[bpt/guile.git] / module / language / cps / dfg.scm

;;; Continuation-passing style (CPS) intermediate language (IL)

;; Copyright (C) 2013, 2014, 2015 Free Software Foundation, Inc.

;;;; This library is free software; you can redistribute it and/or
;;;; modify it under the terms of the GNU Lesser General Public
;;;; License as published by the Free Software Foundation; either
;;;; version 3 of the License, or (at your option) any later version.
;;;;
;;;; This library is distributed in the hope that it will be useful,
;;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
;;;; Lesser General Public License for more details.
;;;;
;;;; You should have received a copy of the GNU Lesser General Public
;;;; License along with this library; if not, write to the Free Software
;;;; Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA

;;; Commentary:
;;;
;;; Many passes rely on a local or global static analysis of a function.
;;; This module implements a simple data-flow graph (DFG) analysis,
;;; tracking the definitions and uses of variables and continuations.
;;; It also builds a table of continuations and scope links, to be able
;;; to easily determine if one continuation is in the scope of another,
;;; and to get to the expression inside a continuation.
;;;
;;; Note that the data-flow graph of continuation labels is a
;;; control-flow graph.
;;;
;;; We currently don't expose details of the DFG type outside this
;;; module, preferring to only expose accessors.  That may change in the
;;; future but it seems to work for now.
;;;
;;; Code:

(define-module (language cps dfg)
  #:use-module (ice-9 match)
  #:use-module (ice-9 format)
  #:use-module (srfi srfi-1)
  #:use-module (srfi srfi-9)
  #:use-module (srfi srfi-26)
  #:use-module (language cps)
  #:use-module (language cps intset)
  #:export (build-cont-table
            lookup-cont

            compute-dfg
            dfg-cont-table
            dfg-min-label
            dfg-label-count
            dfg-min-var
            dfg-var-count
            with-fresh-name-state-from-dfg
            lookup-def
            lookup-uses
            lookup-predecessors
            lookup-successors
            lookup-block-scope
            find-call
            call-expression
            find-expression
            find-defining-expression
            find-constant-value
            continuation-bound-in?
            variable-free-in?
            constant-needs-allocation?
            control-point?
            lookup-bound-syms

            compute-idoms
            compute-dom-edges

            ;; Data flow analysis.
            compute-live-variables
            dfa-k-idx dfa-k-sym dfa-k-count dfa-k-in dfa-k-out
            dfa-var-idx dfa-var-sym dfa-var-count
            print-dfa))

;; These definitions are here because currently we don't do cross-module
;; inlining.  They can be removed once that restriction is gone.
(define-inlinable (for-each f l)
  (unless (list? l)
    (scm-error 'wrong-type-arg "for-each" "Not a list: ~S" (list l) #f))
  (let for-each1 ((l l))
    (unless (null? l)
      (f (car l))
      (for-each1 (cdr l)))))

(define-inlinable (for-each/2 f l1 l2)
  (unless (= (length l1) (length l2))
    (scm-error 'wrong-type-arg "for-each" "List of wrong length: ~S"
               (list l2) #f))
  (let for-each2 ((l1 l1) (l2 l2))
    (unless (null? l1)
      (f (car l1) (car l2))
      (for-each2 (cdr l1) (cdr l2)))))

(define (build-cont-table fun)
  (let ((max-k (fold-conts (lambda (k cont max-k) (max k max-k))
                           -1 fun)))
    (fold-conts (lambda (k cont table)
                  (vector-set! table k cont)
                  table)
                (make-vector (1+ max-k) #f)
                fun)))

;; Data-flow graph for CPS: both for values and continuations.
(define-record-type $dfg
  (make-dfg conts preds defs uses scopes scope-levels
            min-label max-label label-count
            min-var max-var var-count)
  dfg?
  ;; vector of label -> $kargs, etc
  (conts dfg-cont-table)
  ;; vector of label -> (pred-label ...)
  (preds dfg-preds)
  ;; vector of var -> def-label
  (defs dfg-defs)
  ;; vector of var -> (use-label ...)
  (uses dfg-uses)
  ;; vector of label -> label
  (scopes dfg-scopes)
  ;; vector of label -> int
  (scope-levels dfg-scope-levels)

  (min-label dfg-min-label)
  (max-label dfg-max-label)
  (label-count dfg-label-count)

