(inner (lambda-body x)))]
['if (append (f x)
(flat-map inner (cdr x)))]
+ ['closure (flat-map inner (caddr x))]
[else (f x)]))
(define (ast-find p x)
[else (p x)]))
(define (let-bindings e)
- (define (pattern-match x body)
- (if (eqv? (ast-type x) 'var)
- (list (cons x body))
- (let* ([constructor (car x)]
+ (define (pattern-match binding body)
+ (if (eqv? (ast-type binding) 'var)
+ (list (cons binding body))
+ (let* ([constructor (car binding)]
[destructor (lambda (i) (dtor-name constructor i))])
(flat-map (lambda (y i)
- (pattern-match y (list (destructor i) body)))
- (cdr x)
- (range 0 (length (cdr x)))))))
+ (pattern-match y `((,(destructor i) ,@body))))
+ (cdr binding)
+ (range 0 (length (cdr binding)))))))
(flat-map (lambda (x) (pattern-match (car x) (cdr x))) (cadr e)))
(define let-body cddr)
program))
(define (program-body program)
+ ; hack to have multi-expression bodies
`(let ()
,@(filter (lambda (x) (eqv? (statement-type x) 'expr))
program)))
+
+ ; (A ((foo (Int Bool))
+ ; (bar (Bool)))
+
+(define data-layout cdr)
+
; gets both constructors and destructors
; (data A (foo Int Bool)
; (bar Bool))
; |
; v
- ; (foo . (abs Int (abs Bool A)))
- ; (foo~0 . (abs A Int)
- ; (foo~1 . (abs A Bool)
- ; (bar . (abs Bool A)
- ; (bar~0 . (abs A Bool)
+ ; (foo . (constructor . (abs Int (abs Bool A))))
+ ; (foo~0 . (0 . (abs A Int)))
+ ; (foo~1 . (1 . (abs A Bool)))
+ ; (bar . (constructor . (abs Bool A)))
+ ; (bar~0 . (0 . (abs A Bool)))
-(define (data-tors data-def)
+(define (data-tors data-layout)
(define (constructor-type t products)
(fold-right (lambda (x acc) `(abs ,x ,acc)) t products))
(define (destructor ctor-name prod-type part-type index)
(let ([name (dtor-name ctor-name index)])
- (cons name `(abs ,prod-type ,part-type))))
+ (cons name (cons index `(abs ,prod-type ,part-type)))))
- (let ([type-name (cadr data-def)]
- [ctors (cddr data-def)])
+ (let ([type-name (car data-layout)]
+ [ctors (cdr data-layout)])
(fold-right
(lambda (ctor acc)
(let* ([ctor-name (car ctor)]
[products (cdr ctor)]
- [maker (cons ctor-name (constructor-type type-name products))]
+ [maker (cons ctor-name (cons 'constructor (constructor-type type-name products)))]
[dtors (map (lambda (t i) (destructor ctor-name type-name t i))
products
(cons maker (append dtors acc))))
'()
- ctrs)))
+ ctors)))
+
+ ; creates a type environment for a given adt definition
+(define (data-tors-env data-layout)
+ (map (lambda (x) (cons (car x) (cddr x))) (data-tors data-layout)))
(define (dtor-name ctor-name index)
(string->symbol
(define lambda-args cadr)
(define lambda-body caddr)
+(define (references prog)
+ (ast-collect
+ (lambda (x)
+ (case (ast-type x)
+ ['var (list x)]
+ [else '()]))
+ prog))
+
+(define (graph bs)
+ (define (go bs orig-bs)
+ (if (null? bs)
+ '(() . ())
+ (let* [(bind (car bs))
+
+ (vert (car bind))
+ (refs (filter ; only count a reference if its a binding
+ (lambda (x) (assoc x orig-bs))
+ (references (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))
+
+
; utils
+
(define (range s n)
(if (= 0 n) '()
(append (range s (- n 1))
(apply printf s)
(display "\n")))
+(define wordsize 8)
+
+(define (type-size type env)
+
+ (define (adt-size adt)
+ (let ([sizes
+ (map (lambda (sum)
+ (fold-left (lambda (acc x) (+ acc (type-size x)))
+ wordsize ; one word needed to store tag
+ (cdr sum)))
+ (cdr adt))])
+ (apply max sizes)))
+
+ (case type
+ ['Int wordsize]
+ ['Bool wordsize]
+ [else
+ (let ([adt (assoc type (env-adts env))])
+ (if adt
+ (adt-size adt)
+ (error #f "unknown size" type)))]))
+
+ ; an environment consists of adt layouts in scope,
+ ; and any bound variables.
