X-Git-Url: https://git.lukelau.me/?p=scheme.git;a=blobdiff_plain;f=typecheck.scm;h=b2b001f1d27220211e5f67e651d641c9895f5b5c;hp=e96f6943767e1c5ab463398d11146d8f8ae450ce;hb=HEAD;hpb=4a6161c0db78e4739433377861c0fa89b92619be

diff --git a/typecheck.scm b/typecheck.scm
index e96f694..b2b001f 100644
--- a/typecheck.scm
+++ b/typecheck.scm
@@ -1,17 +1,17 @@
 (load "ast.scm")
+(load "stdlib.scm")
 
 (define (abs? t)
   (and (list? t) (eq? (car t) 'abs)))
 
 (define (tvar? t)
-  (and (not (list? t)) (not (concrete? t)) (symbol? t)))
+  (and (not (list? t))
+       (not (concrete? t))
+       (symbol? t)))
 
 (define (concrete? t)
-  (case t
-    ('int #t)
-    ('bool #t)
-    ('void #t)
-    (else #f)))
+  (and (symbol? t)
+       (char-upper-case? (string-ref (symbol->string t) 0))))
 
 (define (pretty-type t)
   (cond ((abs? t)
@@ -23,9 +23,22 @@
 	  (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
+  (if (null? env) (error #f "empty env" env n)			; it's a type equality
       (if (eq? (caar env) n)
 	  (cdar env)
 	  (env-lookup (cdr env) n))))
@@ -69,53 +82,19 @@
 
 (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
-	  (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)
+    ('+ '(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 (error #f "Couldn't find type for builtin" x))))
+
+(define (check-let dls env x)
+
+  ; acc is a pair of (env . annotated bindings)
+  (define (process-component acc comps)
     (let*
 					; create a new env with tvars for each component
 					; e.g. scc of (x y)
@@ -124,24 +103,25 @@
 	  (fold-left
 	   (lambda (acc c)
 	     (env-insert acc c (fresh-tvar)))
-			       acc comps)]
+	   (car acc) comps)]
 					; typecheck each component
 	 [type-results
 	  (map
 	   (lambda (c)
 	     (let ([body (cadr (assoc c (let-bindings x)))])
-				   (check scc-env body)))
+	       (check dls scc-env body)))
 	   comps)]
 					; collect all the constraints in the scc
 	 [cs
 	  (fold-left
 	   (lambda (acc res c)
-				 (consolidate
-				  acc
-				  (consolidate (car res)
+	     (constraint-merge
+	      (constraint-merge
 					; unify with tvars from scc-env
 					; result ~ tvar
-					       (~ (cadr res) (env-lookup scc-env c)))))
+	       (~ (env-lookup scc-env c) (cadr res))
+	       (car res))				  
+	      acc))
 	   '() type-results comps)]
 					; substitute *only* the bindings in this scc
 	 [new-env
@@ -149,83 +129,265 @@
 		 (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)))))
+	       scc-env)]
 
-	    ('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
-			      resolved-arg-type
-			      (cadr body-type-res)))))
+	 [annotated-bindings (append (cdr acc) ; the previous annotated bindings
+				     (map list
+					  comps
+					  (map caddr type-results)))])
+      (cons new-env annotated-bindings)))
+  					; 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))))]
+	 [results (fold-left process-component (cons env '()) components)]
+	 [new-env (car results)]
+	 [annotated-bindings (cdr results)]
 
-	    ('app ; (f a)
+	 [body-results (map (lambda (body) (check dls new-env body)) (let-body x))]
+	 [let-type (cadr (last body-results))]
+	 [cs (fold-left (lambda (acc cs) (constraint-merge acc cs)) '() (map car body-results))]
+
+	 [annotated `((let ,annotated-bindings ,@(map caddr body-results)) : ,let-type)])
+    (list cs let-type annotated)))
+
+(define (check-app dls env x)
   (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))
+					; TODO: what about ((f a) 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)]
+
+	     [annotated `(((,(car x) : ,func-type)
+			   (,(cadr x) : ,func-type)) : ,resolved-return-type)])
+	(list cs resolved-return-type annotated)))
 
 					; 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))
+  (let* ([arg-type-res (check dls env (cadr x))]
+	 [arg-type (cadr arg-type-res)]
+	 [func-type-res (check dls env (car x))]
+	 [func-type (cadr func-type-res)]
 	 
