#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] [arg-type : Type] [body : Exp]) (appE [fun : Exp] [arg : Exp])) (define-type Type (numT) (boolT) (arrowT [arg : Type] [result : Type])) (define-type Binding (bind [name : Symbol] [val : Value])) (define-type-alias Env (Listof Binding)) (define-type Type-Binding (tbind [name : Symbol] [type : Type])) (define-type-alias Type-Env (Listof Type-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]} ANY} s) (let ([bs (s-exp->list (first (s-exp->list (second (s-exp->list s)))))]) (appE (lamE (s-exp->symbol (first bs)) (parse-type (third bs)) (parse (third (s-exp->list s)))) (parse (fourth bs))))] [(s-exp-match? `{lambda {[SYMBOL : ANY]} ANY} s) (let ([arg (s-exp->list (first (s-exp->list (second (s-exp->list s)))))]) (lamE (s-exp->symbol (first arg)) (parse-type (third arg)) (parse (third (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")])) (define (parse-type [s : S-Exp]) : Type (cond [(s-exp-match? `num s) (numT)] [(s-exp-match? `bool s) (boolT)] [(s-exp-match? `(ANY -> ANY) s) (arrowT (parse-type (first (s-exp->list s))) (parse-type (third (s-exp->list s))))] [else (error 'parse-type "invalid input")])) (module+ test (test (parse `2) (numE 2)) (test (parse `x) (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 `{let {[x : num {+ 1 2}]} y}) (appE (lamE 'x (numT) (idE 'y)) (plusE (numE 1) (numE 2)))) (test (parse `{lambda {[x : num]} 9}) (lamE 'x (numT) (numE 9))) (test (parse `{double 9}) (appE (idE 'double) (numE 9))) (test/exn (parse `{{+ 1 2}}) "invalid input") (test (parse-type `num) (numT)) (test (parse-type `bool) (boolT)) (test (parse-type `(num -> bool)) (arrowT (numT) (boolT))) (test/exn (parse-type `1) "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 t body) (closV n body env)] [(appE fun arg) (type-case Value (interp fun env) [(closV n body c-env) (interp body (extend-env (bind n (interp arg env)) c-env))] [else (error 'interp "not a function")])])) (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 (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 : num]} {+ x x}}) mt-env) (closV 'x (plusE (idE 'x) (idE 'x)) mt-env)) (test (interp (parse `{let {[x : num 5]} {+ x x}}) mt-env) (numV 10)) (test (interp (parse `{let {[x : num 5]} {let {[x : num {+ 1 x}]} {+ x x}}}) mt-env) (numV 12)) (test (interp (parse `{let {[x : num 5]} {let {[y : num 6]} x}}) mt-env) (numV 5)) (test (interp (parse `{{lambda {[x : num]} {+ x x}} 8}) mt-env) (numV 16)) (test/exn (interp (parse `{1 2}) mt-env) "not a function") (test/exn (interp (parse `{+ 1 {lambda {[x : num]} x}}) mt-env) "not a number") (test/exn (interp (parse `{let {[bad : (num -> num) {lambda {[x : num]} {+ x y}}]} {let {[y : num 5]} {bad 2}}}) mt-env) "free variable")) ;; 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 (make-lookup [name-of : ('a -> Symbol)] [val-of : ('a -> 'b)]) (lambda ([name : Symbol] [vals : (Listof 'a)]) : 'b (type-case (Listof 'a) vals [empty (error 'find "free variable")] [(cons val rst-vals) (if (equal? name (name-of val)) (val-of (first vals)) ((make-lookup name-of val-of) name rst-vals))]))) (define lookup (make-lookup bind-name bind-val)) (module+ test (test/exn (lookup 'x mt-env) "free variable") (test (lookup 'x (extend-env (bind 'x (numV 8)) mt-env)) (numV 8)) (test (lookup 'x (extend-env (bind 'x (numV 9)) (extend-env (bind 'x (numV 8)) mt-env))) (numV 9)) (test (lookup 'y (extend-env (bind 'x (numV 9)) (extend-env (bind 'y (numV 8)) mt-env))) (numV 8))) ;; typecheck ---------------------------------------- (define (typecheck [a : Exp] [tenv : Type-Env]) (type-case Exp a [(numE n) (numT)] [(plusE l r) (typecheck-nums l r tenv)] [(multE l r) (typecheck-nums l r tenv)] [(idE n) (type-lookup n tenv)] [(lamE n arg-type body) (arrowT arg-type (typecheck body (extend-env (tbind n arg-type) tenv)))] [(appE fun arg) (type-case Type (typecheck fun tenv) [(arrowT arg-type result-type) (if (equal? arg-type (typecheck arg tenv)) result-type (type-error arg (to-string arg-type)))] [else (type-error fun "function")])])) (define (typecheck-nums l r tenv) (type-case Type (typecheck l tenv) [(numT) (type-case Type (typecheck r tenv) [(numT) (numT)] [else (type-error r "num")])] [else (type-error l "num")])) (define (type-error a msg) (error 'typecheck (string-append "no type: " (string-append (to-string a) (string-append " not " msg))))) (define type-lookup (make-lookup tbind-name tbind-type)) (module+ test (test (typecheck (parse `10) mt-env) (numT)) (test (typecheck (parse `{+ 10 17}) mt-env) (numT)) (test (typecheck (parse `{* 10 17}) mt-env) (numT)) (test (typecheck (parse `{lambda {[x : num]} 12}) mt-env) (arrowT (numT) (numT))) (test (typecheck (parse `{lambda {[x : num]} {lambda {[y : bool]} x}}) mt-env) (arrowT (numT) (arrowT (boolT) (numT)))) (test (typecheck (parse `{{lambda {[x : num]} 12} {+ 1 17}}) mt-env) (numT)) (test (typecheck (parse `{let {[x : num 4]} {let {[f : (num -> num) {lambda {[y : num]} {+ x y}}]} {f x}}}) mt-env) (numT)) (test/exn (typecheck (parse `{1 2}) mt-env) "no type") (test/exn (typecheck (parse `{{lambda {[x : bool]} x} 2}) mt-env) "no type") (test/exn (typecheck (parse `{+ 1 {lambda {[x : num]} x}}) mt-env) "no type") (test/exn (typecheck (parse `{* {lambda {[x : num]} x} 1}) mt-env) "no type"))