+ ; bound variables are an assoc list with their stack offset
+(define make-env list)
+(define env-adts car)
+(define env-bindings cadr)
+
(define (codegen-add xs si env)
(define (go ys)
(if (null? ys)
('linux (emit "mov $1, %rax"))) ; syscall 1 (write)
(emit "syscall"))
-(define wordsize 8)
-
(define (codegen-let bindings body si env)
; is this a closure that captures itself?
(and (eqv? (ast-type expr) 'closure)
(memv name (caddr expr))))
- (let* ((stack-offsets (map (lambda (name x) ; assoc map of binding name to offset
+
+ ;; (define (emit-scc scc env)
+ ;; ; acc is a pair of the env and list of touchups
+ ;; (define (emit-binding acc binding)
+ ;; (let ([binding-name (car binding)]
+ ;; [binding-body (cadr binding)]
+
+ ;; [other-bindings (filter
+ ;; (lambda (x) (not (eqv? binding-name x)))
+ ;; scc)]
+ ;; [mutually-recursives
+ ;; (filter
+ ;; (lambda (other-binding)
+ ;; (memv other-binding (references binding-body)))
+ ;; other-bindings)]
+
+ ;; [new-touchups (append touchups (cdr acc))])
+
+ ;; ; TODO: assert that the only mutually recursives are closures
+ ;; (for-each
+ ;; (lambda (binding)
+ ;; (when (not (eqv? (ast-type (cadr binding))
+
+ ;; (emit "asdf")
+ ;; (cons new-env new-touchups)
+ ;; ))
+
+ ;; (fold-left emit-binding (cons env '()) scc))))
+
+ (let* ([stack-offsets (map (lambda (name x) ; assoc map of binding name to offset
(cons name (- si (* x wordsize))))
(map car bindings)
- (range 0 (length bindings))))
- (inner-si (- si (* (length bindings) wordsize)))
+ (range 0 (length bindings)))]
+ [inner-si (- si (* (length bindings) wordsize))]
- (get-offset (lambda (n) (cdr (assoc n stack-offsets))))
+ [get-offset (lambda (n) (cdr (assoc n stack-offsets)))]
[inner-env
(fold-left
(lambda (env comps)
- (let ([scc-env
+ (let* ([scc-binding-offsets
(fold-left
(lambda (acc name)
(cons (cons name (get-offset name))
acc))
- env
- comps)])
+ (env-bindings env)
+ comps)]
+ [scc-env (make-env (env-adts env) scc-binding-offsets)])
(for-each
(lambda (name)
(let ([expr (cadr (assoc name bindings))])
; codegen-closure realise this!
