#lang plait
(define-type FLANG
[Num (val : Number)]
[Add (l : FLANG) (r : FLANG)]
[Sub (l : FLANG) (r : FLANG)]
[Mul (l : FLANG) (r : FLANG)]
[Div (l : FLANG) (r : FLANG)]
[Id (name : Symbol)]
[Let1 (id : Symbol) (named-expr : FLANG) (bound-body : FLANG)]
[Lam (param : Symbol) (body : FLANG)]
[Call (fun : FLANG) (val : FLANG)]) ; first type!
(define (parse-error sx)
(error 'parse-sx (string-append "parse error: " (to-string sx))))
(define (sx-ref sx n) (list-ref (s-exp->list sx) n))
(define (parse-sx sx)
(cond
[(s-exp-number? sx) (Num (s-exp->number sx))]
[(s-exp-symbol? sx) (Id (s-exp->symbol sx))]
[(s-exp-match? `(let1 (SYMBOL ANY) ANY) sx)
(let* ([def (sx-ref sx 1)]
[id (s-exp->symbol (sx-ref def 0))]
[val (parse-sx (sx-ref def 1))]
[expr (parse-sx (sx-ref sx 2))])
(Let1 id val expr))]
[(s-exp-match? `(lam SYMBOL ANY) sx)
(let* ([id (s-exp->symbol (sx-ref sx 1))]
[body (parse-sx (sx-ref sx 2))])
(Lam id body))]
[(s-exp-match? `(ANY ANY) sx)
(Call (parse-sx (sx-ref sx 0))
(parse-sx (sx-ref sx 1)))]
[(s-exp-list? sx)
(let* ([l (λ () (parse-sx (sx-ref sx 1)))]
[r (λ () (parse-sx (sx-ref sx 2)))])
(case (s-exp->symbol (sx-ref sx 0))
[(+) (Add (l) (r))]
[(-) (Sub (l) (r))]
[(*) (Mul (l) (r))]
[(/) (Div (l) (r))]
[else (parse-error sx)]))]
[else (parse-error sx)]))
(define-type ENV
[EmptyEnv]
[Extend (name : Symbol) (val : VAL) (rest : ENV)])
(define-type VAL
[NumV (n : Number)]
[FunV (arg : Symbol) (body : FLANG) (env : ENV)])
(define (lookup name env)
(type-case ENV env
[(EmptyEnv) (error 'lookup (string-append "no binding for " (to-string name)))]
[(Extend id val rest-env)
(if (eq? id name)
val
(lookup name rest-env))]))
;; gets a Racket numeric binary operator,
;; uses it within a NumV wrapper
(define (arith-op op val1 val2)
(local
[(define (NumV->number v)
(type-case VAL v
[(NumV n) n]
[else (error 'arith-op
(string-append "expects a number, got: " (to-string v)))]))]
(NumV (op (NumV->number val1)
(NumV->number val2)))))
;; evaluates FLANG expressions by reducing them to values
(define (interp expr env)
(type-case FLANG expr
[(Num n) (NumV n)]
[(Add l r) (arith-op + (interp l env) (interp r env))]
[(Sub l r) (arith-op - (interp l env) (interp r env))]
[(Mul l r) (arith-op * (interp l env) (interp r env))]
[(Div l r) (arith-op / (interp l env) (interp r env))]
[(Let1 bound-id named-expr bound-body)
(interp bound-body
(Extend bound-id (interp named-expr env) env))]
[(Id name) (lookup name env)]
[(Lam bound-id bound-body)
(FunV bound-id bound-body env)]
[(Call fun-expr arg-expr)
(let ([fval (interp fun-expr env)])
(type-case VAL fval
[(FunV bound-id bound-body f-env)
(interp bound-body
(Extend bound-id (interp arg-expr env) f-env))]
[else (error 'eval
(string-append "`call' expects a function, got: "
(to-string fval)))]))]))
;; evaluate a FLANG program contained in an s-expression
(define (run s-exp)
(let ([result (interp (parse-sx s-exp) (EmptyEnv))])
(type-case VAL result
[(NumV n) n]
[else (error 'run
(string-append "evaluation returned a non-number: " (to-string result)))])))
(test (run `{{lam x {+ x 1}} 4}) 5)
(test (run `{let1 {add3 {lam x {+ x 3}}}
{add3 1}})
4)
(test (run `{let1 {add3 {lam x {+ x 3}}}
{let1 {add1 {lam x {+ x 1}}}
{let1 {x 3}
{add1 {add3 x}}}}}) 7)
(test (run `{let1 {identity {lam x x}}
{let1 {foo {lam x {+ x 1}}}
{{identity foo}
123}}}) 124)