msl-starter.plai~

#lang plai-typed

(define-type msl
  [msl-num (n : number)]
  [msl-add (lhs : msl) (rhs : msl)]
  )

;; eval msl -> number
;; evaluate an msl expression
;; examples
;; (msl-num 7) -> 7
;; (msl-add (msl-num 3) (msl-num 4)) -> 7
;; (msl-add (msl-add (msl-num 3) (msl-num 4)) (msl-num 35)) -> 42
(define (eval [expr : msl])
  (type-case msl expr
    [msl-num (n) n]
    [msl-add (lhs rhs) (+ (eval lhs) (eval rhs))]))

;; parse s-expression -> msl
;; convert a quoted s expression into the equivalent msl form
;; examples
;; '7 -> (msl-num 7)
;; '(+ 3 4) -> (msl-add (msl-num 3) (msl-num 4))
;; '(+ (+ 3 4) 35) -> (msl-add (msl-add (msl-num 3) (msl-num 4)) (msl-num 35))
(define (parse [s : s-expression]) : msl
  (cond
    [(s-exp-number? s) (msl-num (s-exp->number s))]
    [(s-exp-list? s)
     (let ([sl (s-exp->list s)])
       (case (s-exp->symbol (first sl))
         [(+) (msl-add (parse (second sl)) (parse (third sl)))]
         [else (error 'parse "invalid list input")]))]
    [else (error 'parse "invalid input")]))