(codegen-expr expr
inner-si
+ (make-env
+ (env-adts scc-env)
(cons (cons name 'self-captive)
- scc-env))
+ (env-bindings scc-env))))
(codegen-expr expr inner-si scc-env))
(emit "movq %rax, ~a(%rbp)" (get-offset name))))
comps)
scc-env))
- env (reverse (sccs (graph bindings))))])
+ env
+ (reverse (sccs (graph bindings))))])
(for-each (lambda (form)
(codegen-expr form inner-si inner-env))
body)))
(define (codegen-var name si env)
- (when (not (assoc name env))
- (error #f (format "Variable ~a is not bound" name)))
- (let ((offset (cdr (assoc name env))))
- (emit "movq ~a(%rbp), %rax" offset)))
+ (let ([binding (assoc name (env-bindings env))])
+ (if (not binding)
+ (error #f (format "Variable ~a is not bound" name))
+ (emit "movq ~a(%rbp), %rax" (cdr binding)))))
(define cur-lambda 0)
(define (fresh-lambda)
; store the captured vars
(for-each
(lambda (var-name heap-offset)
- (let ([stack-offset (cdr (assoc var-name env))])
+ (let ([stack-offset (cdr (assoc var-name (env-bindings env)))])
(emit "### captive ~a" var-name)
(if (eqv? stack-offset 'self-captive)
; captive refers to this closure:
(* (- wordsize) (+ 1 i)))
(range 0 (length params))))
- (env (map cons params stack-offsets)))
+ [bindings (map cons params stack-offsets)]
+ [env (make-env '() bindings)])
(emit "~a:" label)
(display "## lambda captives: ")
(codegen-expr else si env)
(emit "~a:" exit-label)))
+(define (data-tor env e)
+ (and (list? e)
+ (assoc (car e) (flat-map data-tors (env-adts env)))))
+
+(define (codegen-data-tor e si env)
+
+ (define (codegen-destructor tor)
+ (codegen-expr (cadr e) si env)
+ (let ([index (cadr tor)]
+ [products 2]
+ [to-traverse (list-head products index)]
+ [offset (fold-left
+ (lambda (acc t) (+ acc (type-size t)))
+ wordsize ; skip tag in first word
+ to-traverse)])
+ 3
+ ))
+
+ (let ([tor (data-tor env e)]
+ [constructor (eqv? 'constructor (cadr tor))])
+ (if constructor
+ (codegen-constructor tor)
+ (codegen-destructor tor))))
+
(define (codegen-expr e si env)
(emit "# ~a" e)
(case (ast-type e)
('= (codegen-eq (cadr e) (caddr e) si env))
('bool->int (codegen-expr (cadr e) si env))
('print (codegen-print (cadr e) si env))
- (else (codegen-call (car e) (cdr e) si env))))
+ (else
+ (if (data-tor env e)
+ (codegen-data-tor e si env)
+ (codegen-call (car e) (cdr e) si env)))))
; this is a builtin being passed around as a variable
('builtin (emit "movq $~a, %rax" (builtin-id e)))
(emit "~a:" (car s))
(emit "\t.string \"~a\"" (cdr s)))
-;; (define (amd64-abi f)
-;; ; preserve registers
-;; (emit "push %rbp")
-;; ;; (emit "push %rbx")
-;; ;; (for-each (lambda (i)
-;; ;; (emit (string-append
-;; ;; "push %r"
-;; ;; (number->string i))))
-;; ;; '(12 13 14 15))
-
-;; (emit "movq %rsp, %rbp") ; set up the base pointer
-
-;; (f) ; call stuff
-;; ; restore preserved registers
-;; ;; (for-each (lambda (i)
-;; ;; (emit (string-append
-;; ;; "pop %r"
-;; ;; (number->string i))))
-;; ;; '(15 14 13 12))
-;; ;; (emit "pop %rbx")
-;; (emit "pop %rbp")
-;; (emit "ret"))
-
; 24(%rbp) mem arg 1
; 16(%rbp) mem arg 0 prev frame
; -----------------------
(set! cur-lambda 0)
(let* ([body (program-body program)]
+ [data-layouts (map data-layout (program-datas program))]
+
(extract-res-0 (extract-strings body))
(strings (car extract-res-0))
