From 9d93b066cfd6505849dff12146159bedeadf96b9 Mon Sep 17 00:00:00 2001
From: Luke Lau <luke_lau@icloud.com>
Date: Thu, 1 Aug 2019 16:19:56 +0100
Subject: [PATCH] WIP on typechecker refactor

Need to figure out the best way to union merge constraints, where they
have the same key but one has a more concrete term
---
 tests.scm     |  28 ++++++-
 typecheck.scm | 210 ++++++++++++++++++++++++--------------------------
 2 files changed, 126 insertions(+), 112 deletions(-)

diff --git a/tests.scm b/tests.scm
index c4b81f1..15e14ea 100644
--- a/tests.scm
+++ b/tests.scm
@@ -8,7 +8,14 @@
 		   expected actual))))
 
 (define (test . xs) (apply test-f (cons equal? xs)))
-(define (test-types . xs) (apply test-f (cons types-equal? xs)))
+
+(define-syntax test-types
+  (syntax-rules ()
+    ((_ a e)
+     (begin
+       (display (quote a))
+       (newline)
+       (test-f types-equal? a e)))))
 
 (define (read-file file)
   (call-with-input-file file
@@ -38,7 +45,7 @@
 
 					; recursive types
 
-(test-types (substitute '((t1 (abs t1 t10))) 't1) '(abs t1 t10))
+(test-types (substitute '((t1 . (abs t1 t10))) 't1) '(abs t1 t10))
 
 (test-types (typecheck '(let ([bar (lambda (y) y)]
 			      [foo (lambda (x) (foo (bar #t)))])
@@ -68,6 +75,23 @@
 			  bar))
 	    'int)
 
+					; mutual recursion
+(test-types (typecheck '(let ([f (lambda (n) (if (= n 0)
+						 0
+						 (+ 1 (g (- n 1)))))]
+			      [g (lambda (m) (f m))])
+			  (f 10)))
+	    'int)
+
+(test-types (typecheck '(let ([pow (lambda (p y)
+				     (let ([go (lambda (n x)
+						 (if (= n 0)
+						     x
+						     (go (- n 1) (* x y))))])
+				       (go p 1)))])
+			  (pow 4 2)))
+	    'int)
+
 (test-prog '(+ 1 2) 3)
 (test-prog '(bool->int (= 2 0)) 0)
 (test-prog '((lambda (x) ((lambda (y) (+ x y)) 42)) 100) 142)
diff --git a/typecheck.scm b/typecheck.scm
index e96f694..6a99869 100644
--- a/typecheck.scm
+++ b/typecheck.scm
@@ -23,6 +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
@@ -78,14 +91,12 @@
     ('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
 	(case (ast-type x)
@@ -100,9 +111,9 @@
 		  (else-type-res (check env (cadddr x)))
 		  (then-eq-else-cs (~ (cadr then-type-res)
 				      (cadr else-type-res)))
-		    (cs (consolidate
+		  (cs (constraint-merge
 		       (car then-type-res)
-			 (consolidate (car else-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))
@@ -136,12 +147,13 @@
 			     [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
@@ -150,6 +162,9 @@
 					 (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)))))
@@ -167,6 +182,7 @@
 		;; (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)
@@ -192,12 +208,10 @@
 		      
 					; f ~ a -> t0
 		      (func-c (~
-				 func-type
-				 (list 'abs
-				       arg-type
-				       (fresh-tvar))))
-			(cs (consolidate
-			     (consolidate func-c (car arg-type-res))
+			       (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))
@@ -215,17 +229,20 @@
 		     (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")
+    (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
+					; returns a list of constraints
 (define (~ a b)
   (let ([res (unify? a b)])
     (if res
@@ -235,105 +252,78 @@
 
 (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 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-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))
-- 
2.30.2