(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
('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)
(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)
+ (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))
(let* ([components (reverse (sccs (graph (let-bindings x))))]
[process-component
(lambda (acc comps)
- (display comps)
- (newline)
(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)
- (begin (display scc-env) (newline)
(let ([body (cadr (assoc c (let-bindings x)))])
- (display body)(newline)(check scc-env body))))
+ (check scc-env body)))
comps)]
+ ; collect all the constraints in the scc
[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))
+ (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)
- (substitute-env cs scc-env)))]
+ new-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)))
;; (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)
(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))
+ (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)))
(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))
(display ":\n\t")
(display (pretty-type (cadr res)))
(display "\n\t[")
- (display (car res))
+ (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))
- (let* [(arg-cs (unify (cadr a) (cadr b)))
- (body-cs (unify (substitute arg-cs (caddr a))
+ ; 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))))]
- (consolidate arg-cs body-cs)))
- (else (error #f "could not unify"))))
+ (constraint-merge body-cs arg-cs))]
+ [else #f]))
- ; TODO: what's the most appropriate substitution?
- ; should all constraints just be limited to a pair?
(define (substitute cs t)
- ; 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)))]
- (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 (~ 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)))))))
-
- ; 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)
- (error #f "todo"))
+ (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 bs) (list x) '())]
+ ['var (if (assoc x orig-bs) (list x) '())]
[else '()]))
prog))
+ (if (null? bs)
+ '(() . ())
(let* [(bind (car bs))
(vert (car bind))
(rest (if (null? (cdr bs))
(cons '() '())
- (graph (cdr bs))))
+ (go (cdr bs) orig-bs)))
(total-verts (cons vert (car rest)))
(total-edges (append edges (cdr rest)))]
- (cons total-verts total-edges)))
+ (cons total-verts total-edges))))
+ (go bs bs))
(define (successors graph v)
(define (go v E)
(list w)
(cons w (new-scc)))))])
(set! result (cons scc result))))))])
-
(for-each
(lambda (v)
(when (not (hashtable-contains? indices v)) ; v.index == -1
projects / scheme.git / blobdiff