#lang plait (define-type Value (numV [n : Number]) (closV [arg : Symbol] [body : Exp] [env : Env])) (define-type Exp (numE [n : Number]) (idE [s : Symbol]) (plusE [l : Exp] [r : Exp]) (multE [l : Exp] [r : Exp]) (lamE [n : Symbol] [body : Exp]) (appE [fun : Exp] [arg : Exp]) (if0E [tst : Exp] [thn : Exp] [els : Exp]) (letrecE [n : Symbol] [rhs : Exp] [body : Exp])) (define-type Binding (bind [name : Symbol] [val : (-> Value)])) (define-type-alias Env (Listof Binding)) (define mt-env empty) (define extend-env cons) (module+ test (print-only-errors #t)) ;; parse ---------------------------------------- (define (parse [s : S-Exp]) : Exp (cond [(s-exp-match? `NUMBER s) (numE (s-exp->number s))] [(s-exp-match? `SYMBOL s) (idE (s-exp->symbol s))] [(s-exp-match? `{+ ANY ANY} s) (plusE (parse (second (s-exp->list s))) (parse (third (s-exp->list s))))] [(s-exp-match? `{* ANY ANY} s) (multE (parse (second (s-exp->list s))) (parse (third (s-exp->list s))))] [(s-exp-match? `{let {[SYMBOL ANY]} ANY} s) (let ([bs (s-exp->list (first (s-exp->list (second (s-exp->list s)))))]) (appE (lamE (s-exp->symbol (first bs)) (parse (third (s-exp->list s)))) (parse (second bs))))] [(s-exp-match? `{lambda {SYMBOL} ANY} s) (lamE (s-exp->symbol (first (s-exp->list (second (s-exp->list s))))) (parse (third (s-exp->list s))))] [(s-exp-match? `{letrec {[SYMBOL ANY]} ANY} s) (let ([bs (s-exp->list (first (s-exp->list (second (s-exp->list s)))))]) (letrecE (s-exp->symbol (first bs)) (parse (second bs)) (parse (third (s-exp->list s)))))] [(s-exp-match? `{if0 ANY ANY ANY} s) (if0E (parse (second (s-exp->list s))) (parse (third (s-exp->list s))) (parse (fourth (s-exp->list s))))] [(s-exp-match? `{ANY ANY} s) (appE (parse (first (s-exp->list s))) (parse (second (s-exp->list s))))] [else (error 'parse "invalid input")])) (module+ test (test (parse `2) (numE 2)) (test (parse `x) ; note: backquote instead of normal quote (idE 'x)) (test (parse `{+ 2 1}) (plusE (numE 2) (numE 1))) (test (parse `{* 3 4}) (multE (numE 3) (numE 4))) (test (parse `{+ {* 3 4} 8}) (plusE (multE (numE 3) (numE 4)) (numE 8))) (test (parse `{lambda {x} 9}) (lamE 'x (numE 9))) (test (parse `{let {[x {+ 1 2}]} y}) (appE (lamE 'x (idE 'y)) (plusE (numE 1) (numE 2)))) (test (parse `{if0 1 2 3}) (if0E (numE 1) (numE 2) (numE 3))) (test (parse `{letrec {[x {+ 1 2}]} y}) (letrecE 'x (plusE (numE 1) (numE 2)) (idE 'y))) (test (parse `{double 9}) (appE (idE 'double) (numE 9))) (test/exn (parse `{{+ 1 2}}) "invalid input")) ;; interp ---------------------------------------- (define (interp [a : Exp] [env : Env]) : Value (type-case Exp a [(numE n) (numV n)] [(idE s) (lookup s env)] [(plusE l r) (num+ (interp l env) (interp r env))] [(multE l r) (num* (interp l env) (interp r env))] [(lamE n body) (closV n body env)] [(appE fun arg) (type-case Value (interp fun env) [(closV n body c-env) (let ([val (interp arg env)]) (interp body (extend-env (bind n (lambda () val)) c-env)))] [else (error 'interp "not a