mzlib"))
(provide infix->prefix)
(define (infix->prefix exp)
; Convert an infix expression to prefix
(define ip infix->prefix)
(define (nott sym) (lambda (x) (not (eq? x sym))))
(define (non-op? s) (not (member s '(+ - * / ^))))
(match exp
[(? number? r) r] ; number
[(? symbol? s) s] ; variable
[((? non-op? s) (x ...)) `(,s ,@(map ip x))] ; function call
[(p) (ip p)] ; parentheses
[('- exp) `(- ,(ip exp))] ; sign
[('+ exp) `(+ ,(ip exp))] ; sign
[((and p (? (nott '+))) ... '+ q ...) `(+ ,(ip p) ,(ip q))]
[((and p (? (nott '-))) ... '- q ...) `(- ,(ip p) ,(ip q))]
[((and p (? (nott '*))) ... '* q ...) `(* ,(ip p) ,(ip q))]
[((and p (? (nott '/))) ... '/ q ...) `(/ ,(ip p) ,(ip q))]
[((and p (? (nott '^))) ... '^ q ...) `(^ ,(ip p) ,(ip q))]
[_ (error "infix->prefix: The following is not a legal infix
representation of an arithmetical expression: " exp)]))
)
>(require (lib "defmacros.ss"))
>(define-macro (: . infix)
(infix->prefix infix))
>(define x 3)
> (: sin(x) + 1 * tan(2))
-2.0439198552016515
The observant reader will by now have noticed that / and ^ associate
the wrong way, but that's not my problem. My problem is the expansion
time of the above match expression. If the two lines with / and ^ is
commented out the above is evalueted almost immediately.
Is there a more a suitable way to write the match expression?
--
Jens Axel Søgaard