 					; f ~ a -> t0
-			(func-c (~
-				 func-type
-				 (list 'abs
-				       arg-type
-				       (fresh-tvar))))
-			(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")
+	 [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)]
+	 [resolved-return-type (caddr resolved-func-type)]
+
+	 [annotated `((,(caddr func-type-res)
+		       ,(caddr arg-type-res)) : ,resolved-return-type)])
+
     (if (abs? resolved-func-type)
 	(let ((return-type (substitute cs (caddr resolved-func-type))))
-			 (list cs return-type))
-		       (error #f "not a function"))))))))
+	  (list cs return-type annotated))
+	(error #f "not a function"))))
+
+(define (check-case dls env x)
+
+  (define (check-match switch-type x)
+    
+    (define (get-bindings product-types pattern)
+      (define (go product-type product)
+	(case (ast-type product)
+	  ['var (list (cons product product-type))]
+					; an inner pattern match
+	  ['app (let* ([inner-sum (car product)]
+		       [inner-sums (cdr (assoc product-type dls))]
+		       [inner-product-types (cdr (assoc inner-sum inner-sums))])
+		  (get-bindings inner-product-types product))]
+	  [else '()]))
+      (flat-map go product-types (cdr pattern)))
+
+    
+    (let ([pattern (car x)]
+	  [expr (cadr x)])
+      (case (ast-type pattern)
+	['app
+					; a pattern match with bindings
+	  (let ([sum (assoc (car pattern) (cdr (assoc switch-type dls)))])
+	    (unless sum (error #f "can't pattern match ~a with ~a" switch-type pattern))
+	    (let* ([names (cdr pattern)]
+		   [product-types (cdr sum)]
+		   [new-env (append (get-bindings product-types pattern) env)])
+
+	      (check dls new-env expr)))]
+					; pattern match with binding and no constructor
+	['var (check dls (env-insert env pattern switch-type) expr)]
+					; a pattern match without bindings
+	[else (check dls env expr)])))
+  
+  (let* ([switch-type-res (check dls env (case-switch x))]
+	 [switch-type (cadr switch-type-res)]
+	 
+	 [case-expr-type-res (map (lambda (x) (check-match switch-type x)) (case-cases x))]
+	 [case-expr-types (map cadr case-expr-type-res)]
+
+	 [case-expr-equality-cs (fold-left constraint-merge '()
+					   (map (lambda (t) (~ t (car case-expr-types)))
+						(cdr case-expr-types)))]
+
+	 [resolved-type (substitute case-expr-equality-cs (car case-expr-types))]
+
+	 [annotated `((case ,(caddr switch-type-res)
+			,@(map (lambda (c e et)
+				 `(,c ((,e : ,et))))
+			       (map car (case-cases x))
+			       (map cadr (case-cases x))
+			       case-expr-types)) : ,resolved-type)]
+	 
+	 [cs (fold-left constraint-merge '()
+			(cons (car switch-type-res) case-expr-equality-cs))])
+    (list cs resolved-type annotated)))
+
+; returns a list (constraints type annotated)
+(define (check dls env x)
+  (define (make-result cs type)
+    (list cs type `(,x : ,type)))
+  ;; (display "check: ")
+  ;; (display x)
+  ;; (display "\n\t")
+  ;; (display env)
+  ;; (newline)
+  (let
+      ((res
+	(case (ast-type x)
+	  ('int-literal (make-result '() 'Int))
+	  ('string-literal (make-result '() 'String))
+	  ('builtin (make-result '() (builtin-type x)))
+
+	  ('if
+	   (let* ((cond-type-res (check dls env (cadr x)))
+		  (then-type-res (check dls env (caddr x)))
+		  (else-type-res (check dls env (cadddr x)))
+		  (then-eq-else-cs (~ (cadr then-type-res)
+				      (cadr else-type-res)))
+		  (cs (constraint-merge
+		       (car then-type-res)
+		       (constraint-merge (~ (cadr cond-type-res) 'Bool)
+					 (constraint-merge (car else-type-res)
+							   then-eq-else-cs))))
+		  (return-type (substitute cs (cadr then-type-res)))	      
+		  [annotated `((if ,(caddr cond-type-res)
+				   ,(caddr then-type-res)
+				   ,(caddr else-type-res)) : ,return-type)])
+	     (list cs return-type annotated)))
+	  
+	  ('var (make-result '() (env-lookup env x)))
+	  ('let (check-let dls env x))
+
+	  
+	  ('lambda
+	      (let* ([new-env (env-insert env (lambda-arg x) (fresh-tvar))]
+
+		     [body-type-res (check dls 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)]
+
+		     [lambda-type `(abs ,resolved-arg-type ,(cadr body-type-res))]
+
+		     [annotated `((lambda (,(lambda-arg x)) ,(caddr body-type-res)) : ,lambda-type)])
+		
+		(list (car body-type-res) ; constraints
+		      lambda-type  ; type
+		      annotated)))
+
+	  
+	  ('app (check-app dls env x))
+	  ['case (check-case dls env x)])))
+	      
+		
     ;; (display "result of ")
     ;; (display x)
     ;; (display ":\n\t")
     ;; (display (pretty-type (cadr res)))
     ;; (display "\n\t[")
-      ;; (display (car res))
+    ;; (display (pretty-constraints (car res)))
     ;; (display "]\n")
     res))
-  (cadr (check '() (normalize prog))))
 