  (min-var dfg-min-var)
  (max-var dfg-max-var)
  (var-count dfg-var-count))

(define-inlinable (vector-push! vec idx val)
  (let ((v vec) (i idx))
    (vector-set! v i (cons val (vector-ref v i)))))

(define (compute-reachable dfg min-label label-count)
  "Compute and return the continuations that may be reached if flow
reaches a continuation N.  Returns a vector of intsets, whose first
index corresponds to MIN-LABEL, and so on."
  (let (;; Vector of intsets, indicating that continuation N can
        ;; reach a set M...
        (reachable (make-vector label-count #f)))

    (define (label->idx label) (- label min-label))

    ;; Iterate labels backwards, to converge quickly.
    (let lp ((label (+ min-label label-count)) (changed? #f))
      (cond
       ((= label min-label)
        (if changed?
            (lp (+ min-label label-count) #f)
            reachable))
       (else
        (let* ((label (1- label))
               (idx (label->idx label))
               (old (vector-ref reachable idx))
               (new (fold (lambda (succ set)
                            (cond
                             ((vector-ref reachable (label->idx succ))
                              => (lambda (succ-set)
                                   (intset-union set succ-set)))
                             (else set)))
                          (or (vector-ref reachable idx)
                              (intset-add empty-intset label))
                          (visit-cont-successors list
                                                 (lookup-cont label dfg)))))
          (cond
           ((eq? old new)
            (lp label changed?))
           (else
            (vector-set! reachable idx new)
            (lp label #t)))))))))

(define (find-prompts dfg min-label label-count)
  "Find the prompts in DFG between MIN-LABEL and MIN-LABEL +
LABEL-COUNT, and return them as a list of PROMPT-LABEL, HANDLER-LABEL
pairs."
  (let lp ((label min-label) (prompts '()))
    (cond
     ((= label (+ min-label label-count))
      (reverse prompts))
     (else
      (match (lookup-cont label dfg)
        (($ $kargs names syms body)
         (match (find-expression body)
           (($ $prompt escape? tag handler)
            (lp (1+ label) (acons label handler prompts)))
           (_ (lp (1+ label) prompts))))
        (_ (lp (1+ label) prompts)))))))

(define (compute-interval reachable min-label label-count start end)
  "Compute and return the set of continuations that may be reached from
START, inclusive, but not reached by END, exclusive.  Returns an
intset."
  (intset-subtract (vector-ref reachable (- start min-label))
                   (vector-ref reachable (- end min-label))))

(define (find-prompt-bodies dfg min-label label-count)
  "Find all the prompts in DFG from the LABEL-COUNT continuations
starting at MIN-LABEL, and compute the set of continuations that is
reachable from the prompt bodies but not from the corresponding handler.
Returns a list of PROMPT, HANDLER, BODY lists, where the BODY is an
intset."
  (match (find-prompts dfg min-label label-count)
    (() '())
    (((prompt . handler) ...)
     (let ((reachable (compute-reachable dfg min-label label-count)))
       (map (lambda (prompt handler)
              ;; FIXME: It isn't correct to use all continuations
              ;; reachable from the prompt, because that includes
              ;; continuations outside the prompt body.  This point is
              ;; moot if the handler's control flow joins with the the
              ;; body, as is usually but not always the case.
              ;;
              ;; One counter-example is when the handler contifies an
              ;; infinite loop; in that case we compute a too-large
              ;; prompt body.  This error is currently innocuous, but we
              ;; should fix it at some point.
              ;;
              ;; The fix is to end the body at the corresponding "pop"
              ;; primcall, if any.
              (let ((body (compute-interval reachable min-label label-count
                                            prompt handler)))
                (list prompt handler body)))
            prompt handler)))))

