X-Git-Url: http://git.lukelau.me/?p=scheme.git;a=blobdiff_plain;f=typecheck.scm;h=e96f6943767e1c5ab463398d11146d8f8ae450ce;hp=a396a246ee67cf1c65d975d1021a0f91693f36b5;hb=f605bff88ce12e5f4384ab308c036350bfa86cb5;hpb=4432a2c44d76e70258f4b1d38114745726ffd1fc

diff --git a/typecheck.scm b/typecheck.scm
index a396a24..e96f694 100644
--- a/typecheck.scm
+++ b/typecheck.scm
@@ -1,19 +1,37 @@
-(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)
+    ('void #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 +42,404 @@
     (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)
+	 (normalize `(,(list (normalize (car prog)) (normalize (cadr prog)))
+		      ,@(cddr prog))))) ; (f a b)
+    ('let
+	(append (list 'let
+		      (map (lambda (x) `(,(car x) ,(normalize (cadr x))))
+			   (let-bindings prog)))
+		(map normalize (let-body prog))))
+    (else (ast-traverse normalize 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))
+    ('print '(abs string void))
+    (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))
+	    ('string-literal (list '() 'string))
+	    ('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 (~ (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
+					; takes in the current environment and a scc
+					; returns new environment with scc's types added in
+	      (let* ([components (reverse (sccs (graph (let-bindings x))))]
+		     [process-component
+		      (lambda (acc comps)
+			(let*
+					; create a new env with tvars for each component
+					; e.g. scc of (x y)
+					; scc-env = ((x . t0) (y . t1))
+			    ([scc-env
+			      (fold-left
+			       (lambda (acc c)
+				 (env-insert acc c (fresh-tvar)))
+			       acc comps)]
+					; typecheck each component
+			     [type-results
+			      (map
+			       (lambda (c)
+				 (let ([body (cadr (assoc c (let-bindings x)))])
+				   (check scc-env body)))
+			       comps)]
+					; collect all the constraints in the scc
+			     [cs
+			      (fold-left
+			       (lambda (acc res c)
+				 (consolidate
+				  acc
+				  (consolidate (car res)
+					; unify with tvars from scc-env
+					; result ~ tvar
+					       (~ (cadr res) (env-lookup scc-env c)))))
+			       '() type-results comps)]
+					; substitute *only* the bindings in this scc
+			     [new-env
+			      (map (lambda (x)
+				     (if (memv (car x) comps)
+					 (cons (car x) (substitute cs (cdr x)))
+					 x))
+				   scc-env)])
+			  new-env))]
+		     [new-env (fold-left process-component env components)])
+		(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)
+	     (if (eqv? (car x) (cadr x))
+					; recursive function (f f)
+		 (let* [(func-type (env-lookup env (car x)))
+			(return-type (fresh-tvar))
+			(other-func-type `(abs ,func-type ,return-type))
+			(cs (~ func-type other-func-type))
+			(resolved-return-type (substitute cs return-type))]
+		   (list cs resolved-return-type))
+
+					; regular function
+		 (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 (~
+				 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 (pretty-type (cadr res)))
+      ;; (display "\n\t[")
+      ;; (display (car res))
+      ;; (display "]\n")
       res))
+  (cadr (check '() (normalize prog))))
 
+					; returns a list of pairs of constraints
+(define (~ a b)
+  (let ([res (unify? a b)])
+    (if res
+	res
+	(error #f
+	       (format "couldn't unify ~a ~~ ~a" a b)))))
 
-(define (abs? t)
-  (and (list? t) (eq? (car t) 'abs)))
+(define (unify? a b)
+  (cond [(eq? a b) '()]
+	[(or (tvar? a) (tvar? b)) (list (list a b))]
+	[(and (abs? a) (abs? b))
+	 (let* [(arg-cs (unify? (cadr a) (cadr b)))
+		(body-cs (unify? (substitute arg-cs (caddr a))
+				 (substitute arg-cs (caddr b))))]
+	   (consolidate arg-cs body-cs))]
+	[else #f]))
 
-(define (tvar? t)
-  (and (not (list? t)) (not (concrete? t)) (symbol? t)))
+					; TODO: what's the most appropriate substitution?
+					; should all constraints just be limited to a pair?
+					; this is currently horrific and i don't know what im doing.
+					; should probably use ast-find here or during consolidation
+					; to detect substitutions more than one layer deep
+					; e.g. (abs t1 int) ~ (abs bool int)
+					; substituting these constraints with t1 should resolve t1 with bool
+(define (substitute cs t)
+					; gets the first concrete type
+					; otherwise returns the last type variable
 
