X-Git-Url: http://git.lukelau.me/?p=scheme.git;a=blobdiff_plain;f=typecheck.scm;h=55c2fd8201f2467ff3e136189412b6dc351780fd;hp=0e4e265f2d2a47f81b8a13ea4ade24914c3b33a1;hb=8aacba5976424791fb51d5d36118269d32c4096a;hpb=ba17902b367783f058108f2eb9dff163d34b735f diff --git a/typecheck.scm b/typecheck.scm index 0e4e265..55c2fd8 100644 --- a/typecheck.scm +++ b/typecheck.scm @@ -1,18 +1,36 @@ -(define (app? x) - (and (list? x) (>= (length x) 2) (not (eq? (car x) 'lambda)))) +(load "ast.scm") -(define (lambda? x) - (and (list? x) (eq? (car x) 'lambda))) +(define (abs? t) + (and (list? t) (eq? (car t) 'abs))) + +(define (tvar? t) + (and (not (list? t)) (not (concrete? t)) (symbol? t))) + +(define (concrete? t) + (case t + ('int #t) + ('bool #t) + (else #f))) -(define lambda-arg caadr) -(define lambda-body caddr) +(define (pretty-type t) + (cond ((abs? t) + (string-append + (if (abs? (cadr t)) + (string-append "(" (pretty-type (cadr t)) ")") + (pretty-type (cadr t))) + " -> " + (pretty-type (caddr t)))) + (else (symbol->string t)))) ; ('a, ('b, 'a)) -(define (env-lookup env x) +(define (env-lookup env n) (if (null? env) (error #f "empty env") ; it's a type equality - (if (eq? (caar env) x) + (if (eq? (caar env) n) (cdar env) - (env-lookup (cdr env) x)))) + (env-lookup (cdr env) n)))) + +(define (env-insert env n t) + (cons (cons n t) env)) (define abs-arg cadr) @@ -23,40 +41,86 @@ (string->symbol (string-append "t" (number->string (- cur-tvar 1)))))) +(define (last xs) + (if (null? (cdr xs)) + (car xs) + (last (cdr xs)))) + (define (normalize prog) ; (+ a b) -> ((+ a) b) (cond - ((lambda? prog) '(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) + `(,(normalize (car prog)) ,(normalize (cadr prog))) ; (f a) + `(,(list (normalize (car prog)) (normalize (cadr prog))) + ,(normalize (caddr 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) `(,(car x) ,(normalize (cadr x)))) + (let-bindings prog))) + (map normalize (let-body prog)))) (else prog))) +(define (builtin-type x) + (case x + ('+ '(abs int (abs int int))) + ('- '(abs int (abs int int))) + ('* '(abs int (abs int int))) + ('! '(abs bool bool)) + ('bool->int '(abs bool int)) + (else #f))) +; we typecheck the lambda calculus only (only single arg lambdas) (define (typecheck prog) (define (check env x) + ;; (display "check: ") + ;; (display x) + ;; (display "\n\t") + ;; (display env) + ;; (newline) (let ((res (cond ((integer? x) (list '() 'int)) ((boolean? x) (list '() 'bool)) - ((eq? x 'inc) (list '() '(abs int int))) - ((eq? x '+) (list '() '(abs int (abs int int)))) + ((builtin-type x) (list '() (builtin-type x))) ((symbol? x) (list '() (env-lookup env x))) + ((let? x) + (let ((new-env (fold-left + (lambda (acc bind) + (let ((t (check + (env-insert acc (car bind) (fresh-tvar)) + (cadr bind)))) + (env-insert acc (car bind) (cadr t)))) + env (let-bindings x)))) + (check new-env (last (let-body x))))) + ((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) @@ -70,7 +134,9 @@ (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))) @@ -86,7 +152,7 @@ (if (abs? resolved-func-type) (let ((return-type (substitute cs (caddr resolved-func-type)))) (list cs return-type)) - (error #f "wah"))))))) + (error #f "not a function"))))))) ;; (display "result of ") ;; (display x) ;; (display ":\n\t") @@ -97,19 +163,6 @@ res)) (cadr (check '() (normalize prog)))) - -(define (abs? t) - (and (list? t) (eq? (car t) 'abs))) - -(define (tvar? t) - (and (not (list? t)) (not (concrete? t)) (symbol? t))) - -(define (concrete? t) - (case t - ('int #t) - ('bool #t) - (else #f))) - ; returns a list of pairs of constraints (define (unify a b) (cond ((eq? a b) '()) @@ -119,22 +172,32 @@ (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) - (define (blah c) - (if (null? (cdr c)) - (car c) + ; gets the first concrete type + ; otherwise returns the last type variable + + (define (get-concrete 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) - (blah (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) - (blah 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))