deeglaze · October 4, 2012 22:51
diff --git a/compare.rkt b/compare.rkt
 #lang racket/load

 (module tweaks racket
  (require (for-syntax syntax/parse))
  (provide <- for/union for*/union for*/set
           appl fix do join extend get-cont lookup-env lookup P parse
           compile widen push
           join-stores s->c c->s
           (struct-out ev^)
           (struct-out co^)
           (struct-out ap^)
           (struct-out ap-op^)
           (struct-out ans^)

           (struct-out exp)
           (struct-out var)
           (struct-out num)
           (struct-out bln)
           (struct-out lam)
           (struct-out app)
           (struct-out rec)
           (struct-out ife)
           (struct-out 1op)
           (struct-out 2op)
         
           (struct-out clos)
           (struct-out rlos)

           (struct-out ar)
           (struct-out fn)
           (struct-out ifk)
           (struct-out 1opk)
           (struct-out 2opak)
           (struct-out 2opfk)
         
           (struct-out state)
           (struct-out ev)
           (struct-out co)
           (struct-out ap)
           (struct-out ap-op)
           (struct-out ans))

  (define <- (case-lambda))
  (begin-for-syntax
   (define-syntax-class guards
     #:attributes ((guard-forms 1) (gv 1) (gfromv 1)) #:literals (<-)
     (pattern ((~and (~seq (~or [i:id e:expr]
                                [(is:id ...) e0:expr]) ...)
                     (~seq start:expr ...))
               (~optional (~seq [v:id <- (σ:expr fromv:expr)] ...)
                          #:defaults ([(v 1) #'()]
                                      [(σ 1) #'()]
                                      [(fromv 1) #'()])))
              ;; XXX: Switch these for laziness
              ;;#:with (guard-forms ...) #'(start ... [v (get-val σ fromv)] ...)
              ;;#:with (gv ...) #'() #:with (gfromv ...) #'()
              #:with (guard-forms ...) #'(start ...)
              #:with (gv ...) #'(v ...)
              #:with (gfromv ...) #'(fromv ...)
              )))
  (define-syntax (for/get-vals stx)
    (syntax-parse stx
      [(_ form:id targets:expr gs:guards body1:expr body:expr ...)
       (syntax/loc stx
                   (form targets (gs.guard-forms ...)
                         (let* ([gs.gv gs.gfromv] ...)
                           body1 body ...)))]))

  (define-syntax-rule (for/union guards body1 body ...)
    (for/get-vals for/fold ([res (set)]) guards (set-union res (let () body1 body ...))))
  (define-syntax-rule (for*/union guards body1 body ...)
    (for/get-vals for*/fold ([res (set)]) guards (set-union res (let () body1 body ...))))

  (define-syntax-rule (for*/set guards body1 body ...)
    (for/get-vals for*/fold ([res (set)]) guards (set-add res (let () body1 body ...))))

  ;; (X -> Set X) -> (Set X) -> (Set X)
  (define ((appl f) s)
    (for/union ([x (in-set s)]) (f x)))

  ;; (X -> Set X) (Set X) -> (Set X)
  ;; Calculate fixpoint of (appl f).
  (define (fix f s)
    (let loop ((accum (set)) (front s))
      (if (set-empty? front)
          accum
          (let ((new-front ((appl f) front)))
            (loop (set-union accum front)
                  (set-subtract new-front accum))))))

  ;; An Exp is one of:
  ;; (var Lab Exp)
  ;; (num Lab Number)
  ;; (bln Lab Boolean)
  ;; (lam Lab Sym Exp)
  ;; (app Lab Exp Exp)
  ;; (rec Sym Lam)
  ;; (if Lab Exp Exp Exp)
  (struct exp (lab)            #:transparent)
  (struct var exp (name)       #:transparent)
  (struct num exp (val)        #:transparent)
  (struct bln exp (b)          #:transparent)
  (struct lam exp (var exp)    #:transparent)
  (struct app exp (rator rand) #:transparent)
  (struct rec (name fun)       #:transparent)
  (struct ife exp (t c a)      #:transparent)
  (struct 1op exp (o a)        #:transparent)
  (struct 2op exp (o a b)      #:transparent)

  ;; A Val is one of:
  ;; - Number
  ;; - Boolean
  ;; - (clos Lab Sym Exp Env)
  ;; - (rlos Lab Sym Sym Exp Env)
  (struct clos (l x e ρ)   #:transparent)
  (struct rlos (l f x e ρ) #:transparent)

