Operator precedence parsing macro in Racket

operator_parser.rkt

(define-syntax (: stx)
  (syntax-parse stx
    ; #:literals needs to have bindings in order to work
    ; #:datum-literals only needs symbols so it works with '^'.
    #:datum-literals (+ - * / ^)
    [(_ l ... + r ...) #'(+ (: l ...) (: r ...))]
    [(_ l ... - r ...) #'(- (: l ...) (: r ...))]
    [(_ l ... * r ...) #'(* (: l ...) (: r ...))]
    [(_ l ... / r ...) #'(/ (: l ...) (: r ...))]
    [(_ l ... ^ r ...) #'(expt (: l ...) (: r ...))]
    [(_ ( x ... ) ) #'(: x ...)]
    [(_ x) #'x]))

(: 1 + 2 * 3 - 2 ^ 2) ; => 3
(: 3 * (2 + 1 * 3) ^ 2) ; => 75
(: 3 * 5 ^ (1 + 1) + 3) ; => 78