+ ; 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))