X-Git-Url: http://git.lukelau.me/?p=scheme.git;a=blobdiff_plain;f=typecheck.scm;h=197798e104a7595f5637646cb102f2d9d99f44d5;hp=a396a246ee67cf1c65d975d1021a0f91693f36b5;hb=21a9f0aaa56d6dd767cefb30c606f4c62eecff48;hpb=4432a2c44d76e70258f4b1d38114745726ffd1fc

diff --git a/typecheck.scm b/typecheck.scm
index a396a24..197798e 100644
--- a/typecheck.scm
+++ b/typecheck.scm
@@ -1,19 +1,36 @@
-(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)
 
@@ -24,103 +41,220 @@
     (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)))))))