From d0e9f5296b7510fe057be4a2f9e2a31ed856652c Mon Sep 17 00:00:00 2001
From: Luke Lau <luke_lau@icloud.com>
Date: Sun, 28 Jul 2019 23:56:37 +0100
Subject: [PATCH] Break up lets into SCCs before typechecking

This means each binding gets the most general type possible.
Part of the work towards supporting typechecking recursive functions
---
 ast.scm       |  30 +++++++
 codegen.scm   |  12 +--
 tests.scm     |  28 +++++-
 typecheck.scm | 231 +++++++++++++++++++++++++++++++++++++++++++-------
 4 files changed, 260 insertions(+), 41 deletions(-)

diff --git a/ast.scm b/ast.scm
index a089919..a38a012 100644
--- a/ast.scm
+++ b/ast.scm
@@ -34,6 +34,20 @@
     ('if `(if ,@(map f (cdr x))))
     (else x)))
 
+(define (ast-collect f x)
+  (define (inner y) (ast-collect f y))
+  (case (ast-type x)
+    ['let (append (f x)
+		  (fold-map inner (let-bindings x))
+		  (fold-map inner (let-body x)))]
+    ['app (append (f x)
+		  (fold-map inner x))]
+    ['lambda (append (f x)
+		     (inner (lambda-body x)))]
+    ['if (append (f x)
+		 (fold-map inner (cdr x)))]
+    [else (f x)]))
+
 (define let-bindings cadr)
 (define let-body cddr)
 
@@ -45,3 +59,19 @@
 ; for use elsewhere
 (define lambda-args cadr)
 (define lambda-body caddr)
+
+; utils
+(define (fold-map f x) (fold-left append '() (map f x)))
+(define (repeat x n) (if (<= n 0) '()
+			 (cons x (repeat x (- n 1)))))
+
+
+(define-syntax push!
+  (syntax-rules ()
+    ((_ s x) (set! s (cons x s)))))
+
+(define-syntax pop!
+  (syntax-rules ()
+    ((_ s) (let ([x (car s)])
+	     (set! s (cdr s))
+	     x))))
diff --git a/codegen.scm b/codegen.scm
index 4e05bcf..2d60c0a 100644
--- a/codegen.scm
+++ b/codegen.scm
@@ -67,17 +67,12 @@
   (emit "not %rcx")      ; -%rcx = strlen + 1
   (emit "dec %rcx")
   
-  (case target
-    ('darwin
   (emit "movq %rbx, %rsi") ; string addr
   (emit "movq %rcx, %rdx") ; num bytes
   (emit "movq $1, %rdi")   ; file handle (stdout)
-     (emit "movq $0x2000004, %rax")) ; syscall 4 (write)
-    ('linux
-     (emit "mov %rbx, %rsi")  ; string addr
-     (emit "mov %rcx, %rdx")  ; num bytes
-     (emit "mov $1, %rax")    ; file handle (stdout)
-     (emit "mov $1, %rdi"))) ; syscall 1 (write)
+  (case target
+    ('darwin (emit "mov $0x2000004, %rax")) ; syscall 4 (write)
+    ('linux  (emit "mov $1, %rax"))) ; syscall 1 (write)
   (emit "syscall"))
 
 (define (range s n)
@@ -309,7 +304,6 @@
     (else (error #f "don't know how to codegen this"))))
 
 
-(define (fold-map f x) (fold-left append '() (map f x)))
 
 (define (free-vars prog)
   (define bound '())
diff --git a/tests.scm b/tests.scm
index 4ff6d76..6b66bec 100644
--- a/tests.scm
+++ b/tests.scm
@@ -1,12 +1,15 @@
 (load "codegen.scm")
 (load "typecheck.scm")
 
-(define (test actual expected)
-  (when (not (equal? actual expected))
+(define (test-f pred actual expected)
+  (when (not (pred actual expected))
     (error #f
 	   (format "test failed:\nexpected: ~a\nactual:   ~a"
 		   expected actual))))
 
+(define (test . xs) (apply test-f (cons equal? xs)))
+(define (test-types . xs) (apply test-f (cons types-unify? xs)))
+
 (define (read-file file)
   (call-with-input-file file
     (lambda (p)
@@ -30,9 +33,23 @@
   (let ((str (read-file "/tmp/test-output.txt")))
     (test str output)))
 
-(test (typecheck '(lambda (x) (+ ((lambda (y) (x y 3)) 5) 2)))
+(test-types (typecheck '(lambda (x) (+ ((lambda (y) (x y 3)) 5) 2)))
 	    '(abs (abs int (abs int int)) int))
 
+					; recursive types
+
+(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)))])
+			  foo))
+	    '(abs bool t0))
+
+(test-types (typecheck '(let ([bar (lambda (y) y)]
+			[foo (lambda (x) (foo (bar #t)))])
+		    bar))
+      '(abs t0 t0))
+
 (test-prog '(+ 1 2) 3)
 (test-prog '((lambda (x) ((lambda (y) (+ x y)) 42)) 100) 142)
 
