Start thinking about heap allocation

[scheme.git] / typecheck.scm

diff --git a/typecheck.scm b/typecheck.scm
index 59e652ad9da26f36906a80964c9956179ecdad9f..313db0e2a9d48fbdbc7fcaff2f89eab749f905b7 100644 (file)
--- a/typecheck.scm
+++ b/typecheck.scm
@@ -1,4 +1,28 @@
 (load "ast.scm")
 (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 (concrete? t)
+  (case t
+    ('int #t)
+    ('bool #t)
+    ('void #t)
+    (else #f)))
+
+(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 n)
   (if (null? env) (error #f "empty env")                       ; it's a type equality
                                        ; ('a, ('b, 'a))
 (define (env-lookup env n)
   (if (null? env) (error #f "empty env")                       ; it's a type equality


@@ -23,25 +47,25 @@
       (car xs)
       (last (cdr xs))))
                                
       (car xs)
       (last (cdr xs))))
                                

-                                       

 (define (normalize prog) ; (+ a b) -> ((+ a) b)
 (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 (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)))))
        (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))
      (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
        (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))))
                           (let-bindings prog)))
                (map normalize (let-body prog))))

-   (else prog)))
+    (else (ast-traverse normalize prog))))

 
 (define (builtin-type x)
   (case x
 
 (define (builtin-type x)
   (case x


@@ -49,7 +73,9 @@
     ('- '(abs int (abs int int)))
     ('* '(abs int (abs int int)))
     ('! '(abs bool bool))
     ('- '(abs int (abs int int)))
     ('* '(abs int (abs int int)))
     ('! '(abs bool bool))

+    ('= '(abs int (abs int bool)))

     ('bool->int '(abs bool int))
     ('bool->int '(abs bool int))

+    ('print '(abs string void))

     (else #f)))
 
 ; we typecheck the lambda calculus only (only single arg lambdas)
     (else #f)))
 
 ; we typecheck the lambda calculus only (only single arg lambdas)


@@ -62,29 +88,80 @@
     ;; (newline)
     (let
        ((res
     ;; (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 (unify (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
+                                              (unify (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)))))
            
                (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)))
                       (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 "lambda:\n\t")
                  ;; (display prog)
                  ;; (display "\n\t")


@@ -97,7 +174,16 @@
                              resolved-arg-type
                              (cadr body-type-res)))))
            
                              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 (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)))
                 (let* ((arg-type-res (check env (cadr x)))
                        (arg-type (cadr arg-type-res))
                        (func-type-res (check env (car x)))


@@ -126,38 +212,34 @@
                   (if (abs? resolved-func-type)
                       (let ((return-type (substitute cs (caddr resolved-func-type))))
                         (list cs 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")))))))
+                      (error #f "not a function"))))))))

       ;; (display "result of ")
       ;; (display x)
       ;; (display ":\n\t")
       ;; (display "result of ")
       ;; (display x)
       ;; (display ":\n\t")

-      ;; (display (cadr res))
-      ;; (display "[")
+      ;; (display (pretty-type (cadr res)))
+      ;; (display "\n\t[")

       ;; (display (car res))
       ;; (display "]\n")
       res))
   (cadr (check '() (normalize prog))))
 
       ;; (display (car res))
       ;; (display "]\n")
       res))
   (cadr (check '() (normalize prog))))
 

-
-(define (abs? t)
-  (and (list? t) (eq? (car t) 'abs)))
-
-(define (tvar? t)
-  (and (not (list? t)) (not (concrete? t)) (symbol? t)))
-
-(define (concrete? t)
-  (case t
-    ('int #t)
-    ('bool #t)
-    (else #f)))
-

                                        ; returns a list of pairs of constraints
 (define (unify a b)
                                        ; returns a list of pairs of constraints
 (define (unify 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) '())
        ((or (tvar? a) (tvar? b)) (~ a b))
        ((and (abs? a) (abs? 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"))))
+        (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)))

 
                                        ; TODO: what's the most appropriate substitution?
                                        ; should all constraints just be limited to a pair?
 
                                        ; TODO: what's the most appropriate substitution?
                                        ; should all constraints just be limited to a pair?


@@ -165,15 +247,21 @@
                                        ; gets the first concrete type
                                        ; otherwise returns the last type variable
 
                                        ; 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)
   (define (get-concrete c)

-    (let ((last (null? (cdr c))))
+    (let [(last (null? (cdr c)))]

       (if (not (tvar? (car c)))
          (if (abs? (car 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))))))
              (car c))
          (if last
              (car c)
              (get-concrete (cdr c))))))

+  

   (cond
    ((abs? t) (list 'abs
                   (substitute cs (cadr t))
   (cond
    ((abs? t) (list 'abs
                   (substitute cs (cadr t))


@@ -210,7 +298,8 @@
 
   (cond ((null? y) x)
        ((null? x) y)
 
   (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
                (merged (fold-left
                         (lambda (acc b)
                           (if acc


@@ -225,3 +314,123 @@
           (if merged
               (consolidate removed (cons (car merged) (cdr y)))
               (consolidate (cons a x) (cdr y)))))))
           (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)))])
+         (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 (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))
+  (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 '() '())
+                      (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))
+