X-Git-Url: https://git.lukelau.me/?p=scheme.git;a=blobdiff_plain;f=typecheck.scm;h=6a99869c0697302f361a9e28ac216013f5d018d6;hp=21b874c2fdc043b41297575d84bdd12132d559a5;hb=9d93b066cfd6505849dff12146159bedeadf96b9;hpb=76d1cd698cc577eec3a259a6937b4ada324c1bfd

diff --git a/typecheck.scm b/typecheck.scm
index 21b874c..6a99869 100644
--- a/typecheck.scm
+++ b/typecheck.scm
@@ -10,6 +10,7 @@
   (case t
     ('int #t)
     ('bool #t)
+    ('void #t)
     (else #f)))
 
 (define (pretty-type t)
@@ -22,6 +23,19 @@
 	  (pretty-type (caddr t))))
 	(else (symbol->string t))))
 
+(define (pretty-constraints cs)
+  (string-append "{"
+		 (fold-left string-append
+			    ""
+			    (map (lambda (c)
+				   (string-append
+				    (pretty-type (car c))
+				    ": "
+				    (pretty-type (cdr c))
+				    ", "))
+				 cs))
+		 "}"))
+
 					; ('a, ('b, 'a))
 (define (env-lookup env n)
   (if (null? env) (error #f "empty env")			; it's a type equality
@@ -46,25 +60,25 @@
       (car xs)
       (last (cdr xs))))
 
-					
 (define (normalize prog) ; (+ a b) -> ((+ a) b)
-  (cond
+  (case (ast-type prog)
+    ('lambda 
 					; (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)
+    ('app
      (if (null? (cddr prog))
-	(cons (normalize (car prog)) (normalize (cdr prog))) ; (f a)
-	(list (list (normalize (car prog)) (normalize (cadr prog))) (normalize (caddr prog))))) ; (f a b)
-   ((let? 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) (cons (car x) (normalize (cdr x))))
+		      (map (lambda (x) `(,(car x) ,(normalize (cadr x))))
 			   (let-bindings prog)))
 		(map normalize (let-body prog))))
-   (else prog)))
+    (else (ast-traverse normalize prog))))
 
 (define (builtin-type x)
   (case x
@@ -72,47 +86,103 @@
     ('- '(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)
+  (display "check: ")
+  (display x)
+  (display "\n\t")
+  (display env)
+  (newline)
   (let
       ((res
-	  (cond
-	   ((integer? x) (list '() 'int))
-	   ((boolean? x) (list '() 'bool))
-	   ((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))))
+	(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 (constraint-merge
+		       (car then-type-res)
+		       (constraint-merge (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)
+				 (constraint-merge
+				  (constraint-merge
+					; unify with tvars from scc-env
+					; result ~ tvar
+				   (~ (env-lookup scc-env c) (cadr res))
+				   (car res))				  
+				  acc))
+			       '() 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)])
+			  		(display "cs:")
+		(display cs)
+		(newline)
+			  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)))
 
-	   ((lambda? x)
-	    (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)))
+		     (resolved-arg-type (substitute cs arg-type))]
 		;; (display "lambda:\n\t")
 		;; (display prog)
 		;; (display "\n\t")
 		;; (display cs)
 		;; (display "\n\t")
+		;; (display (format "subd-env: ~a\n" subd-env))
 		;; (display resolved-arg-type)
 		;; (newline)
 		(list (car body-type-res)
@@ -120,19 +190,28 @@
 			    resolved-arg-type
 			    (cadr body-type-res)))))
 	  
-	   ((app? x) ; (f a)
+	  ('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))
 		      
 					; f ~ a -> t0
-		   (func-c (unify func-type
-				  (list 'abs
-					arg-type
-					(fresh-tvar))))
-		   (cs (consolidate
-			(consolidate func-c (car arg-type-res))
+		      (func-c (~
+			       (substitute (car arg-type-res) func-type)
+			       `(abs ,arg-type ,(fresh-tvar))))
+		      (cs (constraint-merge
+			   (constraint-merge func-c (car arg-type-res))
 			   (car func-type-res)))
 		      
 		      (resolved-func-type (substitute cs func-type))
@@ -149,89 +228,208 @@
 		 (if (abs? resolved-func-type)
 		     (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")
+		     (error #f "not a function"))))))))
+    (display "result of ")
+    (display x)
+    (display ":\n\t")
+    (display (pretty-type (cadr res)))
+    (display "\n\t[")
+    (display (pretty-constraints (car res)))
+    (display "]\n")
     res))
+
+					; we typecheck the lambda calculus only (only single arg lambdas)
+(define (typecheck prog)
   (cadr (check '() (normalize prog))))
 
-					; returns a list of pairs of constraints
-(define (unify a b)
-  (cond ((eq? a b) '())
-	((or (tvar? a) (tvar? b)) (~ a b))
-	((and (abs? a) (abs? b))
-	 (consolidate (unify (cadr a) (cadr b))
-		      (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?
+					; returns a list of constraints
+(define (~ a b)
+  (let ([res (unify? a b)])
+    (if res
+	res
+	(error #f
+	       (format "couldn't unify ~a ~~ ~a" a b)))))
+
+(define (unify? a b)
+  (cond [(eq? a b) '()]
+	[(tvar? a) (list (cons a b))]
+	[(tvar? b) (list (cons b a))]
+	[(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))))]
+	   (constraint-merge body-cs arg-cs))]
+	[else #f]))
+
 (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))))
+   [(tvar? t)
+    (if (assoc t cs)
+	(cdr (assoc t cs))
+	t)]
+   [(abs? t) `(abs ,(substitute cs (cadr t))
+		   ,(substitute cs (caddr t)))]
+   [else t]))
 
+					; applies substitutions to all variables in environment
 (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)))))))
+					; composes constraints a onto b and merges, i.e. applies a to b
+					; a should be the "more important" constraints
+(define (constraint-merge a b)
+  (define (f constraint)
+    (cons (car constraint)
+	  (substitute a (cdr constraint))))
+  
+  (define (most-concrete a b)
+    (cond
+     [(tvar? a) b]
+     [(tvar? b) a]
+     [(and (abs? a) (abs? b))
+      `(abs ,(most-concrete (cadr a) (cadr b))
+	    ,(most-concrete (caddr a) (caddr b)))]
+     [(abs? a) b]
+     [(abs? b) a]
+     [else (error #f "impossible! most-concrete")]))
+
+  (define (union p q)
+    (cond
+     [(null? p) q]
+     [(null? q) p]
+     [else
+      (let ([x (car q)])
+	(if (assoc (car x) p)
+	    (if (eqv? (most-concrete (cddr (assoc (car x) p))
+				     (cdr x))
+		      (cdr x))
+		(cons x (union (filter (p) (not (eqv? 
+	
+  
+  (define (union p q)
+    (append (filter (lambda (x) (not (assoc (car x) p)))
+		    q)
+	    p))
+  (union a (map f b)))
+
+
+;; 					; 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 (lambda (acc c)
+		     (and acc
+			  (tvar? (car c)) ; the only substitutions allowed are tvar -> tvar
+			  (tvar? (cdr c))))])
+	  (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))
+