(define* (visit-prompt-control-flow dfg min-label label-count f #:key complete?)
  "For all prompts in DFG in the range [MIN-LABEL, MIN-LABEL +
LABEL-COUNT), invoke F with arguments PROMPT, HANDLER, and BODY for each
body continuation in the prompt."
  (define (label->idx label) (- label min-label))
  (define (idx->label idx) (+ idx min-label))
  (for-each
   (match-lambda
    ((prompt handler body)
     (define (out-or-back-edge? label)
       ;; Most uses of visit-prompt-control-flow don't need every body
       ;; continuation, and would be happy getting called only for
       ;; continuations that postdominate the rest of the body.  Unless
       ;; you pass #:complete? #t, we only invoke F on continuations
       ;; that can leave the body, or on back-edges in loops.
       ;;
       ;; You would think that looking for the final "pop" primcall
       ;; would be sufficient, but that is incorrect; it's possible for
       ;; a loop in the prompt body to be contified, and that loop need
       ;; not continue to the pop if it never terminates.  The pop could
       ;; even be removed by DCE, in that case.
       (or-map (lambda (succ)
                 (or (not (intset-ref body succ))
                     (<= succ label)))
               (lookup-successors label dfg)))
     (let lp ((label min-label))
       (let ((label (intset-next body label)))
         (when label
           (when (or complete? (out-or-back-edge? label))
             (f prompt handler label))
           (lp (1+ label)))))))
   (find-prompt-bodies dfg min-label label-count)))

(define (analyze-reverse-control-flow fun dfg min-label label-count)
  (define (compute-reverse-control-flow-order ktail dfg)
    (let ((label-map (make-vector label-count #f))
          (next -1))
      (define (label->idx label) (- label min-label))
      (define (idx->label idx) (+ idx min-label))

      (let visit ((k ktail))
        ;; Mark this label as visited.
        (vector-set! label-map (label->idx k) #t)
        (for-each (lambda (k)
                    ;; Visit predecessors unless they are already visited.
                    (unless (vector-ref label-map (label->idx k))
                      (visit k)))
                  (lookup-predecessors k dfg))
        ;; Add to reverse post-order chain.
        (vector-set! label-map (label->idx k) next)
        (set! next k))

      (let lp ((n 0) (head next))
        (if (< head 0)
            ;; Add nodes that are not reachable from the tail.
            (let lp ((n n) (m label-count))
              (unless (= n label-count)
                (let find-unvisited ((m (1- m)))
                  (if (vector-ref label-map m)
                      (find-unvisited (1- m))
                      (begin
                        (vector-set! label-map m n)
                        (lp (1+ n) m))))))
            ;; Pop the head off the chain, give it its
            ;; reverse-post-order numbering, and continue.
            (let ((next (vector-ref label-map (label->idx head))))
              (vector-set! label-map (label->idx head) n)
              (lp (1+ n) next))))

      label-map))

  (define (convert-successors k-map)
    (define (idx->label idx) (+ idx min-label))
    (define (renumber label)
      (vector-ref k-map (- label min-label)))
    (let ((succs (make-vector (vector-length k-map) #f)))
      (let lp ((n 0))
        (when (< n (vector-length succs))
          (vector-set! succs (vector-ref k-map n)
                       (map renumber
                            (lookup-successors (idx->label n) dfg)))
          (lp (1+ n))))
      succs))

  (match fun
    (($ $cont kfun ($ $kfun src meta self ($ $cont ktail tail)))
     (let* ((k-map (compute-reverse-control-flow-order ktail dfg))
            (succs (convert-successors k-map)))
       ;; Any expression in the prompt body could cause an abort to
       ;; the handler.  This code adds links from every block in the
       ;; prompt body to the handler.  This causes all values used
       ;; by the handler to be seen as live in the prompt body, as
       ;; indeed they are.
       (visit-prompt-control-flow
        dfg min-label label-count
        (lambda (prompt handler body)
          (define (renumber label)
            (vector-ref k-map (- label min-label)))
          (vector-push! succs (renumber body) (renumber handler))))

       (values k-map succs)))))