-					; returns a list of pairs of constraints
+(define (init-adts-env prog)
+  (flat-map data-tors-type-env (program-data-layouts prog)))
+
+					; we typecheck the lambda calculus only (only single arg lambdas)
+(define (typecheck prog-without-stdlib)
+  (let* ([prog (append stdlib prog-without-stdlib)]
+	 [expanded (expand-pattern-matches prog)])
+    (cadr (check (program-data-layouts prog)
+		 (init-adts-env expanded)
+		 (normalize (program-body expanded))))))
+
+
+					; before passing annotated types onto codegen
+					; we need to restore the pre-normalization structure
+					; (this is important for function arity etc)
+(define (denormalize orig normed)
+
+  (define (collapse-lambdas n x)
+    (case n
+      [0 x]
+      [else
+       (let* ([inner-lambda (lambda-body (ann-expr x))]
+	      [arg (lambda-arg (ann-expr x))]
+	      [inner-collapsed (ann-expr (collapse-lambdas (- n 1) inner-lambda))])
+	 `((lambda ,(cons arg (lambda-args inner-collapsed))
+	     ,(lambda-body inner-collapsed)) : ,(ann-type x)))]))
+
+  (define (collapse-apps n x)
+    (case n
+      [-1 (error #f "nullary functions not handled yet")]
+      [0 x]
+      [else
+       (let* ([inner-app (car (ann-expr x))]
+	      [inner-collapsed (collapse-apps (- n 1) inner-app)])
+	 `(,(append (ann-expr inner-collapsed) (cdr (ann-expr x))) : ,(ann-type x)))]))
+
+  (case (ast-type orig)
+    ['lambda
+	(let ([collapsed (collapse-lambdas (- (length (lambda-args orig)) 1) normed)])
+	  `((lambda ,(lambda-args (ann-expr collapsed))
+	      ,(denormalize (lambda-body orig)
+			    (lambda-body (ann-expr collapsed)))) : ,(ann-type collapsed)))]
+    ['app
+     (let ([collapsed (collapse-apps (- (length orig) 2) normed)])
+       `(,(map (lambda (o n) (denormalize o n)) orig (ann-expr collapsed))
+	 : ,(ann-type collapsed)))]
+    ['let
+	`((let ,(map (lambda (o n) (list (car o) (denormalize (cadr o) (cadr n))))
+		     (let-bindings orig)
+		     (let-bindings (ann-expr normed)))
+	    ,@(map denormalize
+		   (let-body orig)
+		   (let-body (ann-expr normed)))) : ,(ann-type normed))]
+    ['if `((if ,@(map denormalize (cdr orig) (cdr (ann-expr normed))))
+	   : ,(ann-type normed))]
+    ['case `((case ,(denormalize (case-switch orig) (case-switch (ann-expr normed)))
+	       ,@(map (lambda (o n) (cons (car o) (denormalize (cadr o) (cadr n))))
+		      (case-cases orig) (case-cases (ann-expr normed))))
+	     : ,(ann-type normed))]
+    [else normed]))
+
+(define ann-expr car)
+(define ann-type caddr)
+
+					; prerequisites: expand-pattern-matches
+(define (annotate-types prog)
+  (denormalize
+   (program-body prog)
+   (caddr (check (program-data-layouts prog)
+		 (init-adts-env prog)
+		 (normalize (program-body prog))))))
+
+  
+					; returns a list of constraints
 (define (~ a b)
   (let ([res (unify? a b)])
     (if res
@@ -235,211 +397,80 @@
 
 (define (unify? a b)
   (cond [(eq? a b) '()]
-	[(or (tvar? a) (tvar? b)) (list (list 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))))]
-	   (consolidate arg-cs body-cs))]
+	   (constraint-merge body-cs arg-cs))]
 	[else #f]))
 
-					; 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
-
-					; 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))))
-
+   [(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 (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
+					; 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 cs constraint)
+    (cons (car constraint)
+	  (substitute cs (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 a]))
+
+					; for any two constraints that clash, e.g. t1 ~ abs t2 t3
+					; and t1 ~ abs int t3
+					; prepend the most concrete version of the type to the
+					; list of constraints
+  (define (clashes)
+    (define (gen acc x)
+      (if (assoc (car x) a)
+	  (cons (cons (car x) (most-concrete (cdr (assoc (car x) a))
+					     (cdr x)))
+		acc)
+	  acc))
+    (fold-left gen '() b))
+
+  (define (union p q)
+    (append (filter (lambda (x) (not (assoc (car x) p)))
+		    q)
+	    p))
+  (append (clashes) (union a (map (lambda (z) (f a z)) 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-kind
-	      (lambda (acc c)
-		(if (tvar? c) acc #f))]
-	     [test (lambda (acc c)
+	    ([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
+			  (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))