function")])] [(if0E tst thn els) (type-case Value (interp tst env) [(numV n) (if (zero? n) (interp thn env) (interp els env))] [else (error 'interp "not a number")])] [(letrecE n rhs body) (letrec ([new-env (extend-env (bind n (lambda () val)) env)] [val (interp rhs new-env)]) (interp body new-env))])) (module+ test (test (interp (parse `2) mt-env) (numV 2)) (test/exn (interp (parse `x) mt-env) "free variable") (test (interp (parse `x) (extend-env (bind 'x (lambda () (numV 9))) mt-env)) (numV 9)) (test (interp (parse `{+ 2 1}) mt-env) (numV 3)) (test (interp (parse `{* 2 1}) mt-env) (numV 2)) (test (interp (parse `{+ {* 2 3} {+ 5 8}}) mt-env) (numV 19)) (test (interp (parse `{lambda {x} {+ x x}}) mt-env) (closV 'x (plusE (idE 'x) (idE 'x)) mt-env)) (test (interp (parse `{let {[x 5]} {+ x x}}) mt-env) (numV 10)) (test (interp (parse `{let {[x 5]} {let {[x {+ 1 x}]} {+ x x}}}) mt-env) (numV 12)) (test (interp (parse `{let {[x 5]} {let {[y 6]} x}}) mt-env) (numV 5)) (test (interp (parse `{{lambda {x} {+ x x}} 8}) mt-env) (numV 16)) (test (interp (parse `{if0 1 2 3}) mt-env) (numV 3)) (test (interp (parse `{if0 0 2 3}) mt-env) (numV 2)) (test (interp (parse `{letrec {[x 5]} {+ x x}}) mt-env) (numV 10)) (test (interp (parse `{letrec {[fac {lambda {x} {if0 x 1 {* x {fac {+ x -1}}}}}]} {fac 5}}) mt-env) (numV 120)) (test/exn (interp (parse `{1 2}) mt-env) "not a function") (test/exn (interp (parse `{+ 1 {lambda {x} x}}) mt-env) "not a number") (test/exn (interp (parse `{let {[bad {lambda {x} {+ x y}}]} {let {[y 5]} {bad 2}}}) mt-env) "free variable") (test/exn (interp (parse `{if0 {lambda {x} x} 1 2}) mt-env) "not a number") ;; !! A "bad" Curly recursive binding has the same ;; result as bad Plait recursive binding, and so ;; have to use `try` to test it: (test (try (interp (parse `{letrec {[x x]} x}) mt-env) (lambda () (numV 7))) (numV 7))) ;; num+ and num* ---------------------------------------- (define (num-op [op : (Number Number -> Number)] [l : Value] [r : Value]) : Value (cond [(and (numV? l) (numV? r)) (numV (op (numV-n l) (numV-n r)))] [else (error 'interp "not a number")])) (define (num+ [l : Value] [r : Value]) : Value (num-op + l r)) (define (num* [l : Value] [r : Value]) : Value (num-op * l r)) (module+ test (test (num+ (numV 1) (numV 2)) (numV 3)) (test (num* (numV 2) (numV 3)) (numV 6))) ;; lookup ---------------------------------------- (define (lookup [n : Symbol] [env : Env]) : Value (type-case (Listof Binding) env [empty (error 'lookup "free variable")] [(cons b rst-env) (cond [(symbol=? n (bind-name b)) ((bind-val b))] [else (lookup n rst-env)])])) (module+ test (test/exn (lookup 'x mt-env) "free variable") (test (lookup 'x (extend-env (bind 'x (lambda () (numV 8))) mt-env)) (numV 8)) (test (lookup 'x (extend-env (bind 'x (lambda () (numV 9))) (extend-env (bind 'x (lambda () (numV 8))) mt-env))) (numV 9)) (test (lookup 'y (extend-env (bind 'x (lambda () (numV 9))) (extend-env (bind 'y (lambda () (numV 8))) mt-env))) (numV 8)))