(define (compute-idoms dfg min-label label-count)
  (define preds (dfg-preds dfg))
  (define (label->idx label) (- label min-label))
  (define (idx->label idx) (+ idx min-label))
  (define (idx->dfg-idx idx)  (- (idx->label idx) (dfg-min-label dfg)))
  (let ((idoms (make-vector label-count #f)))
    (define (common-idom d0 d1)
      ;; We exploit the fact that a reverse post-order is a topological
      ;; sort, and so the idom of a node is always numerically less than
      ;; the node itself.
      (cond
       ((= d0 d1) d0)
       ((< d0 d1) (common-idom d0 (vector-ref idoms (label->idx d1))))
       (else (common-idom (vector-ref idoms (label->idx d0)) d1))))
    (define (compute-idom preds)
      (define (has-idom? pred)
        (vector-ref idoms (label->idx pred)))
      (match preds
        (() min-label)
        ((pred . preds)
         (if (has-idom? pred)
             (let lp ((idom pred) (preds preds))
               (match preds
                 (() idom)
                 ((pred . preds)
                  (lp (if (has-idom? pred)
                          (common-idom idom pred)
                          idom)
                      preds))))
             (compute-idom preds)))))
    ;; This is the iterative O(n^2) fixpoint algorithm, originally from
    ;; Allen and Cocke ("Graph-theoretic constructs for program flow
    ;; analysis", 1972).  See the discussion in Cooper, Harvey, and
    ;; Kennedy's "A Simple, Fast Dominance Algorithm", 2001.
    (let iterate ((n 0) (changed? #f))
      (cond
       ((< n label-count)
        (let ((idom (vector-ref idoms n))
              (idom* (compute-idom (vector-ref preds (idx->dfg-idx n)))))
          (cond
           ((eqv? idom idom*)
            (iterate (1+ n) changed?))
           (else
            (vector-set! idoms n idom*)
            (iterate (1+ n) #t)))))
       (changed?
        (iterate 0 #f))
       (else idoms)))))

;; Compute a vector containing, for each node, a list of the nodes that
;; it immediately dominates.  These are the "D" edges in the DJ tree.
(define (compute-dom-edges idoms min-label)
  (define (label->idx label) (- label min-label))
  (define (idx->label idx) (+ idx min-label))
  (let ((doms (make-vector (vector-length idoms) '())))
    (let lp ((n 0))
      (when (< n (vector-length idoms))
        (let ((idom (vector-ref idoms n)))
          (vector-push! doms (label->idx idom) (idx->label n)))
        (lp (1+ n))))
    doms))

;; There used to be some loop detection code here, but it bitrotted.
;; We'll need it again eventually but for now it can be found in the git
;; history.

;; Data-flow analysis.
(define-record-type $dfa
  (make-dfa min-label min-var var-count in out)
  dfa?
  ;; Minimum label in this function.
  (min-label dfa-min-label)
  ;; Minimum var in this function.
  (min-var dfa-min-var)
  ;; Var count in this function.
  (var-count dfa-var-count)
  ;; Vector of k-idx -> intset
  (in dfa-in)
  ;; Vector of k-idx -> intset
  (out dfa-out))

(define (dfa-k-idx dfa k)
  (- k (dfa-min-label dfa)))

(define (dfa-k-sym dfa idx)
  (+ idx (dfa-min-label dfa)))

(define (dfa-k-count dfa)
  (vector-length (dfa-in dfa)))

(define (dfa-var-idx dfa var)
  (let ((idx (- var (dfa-min-var dfa))))
    (unless (< -1 idx (dfa-var-count dfa))
      (error "var out of range" var))
    idx))

(define (dfa-var-sym dfa idx)
  (unless (< -1 idx (dfa-var-count dfa))
    (error "idx out of range" idx))
  (+ idx (dfa-min-var dfa)))

(define (dfa-k-in dfa idx)
  (vector-ref (dfa-in dfa) idx))

(define (dfa-k-out dfa idx)
  (vector-ref (dfa-out dfa) idx))

(define (compute-live-variables fun dfg)
  ;; Compute the maximum fixed point of the data-flow constraint problem.
  ;;
  ;; This always completes, as the graph is finite and the in and out sets
  ;; are complete semi-lattices.  If the graph is reducible and the blocks
  ;; are sorted in reverse post-order, this completes in a maximum of LC +
  ;; 2 iterations, where LC is the loop connectedness number.  See Hecht
  ;; and Ullman, "Analysis of a simple algorithm for global flow
  ;; problems", POPL 1973, or the recent summary in "Notes on graph
  ;; algorithms used in optimizing compilers", Offner 2013.
  (define (compute-maximum-fixed-point preds inv outv killv genv)
    (define (fold f seed l)
      (if (null? l) seed (fold f (f (car l) seed) (cdr l))))
    (let lp ((n 0) (changed? #f))
      (cond
       ((< n (vector-length preds))
        (let* ((in (vector-ref inv n))
               (in* (or
                     (fold (lambda (pred set)
                             (cond
                              ((vector-ref outv pred)
                               => (lambda (out)
                                    (if set
                                        (intset-union set out)
                                        out)))
                              (else set)))
                           in
                           (vector-ref preds n))
                     empty-intset)))
          (if (eq? in in*)
              (lp (1+ n) changed?)
              (let ((out* (fold (lambda (gen set)
                                  (intset-add set gen))
                                (fold (lambda (kill set)
                                        (intset-remove set kill))
                                      in*
                                      (vector-ref killv n))
                                (vector-ref genv n))))
                (vector-set! inv n in*)
                (vector-set! outv n out*)
                (lp (1+ n) #t)))))
       (changed?
        (lp 0 #f)))))

