-(define (is-app? x)
- (and (list? x) (not (eq? (car x) 'lambda))))
+(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 (is-lambda? x)
- (and (list? x) (eq? (car x) 'lambda)))
+(define (concrete? t)
+ (case t
+ ('int #t)
+ ('bool #t)
+ ('void #t)
+ (else #f)))
-(define lambda-arg cadr)
-(define lambda-body caddr)
+(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 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 (typecheck env x)
- (display "typechecking:\n\t")
- (display x)
- (display "\t")
- (display env)
- (display "\n")
+(define (last xs)
+ (if (null? (cdr xs))
+ (car xs)
+ (last (cdr xs))))
+
+(define (normalize prog) ; (+ a b) -> ((+ a) b)
+ (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))
+ `(,(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)))
+
+; 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)
(let
((res
- (cond
- ((integer? x) (list '() 'int))
- ((boolean? x) (list '() 'bool))
- ((eq? x 'inc) (list '() '(abs int int)))
- ((symbol? x) (list '() (env-lookup env x)))
-
- ((is-lambda? x)
- (let* ((new-env (cons (cons (lambda-arg x) (fresh-tvar)) env))
- (body-type-res (typecheck new-env (lambda-body x)))
- (subd-env (substitute (car body-type-res) new-env)))
- (display "lambda: ")
- (display body-type-res)
- (display "\n")
+ (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 (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
+ (~ (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)))))
+
+ ('lambda
+ (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))]
+ ;; (display "lambda:\n\t")
+ ;; (display prog)
+ ;; (display "\n\t")
+ ;; (display cs)
+ ;; (display "\n\t")
+ ;; (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)))))
- ((is-app? x) ; (f a)
- (let* ((arg-type-res (typecheck env (cadr x)))
- ; typecheck f with the knowledge that f : a -> x
- (func-type-res (typecheck env (car x)))
+ ('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))
- (c (unify func-type
+
+ ; f ~ a -> t0
+ (func-c (~
+ func-type
(list 'abs
- (cadr arg-type-res)
+ arg-type
(fresh-tvar))))
- (new-env (substitute c env))
- (resolved-func-type (env-lookup new-env (car x))))
- (display "is-app:\n")
- (display c)
- (display "\n")
- (display new-env)
- (display "\n")
- (display resolved-func-type)
- (display "\n")
- (display arg-type-res)
- (display "\n")
+ (cs (consolidate
+ (consolidate func-c (car arg-type-res))
+ (car func-type-res)))
+
+ (resolved-func-type (substitute cs func-type))
+ (resolved-return-type (caddr resolved-func-type)))
+ ;; (display "app:\n")
+ ;; (display cs)
+ ;; (display "\n")
+ ;; (display func-type)
+ ;; (display "\n")
+ ;; (display resolved-func-type)
+ ;; (display "\n")
+ ;; (display arg-type-res)
+ ;; (display "\n")
(if (abs? resolved-func-type)
- (list (append c
- (unify (cadr arg-type-res)
- (cadr resolved-func-type)))
- (caddr resolved-func-type))
- (error #f "wah")))))))
- (display "result of ")
- (display x)
- (display ":\n\t")
- (display (cadr res))
- (display "[")
- (display (car res))
- (display "]\n")
+ (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")
res))
+ (cadr (check '() (normalize prog))))
+ ; returns a list of pairs 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) '()]
+ [(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 #f]))
-(define (tvar? t)
- (and (not (list? t)) (not (concrete? t)) (symbol? t)))
+ ; 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
-(define (concrete? t)
- (case t
- ('int #t)
- ('bool #t)
- (else #f)))
+ ; removes t itself from cs, to prevent infinite recursion
+ (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))))
+
+(define (substitute-env cs env)
+ (map (lambda (x) (cons (car x) (substitute cs (cdr x)))) env))
+
+(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
+(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) ; 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 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))
- ; returns a list of pairs of constraints
-(define (unify a b)
- (cond ((eq? a b) '())
- ((or (tvar? a) (tvar? b)) (list (cons a b)))
- ((and (abs? a) (abs? b))
- (append (unify (cadr a) (cadr b))
- (unify (caddr a) (caddr b))))
- (else (error #f "could not unify"))))
-
- ; takes a list of constraints and a type environment, and makes it work
-(define (substitute c env)
- (let ((go (lambda (x) (let ((tv (cdr x))
- (n (car x)))
- ;; (display tv)
- ;; (display "\n")
- ;; (display n)
- (cons n (fold-left
- (lambda (a y)
- ;; (display y)
- ;; (display ":")
- ;; (display a)
- (cond ((eq? a (car y)) (cdr y))
- ((eq? a (cdr y)) (car y))
- (else a)))
- tv c))))))
- (map go env)))
projects / scheme.git / blobdiff