(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 "\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")
+ (cs (car body-type-res))
+ (subd-env (substitute-env (car body-type-res) new-env))
+ (arg-type (env-lookup subd-env (lambda-arg x)))
+ (resolved-arg-type (substitute cs arg-type)))
+ ;; (display "lambda:\n\t")
+ ;; (display prog)
+ ;; (display "\n\t")
+ ;; (display cs)
+ ;; (display "\n\t")
+ ;; (display resolved-arg-type)
+ ;; (newline)
(list (car body-type-res)
(list 'abs
- (env-lookup subd-env (lambda-arg x))
+ resolved-arg-type
(cadr body-type-res)))))
((app? x) ; (f a)
(list 'abs
arg-type
(fresh-tvar))))
- (cs (append func-c (car arg-type-res) (car func-type-res)))
+ (cs (consolidate
+ (consolidate func-c (car arg-type-res))
+ (car func-type-res)))
(resolved-func-type (substitute cs func-type))
(resolved-return-type (caddr resolved-func-type)))
(unify (caddr a) (caddr b))))
(else (error #f "could not unify"))))
-
; TODO: what's the most appropriate substitution?
; should all constraints just be limited to a pair?
(define (substitute cs t)
; gets the first concrete type
; otherwise returns the last type variable
+
(define (get-concrete c)
- (if (null? (cdr c))
- (car c)
+ (let ((last (null? (cdr c))))
(if (not (tvar? (car c)))
+ (if (abs? (car c))
+ (substitute cs (car c))
+ (car c))
+ (if last
(car c)
- (get-concrete (cdr c)))))
+ (get-concrete (cdr c))))))
+ (cond
+ ((abs? t) (list 'abs
+ (substitute cs (cadr t))
+ (substitute cs (caddr t))))
+ (else
(fold-left
(lambda (t c)
(if (member t c)
(get-concrete c)
t))
- t cs))
+ t cs))))
(define (substitute-env cs env)
(map (lambda (x) (cons (car x) (substitute cs (cdr x)))) env))