(extract-res-1 (extract-lambdas (cdr extract-res-0)))
(emit "movq %rsp, %rbp") ; set up the base pointer
- (codegen-expr xform-prog (- wordsize) '())
+ (codegen-expr xform-prog (- wordsize) (make-env data-layouts '()))
; exit syscall
(emit "mov %rax, %rdi")
(let ((str (read-file "/tmp/test-output.txt")))
(test str output)))
-(test (data-tors '(data A
+(test (data-tors (data-layout '(data A
(foo Int Bool)
- (bar Bool)))
+ (bar Bool))))
+ '((foo . (constructor . (abs Int (abs Bool A))))
+ (foo~0 . (0 . (abs A Int)))
+ (foo~1 . (1 . (abs A Bool)))
+ (bar . (constructor . (abs Bool A)))
+ (bar~0 . (0 . (abs A Bool)))))
+
+(test (data-tors-env
+ (data-layout '(data A
+ (foo Int Bool)
+ (bar Bool))))
'((foo . (abs Int (abs Bool A)))
(foo~0 . (abs A Int))
(foo~1 . (abs A Bool))
(pow 4 2))))
'Int)
+ ; ADTs
+
+
(test-types
(typecheck
'((data A
y)))
'Int)
+
+ ; pattern matching
+(test (let-bindings '(let ([(foo x) a]) x))
+ '((x (foo~0 a))))
+
+(test (let-bindings '(let ([x (foo 42)] [(foo y) x]) x))
+ '((x (foo 42))
+ (y (foo~0 x))))
+
+ ; type annotations
+
+(test (annotate-types
+ '((let ([x 42]
+ [y (+ 1 x)])
+ (- y x))))
+
+ '((let ()
+ ((let ((x 42 : Int)
+ (y ((((+ : (abs Int (abs Int Int))) (1 : Int)) : (abs Int Int)) (x : Int)) : Int))
+ (((((- : (abs Int (abs Int Int))) (y : Int)) : (abs Int Int)) (x : Int)) : Int))))))
+
(test-expr '(+ 1 2) 3)
(test-expr '(bool->int (= 2 0)) 0)
(test-expr '((lambda (x) ((lambda (y) (+ x y)) 42)) 100) 142)
(pow 4 2))
16)
-(test-prog-stdout '(let ([f (lambda (n)
- (if (= n 0)
- 0
- (let ()
- (print "a")
- (g (- n 1)))))]
- [g (lambda (m)
- (let ()
- (print "b")
- (f (- m 1))))])
- (f 10)) "ababababab")
+ ; mutual recursion
+;; (test-prog-stdout '((let ([f (lambda (n)
+;; (if (= n 0)
+;; 0
+;; (let ()
+;; (print "a")
+;; (g (- n 1)))))]
+;; [g (lambda (m)
+;; (let ()
+;; (print "b")
+;; (f (- m 1))))])
+;; (f 10))) "ababababab")
(else (error #f "Couldn't find type for builtin" x))))
(define (check-let env x)
- ; 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)
+
+ ; acc is a pair of (env . annotated bindings)
+ (define (process-component acc comps)
(let*
; create a new env with tvars for each component
; e.g. scc of (x y)
(fold-left
(lambda (acc c)
(env-insert acc c (fresh-tvar)))
- acc comps)]
+ (car acc) comps)]
; typecheck each component
[type-results
(map
(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)))))
+ scc-env)]
+
+ [annotated-bindings (append (cdr acc) ; the previous annotated bindings
+ (map cons
+ comps
+ (map caddr type-results)))])
+ (cons new-env annotated-bindings)))
+ ; 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))))]
+ [results (fold-left process-component (cons env '()) components)]
+ [new-env (car results)]
+ [annotated-bindings (cdr results)]
+
+ [body-results (map (lambda (body) (check new-env body)) (let-body x))]
+ [let-type (cadr (last body-results))]
+ [cs (fold-left (lambda (acc cs) (constraint-merge acc cs)) '() (map car body-results))]
+
+ [annotated `((let ,annotated-bindings ,@(map caddr body-results)))])
+ (list cs let-type annotated)))
+
+; returns a list (constraints type annotated)
(define (check env x)
+ (define (make-result cs type)
+ (list cs type `(,x : ,type)))
;; (display "check: ")
;; (display x)
;; (display "\n\t")
(let
((res
(case (ast-type x)
