(define (lambda? x)
(and (list? x) (eq? (car x) 'lambda)))
-(define lambda-arg cadr)
-(define lambda-body cddr)
+; for use in normalized form
+(define lambda-arg caadr)
+; for use elsewhere
+(define lambda-args cadr)
+(define lambda-body caddr)
(define (var? x)
(and (not (list? x)) (symbol? x)))
(define (normalize prog) ; (+ a b) -> ((+ a) b)
(cond
- ((lambda? prog) (list 'lambda (lambda-arg prog) (normalize (lambda-body prog))))
+ ; (lambda (x y) (+ x y)) -> (lambda (x) (lambda (y) (+ x y)))
+ ((lambda? prog)
+ (if (> (length (lambda-args prog)) 1)
+ (list 'lambda (list (car (lambda-args prog)))
+ (normalize (list 'lambda (cdr (lambda-args prog)) (caddr prog))))
+ (list 'lambda (lambda-args prog) (normalize (caddr prog)))))
((app? prog)
(if (null? (cddr prog))
(cons (normalize (car prog)) (normalize (cdr prog))) ; (f a)
- (normalize (cons (cons (car prog) (list (cadr prog))) (cddr prog))))) ; (f a b)
+ (list (list (normalize (car prog)) (normalize (cadr prog))) (normalize (caddr prog))))) ; (f a b)
((let? prog)
(append (list 'let
(map (lambda (x) (cons (car x) (normalize (cdr x))))
(else prog)))
+; we typecheck the lambda calculus only (only single arg lambdas)
(define (typecheck prog)
(define (check env x)
- ;; (display "check: ")
- ;; (display x)
- ;; (display "\n")
+ (display "check: ")
+ (display x)
+ (display "\n\t")
+ (display env)
+ (newline)
(let
((res
(cond
((lambda? x)
- (let* ((new-env (cons (cons (lambda-arg x) (fresh-tvar)) env))
+ (let* ((new-env (env-insert env (lambda-arg x) (fresh-tvar)))
(body-type-res (check new-env (lambda-body x)))
(subd-env (substitute-env (car body-type-res) new-env)))
- ;; (display "lambda: ")
- ;; (display body-type-res)
- ;; (display "\n")
- ;; (display subd-env)
- ;; (display "\n")
+ (display "lambda: ")
+ (display body-type-res)
+ (display "\n")
+ (display subd-env)
+ (display "\n")
(list (car body-type-res)
(list 'abs
(env-lookup subd-env (lambda-arg x))
(let ((return-type (substitute cs (caddr resolved-func-type))))
(list cs return-type))
(error #f "not a function")))))))
- ;; (display "result of ")
- ;; (display x)
- ;; (display ":\n\t")
- ;; (display (cadr res))
- ;; (display "[")
- ;; (display (car res))
- ;; (display "]\n")
+ (display "result of ")
+ (display x)
+ (display ":\n\t")
+ (display (cadr res))
+ (display "[")
+ (display (car res))
+ (display "]\n")
res))
(cadr (check '() (normalize prog))))