  ;; A Cont is one of:
  ;; - 'mt
  ;; - (ar Exp Env Cont)
  ;; - (fn Val Cont)
  ;; - (ifk Exp Exp Env Cont)
  ;; - (1opk Opr Cont)
  ;; - (2opak Opr Exp Env Cont)
  ;; - (2opfk Opr Val Cont)
  (struct ar (e ρ k)      #:transparent)
  (struct fn (v k)        #:transparent)
  (struct ifk (c a ρ k)   #:transparent)
  (struct 1opk (o k)      #:transparent)
  (struct 2opak (o e ρ k) #:transparent)
  (struct 2opfk (o v k)   #:transparent)

  ;; State
  (struct state (σ)            #:transparent)
  (struct ev state (e ρ k)     #:transparent)
  (struct co state (k v)       #:transparent)
  (struct ap state (f a k)     #:transparent)
  (struct ap-op state (o vs k) #:transparent)
  (struct ans state (v)        #:transparent)

  (define (lookup ρ σ x)
    (hash-ref σ (hash-ref ρ x)))
  (define (lookup-env ρ x)
    (hash-ref ρ x))
  (define (get-cont σ l)
    (hash-ref σ l))
  (define (extend ρ x v)
    (hash-set ρ x v))
  (define (join σ a s)
    (hash-set σ a
              (set-union s (hash-ref σ a (set)))))

  (define-syntax-rule (do guards e)
    (for*/set guards e))
 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
  ;; Widening State to State^

  ;; State^ = (cons (Set Conf) Store)

  ;; Conf
  (struct ev^ (e ρ k)     #:transparent)
  (struct co^ (k v)       #:transparent)
  (struct ap^ (f a k)     #:transparent)
  (struct ap-op^ (o vs k) #:transparent)
  (struct ans^ (v)        #:transparent)

  ;; The following "functions" are called in hot loops,
  ;; so make them macros instead to inline them across the module boundary.
  ;; Conf Store -> State
  (define-syntax-rule (c->s c σ)
    (match c
      [(ev^ e ρ k) (ev σ e ρ k)]
      [(co^ k v)   (co σ k v)]
      [(ap^ f a k) (ap σ f a k)]
      [(ap-op^ o vs k) (ap-op σ o vs k)]
      [(ans^ v) (ans σ v)]))

  ;; State -> Conf
  (define-syntax-rule (s->c s)
    (match s
      [(ev _ e ρ k) (ev^ e ρ k)]
      [(co _ k v)   (co^ k v)]
      [(ap _ f a k) (ap^ f a k)]
      [(ap-op _ o vs k) (ap-op^ o vs k)]
      [(ans _ v) (ans^ v)]))
  
  ;; Set State -> Store
  (define-syntax-rule (join-stores ss)
    (letrec ([join-store (λ (σ1 σ2)
                            (for/fold ([σ σ1])
                                ([k×v (in-hash-pairs σ2)])
                              (hash-set σ (car k×v)
                                        (set-union (cdr k×v)
                                                   (hash-ref σ (car k×v) (set))))))])
      (for/fold ([σ (hash)])
          ([s ss])
        (join-store σ (state-σ s)))))

  (define-syntax-rule (widen b)
    (cond [(number? b) 'number]
          [else (error "Unknown base value" b)]))

  (define-syntax-rule (push s)
    (match s
      [(ev σ e ρ k)
       (define a (exp-lab e))
       (values (join σ a (set k))
               a)]))
  
  (define (parse sexp)
    (match sexp
      [`(let* () ,e) (parse e)]
      [`(let* ((,x ,e) . ,r) ,b)
       (app (gensym)
            (lam (gensym) x (parse `(let* ,r ,b)))
            (parse e))]
      [`(lambda (,x) ,e)
       (lam (gensym) x (parse e))]
      [`(if ,e0 ,e1 ,e2)
       (ife (gensym) (parse e0) (parse e1) (parse e2))]
      [`(rec ,f ,e)
       (rec f (parse e))]
      [`(sub1 ,e)
       (1op (gensym) 'sub1 (parse e))]
      [`(add1 ,e)
       (1op (gensym) 'add1 (parse e))]
      [`(zero? ,e)
       (1op (gensym) 'zero? (parse e))]
      [`(* ,e0 ,e1)
       (2op (gensym) '* (parse e0) (parse e1))]
      [`(,e0 ,e1)
       (app (gensym)
            (parse e0)
            (parse e1))]
      [(? boolean? b) (bln (gensym) b)]
      [(? number? n) (num (gensym) n)]
      [(? symbol? s) (var (gensym) s)]))

