; 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)
(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
(car then-type-res)
(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))
- (newline)
- (substitute-env cs scc-env)))]
+ (consolidate (car res)
+ ; unify with tvars from scc-env
+ ; result ~ tvar
+ (~ (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)))))
- ;; (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* [(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
+ (func-c (~
+ func-type
(list 'abs
arg-type
(fresh-tvar))))
(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 (car res))
+ ;; (display "]\n")
res))
(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))
+(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) '()]
+ [(or (tvar? a) (tvar? b)) (list (list a b))]
+ [(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"))))
+ (consolidate arg-cs body-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))
(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)
; 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-kind
+ (lambda (acc c)
+ (if (tvar? c) acc #f))]
+ [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
+ (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