-(define (is-app? x)
- (and (list? x) (not (eq? (car x) 'lambda))))
+(load "ast.scm")
+(define (abs? t)
+ (and (list? t) (eq? (car t) 'abs)))
+
+(define (tvar? t)
+ (and (not (list? t)) (not (concrete? t)) (symbol? t)))
-(define (is-lambda? x)
- (and (list? x) (eq? (car x) 'lambda)))
+(define (concrete? t)
+ (case t
+ ('int #t)
+ ('bool #t)
+ (else #f)))
-(define lambda-arg cadr)
-(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)
(string->symbol
(string-append "t" (number->string (- cur-tvar 1))))))
-(define (typecheck env x)
- (display "typechecking:\n\t")
- (display x)
- (display "\t")
- (display env)
- (display "\n")
+(define (last xs)
+ (if (null? (cdr xs))
+ (car xs)
+ (last (cdr xs))))
+
+
+(define (normalize prog) ; (+ a b) -> ((+ a) b)
+ (case (ast-type prog)
+ ('lambda
+ ; (lambda (x y) (+ x y)) -> (lambda (x) (lambda (y) (+ x y)))
+ (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
+ (if (null? (cddr prog))
+ `(,(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
+ (append (list 'let
+ (map (lambda (x) `(,(car x) ,(normalize (cadr x))))
+ (let-bindings prog)))
+ (map normalize (let-body prog))))
+ ('if `(if ,(normalize (cadr prog))
+ ,(normalize (caddr prog))
+ ,(normalize (cadddr 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))
+ ('= '(abs int (abs int 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)))
- ((symbol? x) (list '() (env-lookup env x)))
-
- ((is-lambda? x)
- (let* ((new-env (cons (cons (lambda-arg x) (fresh-tvar)) env))
- (body-type-res (typecheck new-env (lambda-body x)))
- (subd-env (substitute (car body-type-res) new-env)))
- (display "lambda: ")
- (display body-type-res)
- (display "\n")
+ (case (ast-type x)
+ ('int-literal (list '() 'int))
+ ('bool-literal (list '() 'bool))
+ ('builtin (list '() (builtin-type x)))
+
+ ('if
+ (let* ((cond-type-res (check env (cadr x)))
+ (then-type-res (check env (caddr x)))
+ (else-type-res (check env (cadddr x)))
+ (then-eq-else-cs (unify (cadr then-type-res)
+ (cadr else-type-res)))
+ (cs (consolidate
+ (car then-type-res)
+ (consolidate (car else-type-res)
+ then-eq-else-cs)))
+ (return-type (substitute cs (cadr then-type-res))))
+ (when (not (eqv? (cadr cond-type-res) 'bool))
+ (error #f "if condition isn't bool"))
+ (list cs return-type)))
+
+ ('var (list '() (env-lookup env x)))
+ ('let
+ (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
+ (let* ((new-env (env-insert env (lambda-arg x) (fresh-tvar)))
+ (body-type-res (check new-env (lambda-body x)))
+ (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)))))
- ((is-app? x) ; (f a)
- (let* ((arg-type-res (typecheck env (cadr x)))
- ; typecheck f with the knowledge that f : a -> x
- (func-type-res (typecheck env (car x)))
+ ('app ; (f a)
+ (let* ((arg-type-res (check env (cadr x)))
+ (arg-type (cadr arg-type-res))
+ (func-type-res (check env (car x)))
(func-type (cadr func-type-res))
- (c (unify func-type
+
+ ; f ~ a -> t0
+ (func-c (unify func-type
(list 'abs
- (cadr arg-type-res)
+ arg-type
(fresh-tvar))))
- (new-env (substitute c env))
- (resolved-func-type (env-lookup new-env (car x))))
- (display "is-app:\n")
- (display c)
- (display "\n")
- (display new-env)
- (display "\n")
- (display resolved-func-type)
- (display "\n")
- (display arg-type-res)
- (display "\n")
+ (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)))
+ ;; (display "app:\n")
+ ;; (display cs)
+ ;; (display "\n")
+ ;; (display func-type)
+ ;; (display "\n")
+ ;; (display resolved-func-type)
+ ;; (display "\n")
+ ;; (display arg-type-res)
+ ;; (display "\n")
(if (abs? resolved-func-type)
- (list (append c
- (unify (cadr arg-type-res)
- (cadr resolved-func-type)))
- (caddr resolved-func-type))
- (error #f "wah")))))))
- (display "result of ")
- (display x)
- (display ":\n\t")
- (display (cadr res))
- (display "[")
- (display (car res))
- (display "]\n")
+ (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")
res))
-
-
-(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)))
+ (cadr (check '() (normalize prog))))
; returns a list of pairs of constraints
(define (unify a b)
(cond ((eq? a b) '())
- ((or (tvar? a) (tvar? b)) (list (cons a b)))
+ ((or (tvar? a) (tvar? b)) (~ a b))
((and (abs? a) (abs? b))
- (append (unify (cadr a) (cadr b))
+ (consolidate (unify (cadr a) (cadr b))
(unify (caddr a) (caddr b))))
(else (error #f "could not unify"))))
- ; takes a list of constraints and a type environment, and makes it work
-(define (substitute c env)
- (let ((go (lambda (x) (let ((tv (cdr x))
- (n (car x)))
- ;; (display tv)
- ;; (display "\n")
- ;; (display n)
- (cons n (fold-left
- (lambda (a y)
- ;; (display y)
- ;; (display ":")
- ;; (display a)
- (cond ((eq? a (car y)) (cdr y))
- ((eq? a (cdr y)) (car y))
- (else a)))
- tv c))))))
- (map go env)))
+ ; 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)
+ (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))))))
+ (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))))
+
+(define (substitute-env cs env)
+ (map (lambda (x) (cons (car x) (substitute cs (cdr x)))) env))
+
+(define (~ a b)
+ (list (list a b)))
+
+(define (consolidate x y)
+ (define (merge a b)
+ (cond ((null? a) b)
+ ((null? b) a)
+ (else (if (member (car b) a)
+ (merge a (cdr b))
+ (cons (car b) (merge a (cdr b)))))))
+ (define (overlap? a b)
+ (if (or (null? a) (null? b))
+ #f
+ (if (fold-left (lambda (acc v)
+ (or acc (eq? v (car a))))
+ #f b)
+ #t
+ (overlap? (cdr a) b))))
+
+ (cond ((null? y) x)
+ ((null? x) y)
+ (else (let* ((a (car y))
+ (merged (fold-left
+ (lambda (acc b)
+ (if acc
+ acc
+ (if (overlap? a b)
+ (cons (merge a b) b)
+ #f)))
+ #f x))
+ (removed (if merged
+ (filter (lambda (b) (not (eq? b (cdr merged)))) x)
+ x)))
+ (if merged
+ (consolidate removed (cons (car merged) (cdr y)))
+ (consolidate (cons a x) (cdr y)))))))
projects / scheme.git / blobdiff