-(define (app? x)
- (and (list? x) (>= (length x) 2) (not (eq? (car x) 'lambda))))
+(load "ast.scm")
-(define (lambda? x)
- (and (list? x) (eq? (car x) 'lambda)))
+(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))))
-(define lambda-arg caadr)
-(define lambda-body caddr)
+(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 x)
+(define (env-lookup env n)
(if (null? env) (error #f "empty env") ; it's a type equality
- (if (eq? (caar env) x)
+ (if (eq? (caar env) n)
(cdar env)
- (env-lookup (cdr env) x))))
+ (env-lookup (cdr env) n))))
+
+(define (env-insert env n t)
+ (cons (cons n t) env))
(define abs-arg cadr)
(string->symbol
(string-append "t" (number->string (- cur-tvar 1))))))
+(define (last xs)
+ (if (null? (cdr xs))
+ (car xs)
+ (last (cdr xs))))
(define (normalize prog) ; (+ a b) -> ((+ a) b)
- (cond
- ((lambda? prog) '(lambda (lambda-arg prog) (normalize (lambda-body prog))))
- ((app? prog)
+ (case (ast-type prog)
+ ('lambda
+ ; (lambda (x y) (+ x y)) -> (lambda (x) (lambda (y) (+ x y)))
+ (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
(if (null? (cddr prog))
- (cons (normalize (car prog)) (normalize (cdr prog))) ; (f a)
- (normalize (cons (cons (car prog) (list (cadr prog))) (cddr prog))))) ; (f a b)
- (else 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
+ (map (lambda (x) `(,(car x) ,(normalize (cadr x))))
+ (let-bindings prog)))
+ (map normalize (let-body prog))))
+ (else (ast-traverse normalize prog))))
+(define (builtin-type x)
+ (case x
+ ('+ '(abs int (abs int int)))
+ ('- '(abs int (abs int int)))
+ ('* '(abs int (abs int int)))
+ ('! '(abs bool bool))
+ ('= '(abs int (abs int bool)))
+ ('bool->int '(abs bool int))
+ ('print '(abs string void))
+ (else #f)))
-(define (typecheck prog)
(define (check env x)
+ (display "check: ")
+ (display x)
+ (display "\n\t")
+ (display env)
+ (newline)
(let
((res
- (cond
- ((integer? x) (list '() 'int))
- ((boolean? x) (list '() 'bool))
- ((eq? x 'inc) (list '() '(abs int int)))
- ((eq? x '+) (list '() '(abs int (abs int int))))
- ((symbol? x) (list '() (env-lookup env x)))
-
- ((lambda? x)
- (let* ((new-env (cons (cons (lambda-arg x) (fresh-tvar)) env))
+ (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 (~ (cadr then-type-res)
+ (cadr else-type-res)))
+ (cs (constraint-merge
+ (car then-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))
+ (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)
+ (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)
+ new-env))]
+ [new-env (fold-left process-component env components)])
+ (check new-env (last (let-body x)))))
+
+ ('lambda
+ (let* [(new-env (env-insert env (lambda-arg x) (fresh-tvar)))
+
(body-type-res (check new-env (lambda-body x)))
- (subd-env (substitute-env (car body-type-res) new-env)))
- ;; (display "lambda: ")
- ;; (display body-type-res)
- ;; (display "\n")
- ;; (display subd-env)
- ;; (display "\n")
+ (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))]
+ ;; (display "lambda:\n\t")
+ ;; (display prog)
+ ;; (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)
(list 'abs
- (env-lookup subd-env (lambda-arg x))
+ 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 (~ 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)))
(arg-type (cadr arg-type-res))
(func-type-res (check env (car x)))
(func-type (cadr func-type-res))
; f ~ a -> t0
- (func-c (unify func-type
- (list 'abs
- arg-type
- (fresh-tvar))))
- (cs (append func-c (car arg-type-res) (car func-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))
(resolved-return-type (caddr resolved-func-type)))
(if (abs? resolved-func-type)
(let ((return-type (substitute cs (caddr resolved-func-type))))
(list cs return-type))
- (error #f "wah")))))))
- ;; (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 (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 constraints
+(define (~ a b)
+ (let ([res (unify? a b)])
+ (if res
+ res
+ (error #f
+ (format "couldn't unify ~a ~~ ~a" a b)))))
-(define (abs? t)
- (and (list? t) (eq? (car t) 'abs)))
+(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))))]
+ (constraint-merge body-cs arg-cs))]
+ [else #f]))
-(define (tvar? t)
- (and (not (list? t)) (not (concrete? t)) (symbol? t)))
+(define (substitute cs t)
+ (cond
+ [(tvar? t)
+ (if (assoc t cs)
+ (cdr (assoc t cs))
+ t)]
+ [(abs? t) `(abs ,(substitute cs (cadr t))
+ ,(substitute cs (caddr t)))]
+ [else t]))
-(define (concrete? t)
- (case t
- ('int #t)
- ('bool #t)
- (else #f)))
+ ; applies substitutions to all variables in environment
+(define (substitute-env cs env)
+ (map (lambda (x) (cons (car x) (substitute cs (cdr x)))) env))
- ; 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))
- (consolidate (unify (cadr a) (cadr b))
- (unify (caddr a) (caddr b))))
- (else (error #f "could not unify"))))
+ ; 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")]))
- ; TODO: what's the most appropriate substitution?
- ; should all constraints just be limited to a pair?
-(define (substitute cs t)
- (define (blah c)
- (if (null? (cdr c))
- (car c)
- (if (not (tvar? (car c)))
- (car c)
- (blah (cdr c)))))
- (fold-left
- (lambda (t c)
- (if (member t c)
- (blah c)
- t))
- t cs))
+ (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 (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)))))))
+ (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 (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 orig-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 '() '())
+ (go (cdr bs) orig-bs)))
+ (total-verts (cons vert (car rest)))
+ (total-edges (append edges (cdr rest)))]
+ (cons total-verts total-edges))))
+ (go bs bs))
+
+(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))
+
projects / scheme.git / blobdiff