infix --> postfix

gistfile1.txt

gosh$ (i2p '(2 ^ < 6 - 7 > + 3 * 4))
(6 7 - ^ 3 4 * +)

infix2postfix.scm

;
; infix --> postfix
; https://gist.github.com/yamasushi/625b1f5b289dedd6cbb5709cb33f6c60

; expr  -> expr  + term1 { print + } | expr - term1 { print - } | term1
; term1 -> term1 * term2 { print * }| term1 / term2 { print / }| term2
; term2 -> <number> { print <number>.val }| ( expr )

; expr -> term1 rest1
; rest1 -> + term1 { print + } rest1_1
;      |  - term1 { print - } rest1_1
;      | ε
; term1 -> term2 rest2
; rest2 -> * term2 { print * } rest2_1
;      |   / term2 { print / } rest2_1
;      | ε
; factor -> <number> { print <number>.val }
;      | ( expr )

(define (i2p x) ($ car $ expr (cons '() x) ) )

(define (restx syms termx par)
	(define (_restx_ par)
		;(format #t "_restx_ par=~s~%" par)
		(let ( 	{inh (car par)}
				{xs  (cdr par) } )
			(if (null? xs)
				`(,inh)
				(let (	{hd (car xs)}
						{tl (cdr xs)} )
					(if (find (cut eq? hd <>) syms)
						($ _restx_
							$ (^y
								;(format #t "| ~s | ~s | ~s |~%" inh (car y) `(,hd) )
								(cons
									(append (car y) `(,hd) )
									(cdr y)
								))
							$ termx (cons inh tl) )
						par
					)
				)
			)
		)
	)
	;(format #t "restx syms=~s par=~s~%" syms par)
	(_restx_ par)
)

(define (expr par) ($ rest1 $ term1 par) )
(define rest1 (cut restx '(+ -) term1 <>) )

(define (term1 par)	($ rest2 $ term2 par) )
(define rest2 (cut restx '(* / %) term2 <>))

(define (term2 par)	($ rest3 $ term3 par) )
(define rest3 (cut restx '(^) term3 <>) )

(define (term3 par) (factor par))

(define (factor par)
	;(format #t "factor par=~s~%" par)
	(let ( 	{inh (car par)}
			{xs  (cdr par) } )
		(if (null? xs)
			(error "factor:error xs=~s" xs)
			(let (	{hd (car xs)}
					{tl (cdr xs)} )
				(cond
					{(of-type? hd <number>)
						(cons
							(append inh `(,hd) )
							tl)}
					{(eq? hd '< )
						($ (cut match-term '> <>) $ expr (cons '() tl) )}
					{else
						(error "factor:error xs=" xs) }
					)
			)
		)
	)
)

(define (match-term t par)
	;(format #t "match-term t=~s , par=~s~%" t par)
	(let ( 	{inh (car par)}
			{xs  (cdr par) } )
		(if (null? xs)
			(error "syntax error xs=" xs)
			(if (equal? (car xs) t)
				(cons inh (cdr xs))
				(error "syntax error xs=" xs)
			)
		)
	)
)