  (unless (and (= (vector-length (dfg-uses dfg)) (dfg-var-count dfg))
               (= (vector-length (dfg-cont-table dfg)) (dfg-label-count dfg)))
    (error "function needs renumbering"))
  (let* ((min-label (dfg-min-label dfg))
         (nlabels (dfg-label-count dfg))
         (min-var (dfg-min-var dfg))
         (nvars (dfg-var-count dfg))
         (usev (make-vector nlabels '()))
         (defv (make-vector nlabels '()))
         (live-in (make-vector nlabels #f))
         (live-out (make-vector nlabels #f)))
    (call-with-values
        (lambda ()
          (analyze-reverse-control-flow fun dfg min-label nlabels))
      (lambda (k-map succs)
        (define (var->idx var) (- var min-var))
        (define (idx->var idx) (+ idx min-var))
        (define (label->idx label)
          (vector-ref k-map (- label min-label)))

        ;; Initialize defv and usev.
        (let ((defs (dfg-defs dfg))
              (uses (dfg-uses dfg)))
          (let lp ((n 0))
            (when (< n (vector-length defs))
              (let ((def (vector-ref defs n)))
                (unless def
                  (error "internal error -- var array not packed"))
                (for-each (lambda (def)
                            (vector-push! defv (label->idx def) n))
                          (lookup-predecessors def dfg))
                (for-each (lambda (use)
                            (vector-push! usev (label->idx use) n))
                          (vector-ref uses n))
                (lp (1+ n))))))

        ;; Liveness is a reverse data-flow problem, so we give
        ;; compute-maximum-fixed-point a reversed graph, swapping in for
        ;; out, usev for defv, and using successors instead of
        ;; predecessors.  Continuation 0 is ktail.
        (compute-maximum-fixed-point succs live-out live-in defv usev)

        ;; Now rewrite the live-in and live-out sets to be indexed by
        ;; (LABEL - MIN-LABEL).
        (let ((live-in* (make-vector nlabels #f))
              (live-out* (make-vector nlabels #f)))
          (let lp ((idx 0))
            (when (< idx nlabels)
              (let ((dfa-idx (vector-ref k-map idx)))
                (vector-set! live-in*  idx (vector-ref live-in  dfa-idx))
                (vector-set! live-out* idx (vector-ref live-out dfa-idx))
                (lp (1+ idx)))))

          (make-dfa min-label min-var nvars live-in* live-out*))))))

(define (print-dfa dfa)
  (match dfa
    (($ $dfa min-label min-var var-count in out)
     (define (print-var-set bv)
       (let lp ((n 0))
         (let ((n (intset-next bv n)))
           (when n
             (format #t " ~A" (+ n min-var))
             (lp (1+ n))))))
     (let lp ((n 0))
       (when (< n (vector-length in))
         (format #t "~A:\n" (+ n min-label))
         (format #t "  in:")
         (print-var-set (vector-ref in n))
         (newline)
         (format #t "  out:")
         (print-var-set (vector-ref out n))
         (newline)
         (lp (1+ n)))))))