-(define (concrete? t)
-  (case t
-    ('int #t)
-    ('bool #t)
-    (else #f)))
+					; removes t itself from cs, to prevent infinite recursion
+  (define cs-without-t
+    (map (lambda (c)
+	   (filter (lambda (x) (not (eqv? t x))) c))
+	 cs))
+
+  (define (get-concrete c)
+    (let [(last (null? (cdr c)))]
+      (if (not (tvar? (car c)))
+	  (if (abs? (car c))
+	      (substitute cs-without-t (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 (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)))))))
+
+					; a1 -> a2 ~ a3 -> a4;
+					; a1 -> a2 !~ bool -> bool
+					; basically can the tvars be renamed
+(define (types-equal? x y)
+  (let ([cs (unify? x y)])
+    (if (not cs) #f
+	(let*
+	    ([test-kind
+	      (lambda (acc c)
+		(if (tvar? c) acc #f))]
+	     [test (lambda (acc c)
+		     (and acc
+			  (fold-left test-kind #t c) ; check only tvar substitutions
+			  (<= (length c) 2)))])	     ; check maximum 2 subs per equality group
+	  (fold-left test #t cs)))))
+
+					; input: a list of binds ((x . y) (y . 3))
+					; returns: pair of verts, edges ((x y) . (x . y))
+(define (graph bs)
+  (define (go bs orig-bs)
+    (define (find-refs prog)
+      (ast-collect
+       (lambda (x)
+	 (case (ast-type x)
+					; only count a reference if its a binding
+	   ['var (if (assoc x orig-bs) (list x) '())]
+	   [else '()]))
+       prog))
+    (if (null? bs)
+	'(() . ())
+	(let* [(bind (car bs))
+
+	       (vert (car bind))
+	       (refs (find-refs (cdr bind)))
+	       (edges (map (lambda (x) (cons vert x))
+			   refs))
+
+	       (rest (if (null? (cdr bs))
+			 (cons '() '())
+			 (go (cdr bs) orig-bs)))
+	       (total-verts (cons vert (car rest)))
+	       (total-edges (append edges (cdr rest)))]
+	  (cons total-verts total-edges))))
+  (go bs bs))
+
+(define (successors graph v)
+  (define (go v E)
+    (if (null? E)
+	'()
+	(if (eqv? v (caar E))
+	    (cons (cdar E) (go v (cdr E)))
+	    (go v (cdr E)))))
+  (go v (cdr graph)))
+
+					; takes in a graph (pair of vertices, edges)
+					; returns a list of strongly connected components
+
+					; ((x y w) . ((x . y) (x . w) (w . x))
+
+					; =>
+					; .->x->y
+					; |  |
+					; |  v
+					; .--w
+
+					; ((x w) (y))
+
+					; this uses tarjan's algorithm, to get reverse
+					; topological sorting for free
+(define (sccs graph)
+  
+  (let* ([indices (make-hash-table)]
+	 [lowlinks (make-hash-table)]
+	 [on-stack (make-hash-table)]
+	 [current 0]
+	 [stack '()]
+	 [result '()])
+
+    (define (index v)
+      (get-hash-table indices v #f))
+    (define (lowlink v)
+      (get-hash-table lowlinks v #f))
+
+    (letrec
+	([strong-connect
+	  (lambda (v)
+	    (begin
+	      (put-hash-table! indices v current)
+	      (put-hash-table! lowlinks v current)
+	      (set! current (+ current 1))
+	      (push! stack v)
+	      (put-hash-table! on-stack v #t)
+
+	      (for-each
+	       (lambda (w)
+		 (if (not (hashtable-contains? indices w))
+					; successor w has not been visited, recurse
+		     (begin
+		       (strong-connect w)
+		       (put-hash-table! lowlinks
+					v
+					(min (lowlink v) (lowlink w))))
+					; successor w has been visited
+		     (when (get-hash-table on-stack w #f)
+		       (put-hash-table! lowlinks v (min (lowlink v) (index w))))))
+	       (successors graph v))
+
+	      (when (= (index v) (lowlink v))
+		(let ([scc
+		       (let new-scc ()
+			 (let ([w (pop! stack)])
+			   (put-hash-table! on-stack w #f)
+			   (if (eqv? w v)
+			       (list w)
+			       (cons w (new-scc)))))])
+		  (set! result (cons scc result))))))])
+      (for-each
+       (lambda (v)
+	 (when (not (hashtable-contains? indices v)) ; v.index == -1
+	   (strong-connect v)))
+       (car graph)))
+    result))
 
-					; returns a list of pairs of constraints
-(define (unify a b)
-  (cond ((eq? a b) '())
-	((or (tvar? a) (tvar? b)) (list (cons a b)))
-	((and (abs? a) (abs? b))
-	 (append (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)))