- ('int-literal (list '() 'Int))
- ('bool-literal (list '() 'Bool))
- ('string-literal (list '() 'String))
- ('builtin (list '() (builtin-type x)))
+ ('int-literal (make-result '() 'Int))
+ ('bool-literal (make-result '() 'Bool))
+ ('string-literal (make-result '() 'String))
+ ('builtin (make-result '() (builtin-type x)))
('if
(let* ((cond-type-res (check env (cadr x)))
(constraint-merge (~ (cadr cond-type-res) 'Bool)
(constraint-merge (car else-type-res)
then-eq-else-cs))))
- (return-type (substitute cs (cadr then-type-res))))
- (list cs return-type)))
+ (return-type (substitute cs (cadr then-type-res)))
+ [annotated `((if ,(caddr cond-type-res)
+ ,(caddr then-type-res)
+ ,(caddr else-type-res)) : ,return-type)])
+ (list cs return-type annotated)))
- ('var (list '() (env-lookup env x)))
+ ('var (make-result '() (env-lookup env x)))
('let (check-let env 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 (format "subd-env: ~a\n" subd-env))
- ;; (display resolved-arg-type)
- ;; (newline)
- (list (car body-type-res)
- (list 'abs
- resolved-arg-type
- (cadr body-type-res)))))
+ (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)]
+
+ [lambda-type `(abs ,resolved-arg-type ,(cadr body-type-res))]
+
+ ; TODO: do we need to annotate the lambda argument?
+ [annotated `(lambda (,(lambda-arg x)) ,(caddr body-type-res))])
+
+ (list (car body-type-res) ; constraints
+ lambda-type ; type
+ annotated)))
+
('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)))
+ (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)]
+
+ [annotated `(((,(car x) : ,func-type)
+ (,(cadr x) : ,func-type)) : ,resolved-return-type)])
+ (list cs resolved-return-type annotated)))
; 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))
+ (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 (~
+ [func-c (~
(substitute (car arg-type-res) func-type)
- `(abs ,arg-type ,(fresh-tvar))))
- (cs (constraint-merge
+ `(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)))
- ;; (display "app:\n")
- ;; (display cs)
- ;; (display "\n")
- ;; (display func-type)
- ;; (display "\n")
- ;; (display resolved-func-type)
- ;; (display "\n")
- ;; (display arg-type-res)
- ;; (display "\n")
+ (car func-type-res))]
+
+ [resolved-func-type (substitute cs func-type)]
+ [resolved-return-type (caddr resolved-func-type)]
+
+ [annotated `((,(caddr func-type-res)
+ ,(caddr arg-type-res)) : ,resolved-return-type)])
+
(if (abs? resolved-func-type)
(let ((return-type (substitute cs (caddr resolved-func-type))))
- (list cs return-type))
+ (list cs return-type annotated))
(error #f "not a function")))))))
;; (display "result of ")
;; (display x)
;; (display "]\n")
res))
+(define (init-adts-env prog)
+ (flat-map data-tors-env (map data-layout (program-datas prog))))
+
; we typecheck the lambda calculus only (only single arg lambdas)
(define (typecheck prog)
+ (cadr (check (init-adts-env prog) (normalize (program-body prog)))))
- (let ([init-env (flat-map data-tors (program-datas prog))])
- (display init-env)
- (newline)
- (cadr (check init-env (normalize (program-body prog))))))
+(define (annotate-types prog)
+ (caddr (check (init-adts-env prog) (normalize (program-body prog)))))
; returns a list of constraints
; 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 / commitdiff