#lang pl
#|
 The grammar:
 <FLANG> ::= <num>
           | True
           | False
           | { + <FLANG> <FLANG> }
           | { - <FLANG> <FLANG> }
           | { * <FLANG> <FLANG> }
           | { / <FLANG> <FLANG> }
           | { > <FLANG> <FLANG> }
           | { = <FLANG> <FLANG> }
           | { if <FLANG> then <FLANG> else <FLANG> }
           | { with { <id> <FLANG> } <FLANG> }
           | <id>
           | { fun { <id> } <FLANG> }
           | { call <FLANG> <FLANG> }
|#
(define-type FLANG
  [Num Number]
  [Add FLANG FLANG]
  [Sub FLANG FLANG]
  [Mul FLANG FLANG]
  [Div FLANG FLANG]
  [Id Symbol]
  [With Symbol FLANG FLANG]
  [Fun Symbol FLANG]
  [Call FLANG FLANG]
  [Bool Boolean]
  [Eq FLANG FLANG]
  [Geq FLANG FLANG]
  [If FLANG FLANG FLANG])
(: parse-sexpr : Sexpr -> FLANG)
;; to convert s-expressions into FLANGs
(define (parse-sexpr sexpr)
  (match sexpr
    [(number: n) (Num n)]
    ['True  (Bool #t)]
    ['False (Bool #f)]
    [(symbol: name) (Id name)]
    [(cons 'with more)
     (match sexpr
       [(list 'with (list (symbol: name) named) body)
        (With name (parse-sexpr named) (parse-sexpr body))]
       [else (error 'parse-sexpr "bad `with' syntax in ~s" sexpr)])]
    [(cons 'fun more)
     (match sexpr
       [(list 'fun (list (symbol: name)) body)
        (Fun name (parse-sexpr body))]
       [else (error 'parse-sexpr "bad `fun' syntax in ~s" sexpr)])]
    [(cons 'if more)
     (match sexpr
       [(list 'if conition 'then result1 'else result2)
        (If (parse-sexpr conition) (parse-sexpr result1) (parse-sexpr result2))]
       [else (error 'parse-sexpr "bad `if' syntax in ~s" sexpr)])]
    [(list '+ lhs rhs) (Add (parse-sexpr lhs) (parse-sexpr rhs))]
    [(list '- lhs rhs) (Sub (parse-sexpr lhs) (parse-sexpr rhs))]
    [(list '* lhs rhs) (Mul (parse-sexpr lhs) (parse-sexpr rhs))]
    [(list '/ lhs rhs) (Div (parse-sexpr lhs) (parse-sexpr rhs))]
    [(list '> lhs rhs) (Geq (parse-sexpr lhs) (parse-sexpr rhs))]
    [(list '= lhs rhs) (Eq (parse-sexpr lhs) (parse-sexpr rhs))]
    [(list 'call fun arg) (Call (parse-sexpr fun) (parse-sexpr arg))]
    [else (error 'parse-sexpr "bad syntax in ~s" sexpr)]))
(: parse : String -> FLANG)
;; parses a string containing a FLANG expression to a FLANG AST
(define (parse str)
  (parse-sexpr (string->sexpr str)))