(define (compute-label-and-var-ranges fun global?)
  (define (min* a b)
    (if b (min a b) a))
  (define-syntax-rule (do-fold make-cont-folder)
    ((make-cont-folder min-label max-label label-count
                       min-var max-var var-count)
     (lambda (label cont
                    min-label max-label label-count
                    min-var max-var var-count)
       (let ((min-label (min* label min-label))
             (max-label (max label max-label)))
         (define (visit-letrec body min-var max-var var-count)
           (match body
             (($ $letk conts body)
              (visit-letrec body min-var max-var var-count))
             (($ $letrec names vars funs body)
              (visit-letrec body
                            (cond (min-var (fold min min-var vars))
                                  ((pair? vars) (fold min (car vars) (cdr vars)))
                                  (else min-var))
                            (fold max max-var vars)
                            (+ var-count (length vars))))
             (($ $continue) (values min-var max-var var-count))))
         (match cont
           (($ $kargs names vars body)
            (call-with-values
                (lambda ()
                  (if global?
                      (visit-letrec body min-var max-var var-count)
                      (values min-var max-var var-count)))
              (lambda (min-var max-var var-count)
                (values min-label max-label (1+ label-count)
                        (cond (min-var (fold min min-var vars))
                              ((pair? vars) (fold min (car vars) (cdr vars)))
                              (else min-var))
                        (fold max max-var vars)
                        (+ var-count (length vars))))))
           (($ $kfun src meta self)
            (values min-label max-label (1+ label-count)
                    (min* self min-var) (max self max-var) (1+ var-count)))
           (_ (values min-label max-label (1+ label-count)
                      min-var max-var var-count)))))
     fun
     #f -1 0 #f -1 0))
  (if global?
      (do-fold make-global-cont-folder)
      (do-fold make-local-cont-folder)))

(define* (compute-dfg fun #:key (global? #t))
  (call-with-values (lambda () (compute-label-and-var-ranges fun global?))
    (lambda (min-label max-label label-count min-var max-var var-count)
      (when (or (zero? label-count) (zero? var-count))
        (error "internal error (no vars or labels for fun?)"))
      (let* ((nlabels (- (1+ max-label) min-label))
             (nvars (- (1+ max-var) min-var))
             (conts (make-vector nlabels #f))
             (preds (make-vector nlabels '()))
             (defs (make-vector nvars #f))
             (uses (make-vector nvars '()))
             (scopes (make-vector nlabels #f))
             (scope-levels (make-vector nlabels #f)))
        (define (var->idx var) (- var min-var))
        (define (label->idx label) (- label min-label))

        (define (add-def! var def-k)
          (vector-set! defs (var->idx var) def-k))
        (define (add-use! var use-k)
          (vector-push! uses (var->idx var) use-k))

        (define* (declare-block! label cont parent
                                 #:optional (level
                                             (1+ (vector-ref
                                                  scope-levels
                                                  (label->idx parent)))))
          (vector-set! conts (label->idx label) cont)
          (vector-set! scopes (label->idx label) parent)
          (vector-set! scope-levels (label->idx label) level))

        (define (link-blocks! pred succ)
          (vector-push! preds (label->idx succ) pred))

        (define (visit-cont cont label)
          (match cont
            (($ $kargs names syms body)
             (for-each (cut add-def! <> label) syms)
             (visit-term body label))
            (($ $kreceive arity k)
             (link-blocks! label k))))

        (define (visit-term term label)
          (match term
            (($ $letk (($ $cont k cont) ...) body)
             ;; Set up recursive environment before visiting cont bodies.
             (for-each/2 (lambda (cont k)
                           (declare-block! k cont label))
                         cont k)
             (for-each/2 visit-cont cont k)
             (visit-term body label))
            (($ $letrec names syms funs body)
             (unless global?
               (error "$letrec should not be present when building a local DFG"))
             (for-each (cut add-def! <> label) syms)
             (for-each (lambda (fun)
                         (match fun
                           (($ $fun free body)
                            (visit-fun body))))
                       funs)
             (visit-term body label))
            (($ $continue k src exp)
             (link-blocks! label k)
             (visit-exp exp label))))

        (define (visit-exp exp label)
          (define (use! sym)
            (add-use! sym label))
          (match exp
            ((or ($ $const) ($ $prim) ($ $closure)) #f)
            (($ $call proc args)
             (use! proc)
             (for-each use! args))
            (($ $callk k proc args)
             (use! proc)
             (for-each use! args))
            (($ $primcall name args)
             (for-each use! args))
            (($ $branch kt exp)
             (link-blocks! label kt)
             (visit-exp exp label))
            (($ $values args)
             (for-each use! args))
            (($ $prompt escape? tag handler)
             (use! tag)
             (link-blocks! label handler))
            (($ $fun free body)
             (when global?
               (visit-fun body)))))

        (define (visit-clause clause kfun)
          (match clause
            (#f #t)
            (($ $cont kclause
                (and clause ($ $kclause arity ($ $cont kbody body)
                               alternate)))
             (declare-block! kclause clause kfun)
             (link-blocks! kfun kclause)