@@ -59,3 +76,8 @@
 (test-prog-stdout '(let () ((lambda (f) (f "foo")) print) 0) "foo")
 (test-prog '((lambda (f) (f 3 3)) (lambda (x y) (bool->int (= x y)))) 1)
 (test-prog '(bool->int ((lambda (f) (! (f 2 3))) =)) 1)
+
+					; recursion (hangs at typechecking)
+(test-prog '(let [(fac (lambda (f n x) (if (= n 0) x (f f (- n 1) (* x x)))))]
+	      (fac fac 3 2))
+	   8)
diff --git a/typecheck.scm b/typecheck.scm
index 7eb4fa9..25a0e45 100644
--- a/typecheck.scm
+++ b/typecheck.scm
@@ -58,8 +58,8 @@
     ('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)
+	 (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))))
@@ -81,11 +81,11 @@
 ; 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)
@@ -111,23 +111,67 @@
 	    
 	    ('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))))
+					; 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)
+			(display comps)
+			(newline)
+			(let*
+			    ([scc-env
+			      (fold-left
+			       (lambda (acc c)
+				 (env-insert acc c (fresh-tvar)))
+			       acc comps)]
+			     [type-results
+			      (map
+			       (lambda (c)
+				 (begin (display scc-env) (newline)
+				 (let ([body (cadr (assoc c (let-bindings x)))])
+				   (display body)(newline)(check scc-env body))))
+			       comps)]
+			     [cs
+			      (fold-left
+			       (lambda (acc res c)
+				 (consolidate
+				  acc
+				  (unify (cadr res) (env-lookup scc-env c))))
+			       '() type-results comps)])
+			  (display "process-component env:\n")
+			  (display (substitute-env cs scc-env))
+			  (newline)
+			  (substitute-env cs scc-env)))]
+		     [new-env (fold-left process-component env components)])
 		(check new-env (last (let-body x)))))
 	    
+	    ;; (let ((new-env (fold-left
+	    ;; 		(lambda (acc bind)
+	    ;; 		  (let* [(bind-tvar (fresh-tvar))
+	    ;; 			 (env-with-tvar (env-insert acc (car bind) bind-tvar))
+	    ;; 			 (bind-res (check env-with-tvar (cadr bind)))
+	    ;; 			 (bind-type (cadr bind-res))
+	    ;; 			 (cs (consolidate (car bind-res)
+	    ;; 					  (unify bind-type bind-tvar)))]
+	    ;; 		    (substitute-env cs env-with-tvar)))
+	    ;; 		env (let-bindings x))))
+	    ;;   (display "sccs of graph\n")
+	    ;;   (display (sccs (graph (let-bindings x))))
+	    ;;   (newline)
+	    ;;   (display "env when checking body:\n\t")
+	    ;;   (display new-env)
+	    ;;   (newline)
+	    ;;   (check new-env (last (let-body x)))))
+	    
 
 	    ('lambda
-	    (let* ((new-env (env-insert env (lambda-arg x) (fresh-tvar)))
+		(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")
@@ -141,6 +185,15 @@
 			      (cadr body-type-res)))))
 	    
 	    ('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 (unify func-type other-func-type))]
+		   (list cs 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)))
@@ -169,14 +222,14 @@
 		   (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 (car res))
+      (display "]\n")
       res))
   (cadr (check '() (normalize prog))))
 
@@ -185,8 +238,10 @@
   (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))))
+	 (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 (error #f "could not unify"))))
 
 					; TODO: what's the most appropriate substitution?
@@ -195,15 +250,21 @@
 					; gets the first concrete type
 					; otherwise returns the last type variable
 
+  (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))))
+    (let [(last (null? (cdr c)))]
       (if (not (tvar? (car c)))
 	  (if (abs? (car c))
-	      (substitute cs (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))
@@ -240,7 +301,8 @@
 
   (cond ((null? y) x)
 	((null? x) y)
-	(else (let* ((a (car y))
+	(else
+	 (let* ((a (car y))
 		(merged (fold-left
 			 (lambda (acc b)
 			   (if acc
@@ -255,3 +317,114 @@
 	   (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)
+  (error #f "todo"))
+
+					; input: a list of binds ((x . y) (y . 3))
+					; returns: pair of verts, edges ((x y) . (x . y))
+(define (graph 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 bs) (list x) '())]
+	 [else '()]))
+     prog))
+  (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 '() '())
+		   (graph (cdr bs))))
+	 (total-verts (cons vert (car rest)))
+	 (total-edges (append edges (cdr rest)))]
+    (cons total-verts total-edges)))
+
+(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))
+
-- 
2.30.2