;; The first three lines of this file were inserted by DrScheme. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "reader.ss" "plai" "lang")
;; A simple interpreter for addition and subtraction.
;;
;; Morgan McGuire morgan@cs.williams.edu


; Grammar
(define num?  number?)
(define (add? e) (and (list? e) (equal? (length e) 3) (eq? (first e) '+))) 
(define (sub? e) (and (list? e) (equal? (length e) 3) (eq? (first e) '-))) 
(define (expr? e)
  (or (num? e) 
      (add? e)
      (sub? e)))


; The calc evaluator (interpreter)
(define (calc e)
  (cond 
    ; Value of a number is itself
    [(num? e) e]
    
    ; Value of a sum is the sum of the evaluation of its arguments
    [(add? e) 
     (let ([lhs (second e)]
           [rhs (third e)])
       (+ (calc lhs) (calc rhs)))]
    
    ; Value of a difference is the difference of the evaluation of its arguments
    [(sub? e) 
     (let ([lhs (second e)]
           [rhs (third e)])
       (- (calc lhs) (calc rhs)))]))


(calc '(+ 1 2))