             (declare-block! kbody body kclause)
             (link-blocks! kclause kbody)

             (visit-cont body kbody)
             (visit-clause alternate kfun))))

        (define (visit-fun fun)
          (match fun
            (($ $cont kfun
                (and cont
                     ($ $kfun src meta self ($ $cont ktail tail) clause)))
             (declare-block! kfun cont #f 0)
             (add-def! self kfun)
             (declare-block! ktail tail kfun)
             (visit-clause clause kfun))))

        (visit-fun fun)

        (make-dfg conts preds defs uses scopes scope-levels
                  min-label max-label label-count
                  min-var max-var var-count)))))

(define* (dump-dfg dfg #:optional (port (current-output-port)))
  (let ((min-label (dfg-min-label dfg))
        (min-var (dfg-min-var dfg)))
    (define (label->idx label) (- label min-label))
    (define (idx->label idx) (+ idx min-label))
    (define (var->idx var) (- var min-var))
    (define (idx->var idx) (+ idx min-var))

    (let lp ((label (dfg-min-label dfg)))
      (when (<= label (dfg-max-label dfg))
        (let ((cont (vector-ref (dfg-cont-table dfg) (label->idx label))))
          (when cont
            (unless (equal? (lookup-predecessors label dfg) (list (1- label)))
              (newline port))
            (format port "k~a:~8t" label)
            (match cont
              (($ $kreceive arity k)
               (format port "$kreceive ~a k~a\n" arity k))
              (($ $kfun src meta self tail clause)
               (format port "$kfun ~a ~a v~a\n" src meta self))
              (($ $ktail)
               (format port "$ktail\n"))
              (($ $kclause arity ($ $cont kbody) alternate)
               (format port "$kclause ~a k~a" arity kbody)
               (match alternate
                 (#f #f)
                 (($ $cont kalt) (format port " -> k~a" kalt)))
               (newline port))
              (($ $kargs names vars term)
               (unless (null? vars)
                 (format port "v~a[~a]~:{ v~a[~a]~}: "
                         (car vars) (car names) (map list (cdr vars) (cdr names))))
               (match (find-call term)
                 (($ $continue kf src ($ $branch kt exp))
                  (format port "if ")
                  (match exp
                    (($ $primcall name args)
                     (format port "(~a~{ v~a~})" name args))
                    (($ $values (arg))
                     (format port "v~a" arg)))
                  (format port " k~a k~a\n" kt kf))
                 (($ $continue k src exp)
                  (match exp
                    (($ $const val) (format port "const ~@y" val))
                    (($ $prim name) (format port "prim ~a" name))
                    (($ $fun free ($ $cont kbody)) (format port "fun k~a" kbody))
                    (($ $closure label nfree) (format port "closure k~a (~a free)" label nfree))
                    (($ $call proc args) (format port "call~{ v~a~}" (cons proc args)))
                    (($ $callk k proc args) (format port "callk k~a~{ v~a~}" k (cons proc args)))
                    (($ $primcall name args) (format port "~a~{ v~a~}" name args))
                    (($ $values args) (format port "values~{ v~a~}" args))
                    (($ $prompt escape? tag handler) (format port "prompt ~a v~a k~a" escape? tag handler)))
                  (unless (= k (1+ label))
                    (format port " -> k~a" k))
                  (newline port))))))
          (lp (1+ label)))))))

(define-syntax-rule (with-fresh-name-state-from-dfg dfg body ...)
  (parameterize ((label-counter (1+ (dfg-max-label dfg)))
                 (var-counter (1+ (dfg-max-var dfg))))
    body ...))