;; ================= Q1.2 ======================

;; =============================================

#| Evaluation rules:
              eval(N,env) = N
              eval(True,env) = #t
              eval(False,env) = #f
              eval({+ E1 E2},env) = eval(E1,env) + eval(E2,env)
              eval({- E1 E2},env) = eval(E1,env) - eval(E2,env)
              eval({* E1 E2},env) = eval(E1,env) * eval(E2,env)
              eval({/ E1 E2},env) = eval(E1,env) / eval(E2,env)
              eval({> E1 E2},env) = eval(E1,env) > eval(E2,env)
              eval({= E1 E2},env) = eval(E1,env) = eval(E2,env)
              eval(x,env) = lookup(x,env)
              eval(if Ec then Ey else En)= eval(En, env) if eval(Ec) = #f
                                           eval(Ey, env) otherwise
              eval({with {x E1} E2},env) = eval(E2,extend(x,eval(E1,env),env))
              eval({fun {x} E},env) = <{fun {x} E}, env>
              eval({call E1 E2},env1) = eval(Ef,extend(x,eval(E2,env1),env2))
              if eval(E1,env1) = <{fun {x} Ef}, env2> = error! otherwise
 |#
;; Types for environments, values, and a lookup function
(define-type ENV
  [EmptyEnv]
  [Extend Symbol VAL ENV])
(define-type VAL
  [NumV Number]
  [FunV Symbol FLANG ENV]
  [BoolV Boolean])
(: lookup : Symbol ENV -> VAL)
(define (lookup name env)
  (cases env
    [(EmptyEnv) (error 'lookup "no binding for ~s" name)]
    [(Extend id val rest-env)
     (if (eq? id name) val (lookup name rest-env))]))
(: arith-op : (Number Number -> Number) VAL VAL -> VAL)
;; gets a Racket numeric binary operator, and uses it within a NumV
;; wrapper
(define (arith-op op val1 val2)
  (: NumV->number : VAL -> Number)
  (define (NumV->number v)
    (cases v
      [(NumV n) n]
      [else (error 'arith-op "expects a number, got: ~s" v)]))
  (NumV (op (NumV->number val1) (NumV->number val2))))
(: logic-op : (Number Number -> Boolean) VAL VAL -> VAL)
;; gets a Racket logic binary operator, and uses it within a NumV
;; wrapper to return the result inside a BoolV wrapper.
(define (logic-op op val1 val2)
  (: NumV->number : VAL -> Number)
  (define (NumV->number v)
    (cases v
      [(NumV n) n]
      [else (error 'logic-op "expects a number, got: ~s" v)]))
  (BoolV (op (NumV->number val1) (NumV->number val2))))
(: extract-bool-val : VAL -> Boolean)
;; Return #f if the wrapped value is False, and #t otherwise
(define (extract-bool-val val)
  (cases val
    [(BoolV b) b]
    [else (error 'extract-bool-val "expects a boolean, got: ~s" val)]))
(: eval : FLANG ENV -> VAL)
;; evaluates FLANG expressions by reducing them to values
(define (eval expr env)
  (cases expr
    [(Num n) (NumV n)]
    [(Bool b) (extract-bool-val b)]
    [(Add l r) (arith-op + (eval l env) (eval r env))]
    [(Sub l r) (arith-op - (eval l env) (eval r env))]
    [(Mul l r) (arith-op * (eval l env) (eval r env))]
    [(Div l r) (arith-op / (eval l env) (eval r env))]
    [(Eq l r) (logic-op = (eval l env) (eval r env))]
    [(Geq l r) (logic-op > (eval l env) (eval r env))]
    [(If cond do-yes do-no)
     (if (eval cond env)
         (eval do-yes env)
         (eval do-no env))]
    [(With bound-id named-expr bound-body)
     (eval bound-body
           (Extend bound-id (eval named-expr env) env))]
    [(Id name) (lookup name env)]
    [(Fun bound-id bound-body)
     (FunV bound-id bound-body env)]
    [(Call fun-expr arg-expr)
     (let ([fval (eval fun-expr env)])
       (cases fval
         [(FunV bound-id bound-body f-env)
          (eval bound-body
                (Extend bound-id (eval arg-expr env) f-env))]
         [else (error 'eval "`call' expects a function, got: ~s"
                      fval)]))]))
(: run : String -> Number)
;; evaluate a FLANG program contained in a string
(define (run str)
  (let ([result (eval (parse str) (EmptyEnv))])
    (cases result
      [(NumV n) n]
      [else (error 'run
                   "evaluation returned a non-number: ~s" result)])))


(test (run "{ if True then 3 else 4 }") => 3)
(test (run "{ if {= 2 4} then 3 else 4 }") => 4)
(test (run "{ if {= 2 4} then { call 3 5 } else 4 }") => 4)
(test (run "{with {is-5? {fun {x} {= x 5}}} {with {foo {fun {x} {if {call is-5? {+ x 1}}then 4 else 0}}} {call foo 123}}}") => 0)
(test (run "{with {is-5? {fun {x} {= x 5}}} {with {foo {fun {x} {if {call is-5? {+ x 1}}4 0}}} {call foo 123}}}") =error> "parse-sexpr: bad `if' syntax in (if (call is-5? (+ x 1)) 4 0)")
(test (run "{with {x {> 3 4}} {with {foo {fun {y} {if x then True else y}}} {call foo 5}}}") => 5)