(define (lookup-cont label dfg)
  (let ((res (vector-ref (dfg-cont-table dfg) (- label (dfg-min-label dfg)))))
    (unless res
      (error "Unknown continuation!" label))
    res))

(define (lookup-predecessors k dfg)
  (vector-ref (dfg-preds dfg) (- k (dfg-min-label dfg))))

(define (lookup-successors k dfg)
  (let ((cont (vector-ref (dfg-cont-table dfg) (- k (dfg-min-label dfg)))))
    (visit-cont-successors list cont)))

(define (lookup-def var dfg)
  (vector-ref (dfg-defs dfg) (- var (dfg-min-var dfg))))

(define (lookup-uses var dfg)
  (vector-ref (dfg-uses dfg) (- var (dfg-min-var dfg))))

(define (lookup-block-scope k dfg)
  (vector-ref (dfg-scopes dfg) (- k (dfg-min-label dfg))))

(define (lookup-scope-level k dfg)
  (vector-ref (dfg-scope-levels dfg) (- k (dfg-min-label dfg))))

(define (find-defining-term sym dfg)
  (match (lookup-predecessors (lookup-def sym dfg) dfg)
    ((def-exp-k)
     (lookup-cont def-exp-k dfg))
    (else #f)))

(define (find-call term)
  (match term
    (($ $kargs names syms body) (find-call body))
    (($ $letk conts body) (find-call body))
    (($ $letrec names syms funs body) (find-call body))
    (($ $continue) term)))

(define (call-expression call)
  (match call
    (($ $continue k src exp) exp)))

(define (find-expression term)
  (call-expression (find-call term)))

(define (find-defining-expression sym dfg)
  (match (find-defining-term sym dfg)
    (#f #f)
    (($ $kreceive) #f)
    (($ $kclause) #f)
    (term (find-expression term))))

(define (find-constant-value sym dfg)
  (match (find-defining-expression sym dfg)
    (($ $const val)
     (values #t val))
    (else
     (values #f #f))))

(define (constant-needs-allocation? var val dfg)
  (define (immediate-u8? val)
    (and (integer? val) (exact? val) (<= 0 val 255)))

  (define (find-exp term)
    (match term
      (($ $kargs names vars body) (find-exp body))
      (($ $letk conts body) (find-exp body))
      (else term)))

  (or-map
   (lambda (use)
     (match (find-expression (lookup-cont use dfg))
       (($ $call) #f)
       (($ $callk) #f)
       (($ $values) #f)
       (($ $primcall 'free-ref (closure slot))
        (eq? var closure))
       (($ $primcall 'free-set! (closure slot value))
        (or (eq? var closure) (eq? var value)))
       (($ $primcall 'cache-current-module! (mod . _))
        (eq? var mod))
       (($ $primcall 'cached-toplevel-box _)
        #f)
       (($ $primcall 'cached-module-box _)
        #f)
       (($ $primcall 'resolve (name bound?))
        (eq? var name))
       (($ $primcall 'make-vector/immediate (len init))
        (eq? var init))
       (($ $primcall 'vector-ref/immediate (v i))
        (eq? var v))
       (($ $primcall 'vector-set!/immediate (v i x))
        (or (eq? var v) (eq? var x)))
       (($ $primcall 'allocate-struct/immediate (vtable nfields))
        (eq? var vtable))
       (($ $primcall 'struct-ref/immediate (s n))
        (eq? var s))
       (($ $primcall 'struct-set!/immediate (s n x))
        (or (eq? var s) (eq? var x)))
       (($ $primcall 'builtin-ref (idx))
        #f)
       (_ #t)))
   (vector-ref (dfg-uses dfg) (- var (dfg-min-var dfg)))))

(define (continuation-scope-contains? scope-k k dfg)
  (let ((scope-level (lookup-scope-level scope-k dfg)))
    (let lp ((k k))
      (or (eq? scope-k k)
          (and (< scope-level (lookup-scope-level k dfg))
               (lp (lookup-block-scope k dfg)))))))

(define (continuation-bound-in? k use-k dfg)
  (continuation-scope-contains? (lookup-block-scope k dfg) use-k dfg))

(define (variable-free-in? var k dfg)
  (or-map (lambda (use)
            (continuation-scope-contains? k use dfg))
          (lookup-uses var dfg)))

;; A continuation is a control point if it has multiple predecessors, or
;; if its single predecessor does not have a single successor.
(define (control-point? k dfg)
  (match (lookup-predecessors k dfg)
    ((pred)
     (let ((cont (vector-ref (dfg-cont-table dfg)
                             (- pred (dfg-min-label dfg)))))
       (visit-cont-successors (case-lambda
                                (() #t)
                                ((succ0) #f)
                                ((succ1 succ2) #t))
                              cont)))
    (_ #t)))

(define (lookup-bound-syms k dfg)
  (match (lookup-cont k dfg)
    (($ $kargs names syms body)
     syms)))