  (define (compile var-case e)
    (let compile ([e e])
      (match e
        [(var l x) (var-case x)]
        [(num l n) (λ (σ ρ k) (set (co σ k n)))]
        [(bln l b) (λ (σ ρ k) (set (co σ k b)))]
        [(lam l x e)
         (define c (compile e))
         (λ (σ ρ k) (set (co σ k (clos l x c ρ))))]
        [(rec f (lam l x e))
         (define c (compile e))
         (λ (σ ρ k) (set (co σ k (rlos l f x c ρ))))]
        [(app l e0 e1)
         (define c0 (compile e0))
         (define c1 (compile e1))
         (λ (σ ρ k)
            ;; "ev" simulated for push's sake.
            (define-values (σ* a) (push (ev σ (app l e0 e1) ρ k)))
            (c0 σ* ρ (ar c1 ρ a)))]
        [(ife l e0 e1 e2)
         (define c0 (compile e0))
         (define c1 (compile e1))
         (define c2 (compile e2))
         (λ (σ ρ k)
            (define-values (σ* a) (push (ev σ (ife l e0 e1 e2) ρ k)))
            (c0 σ* ρ (ifk c1 c2 ρ a)))]
        [(1op l o e)
         (define c (compile e))
         (λ (σ ρ k)
            (define-values (σ* a) (push (ev σ (1op l o e) ρ k)))
            (c σ* ρ (1opk o a)))]
        [(2op l o e0 e1)
         (define c0 (compile e0))
         (define c1 (compile e1))
         (λ (σ ρ k)
            (define-values (σ* a) (push (ev σ (2op l o e0 e1) ρ k)))
            (c0 σ* ρ (2opak o c1 ρ a)))])))

  (define P
    ;; Ian's example, curried, alpha renamed and
    ;; let* in place of define where possible.
    '(let* ((plus (lambda (p1)
                    (lambda (p2)
                      (lambda (pf)
                        (lambda (x) ((p1 pf) ((p2 pf) x)))))))
            (mult (lambda (m1)
                    (lambda (m2)
                      (lambda (mf) (m2 (m1 mf))))))
            (pred (lambda (n)
                    (lambda (rf)
                      (lambda (rx)
                        (((n (lambda (g) (lambda (h) (h (g rf)))))
                          (lambda (ignored) rx))
                         (lambda (id) id))))))
            (sub (lambda (s1)
                   (lambda (s2)
                     ((s2 pred) s1))))

            (church0 (lambda (f0) (lambda (x0) x0)))
            (church1 (lambda (f1) (lambda (x1) (f1 x1))))
            (church2 (lambda (f2) (lambda (x2) (f2 (f2 x2)))))
            (church3 (lambda (f3) (lambda (x3) (f3 (f3 (f3 x3))))))
            (church0? (lambda (z) ((z (lambda (zx) #f)) #t)))
            (c->n (lambda (cn) ((cn (lambda (u) (add1 u))) 0)))
            (church=? (rec c=?
                           (lambda (e1)
                             (lambda (e2)
                               (if (church0? e1)
                                   (church0? e2)
                                   (if (church0? e2)
                                       #f
                                       ((c=? ((sub e1) church1)) ((sub e2) church1)))))))))
       ;; multiplication distributes over addition
       ((church=? ((mult church2) ((plus church1) church3)))
        ((plus ((mult church2) church1)) ((mult church2) church3))))))

 (module fast racket
  (require 'tweaks)

  ;; Expr -> (Store Env Cont -> State)
  (define (fcompile e)
    (compile (λ (x)
                (λ (σ ρ k)
                   (do ([v (lookup ρ σ x)])
                       (co σ k v))))
             e))

  ;; "Bytecode" interpreter
  ;; State -> State
  (define (step-compiled state)
    (match state
      [(co σ k v)
       (match k
         ['mt (set (ans σ v))]
         [(ar c ρ l) (c σ ρ (fn v l))]
         [(fn f l) (do ([k (get-cont σ l)])
                       (ap σ f v k))]
         [(ifk c a ρ l)
          (for/union ([k (get-cont σ l)])
            ((if v c a) σ ρ k))]
         [(1opk o l)
          (do ([k (get-cont σ l)])
              (ap-op σ o (list v) k))]
         [(2opak o c ρ l)
          (c σ ρ (2opfk o v l))]
         [(2opfk o u l)
          (do ([k (get-cont σ l)])
              (ap-op σ o (list v u) k))])]

      [(ap σ fun a k)
       (match fun
         [(clos l x c ρ)
          (define-values (ρ* σ*) (bind state))
          (c σ* ρ* k)]
         [(rlos l f x c ρ)
          (define-values (ρ* σ*) (bind state))
          (c σ* ρ* k)]
         [_ (set state)])]

      [(ap-op σ o vs k)
       (match* (o vs)
         [('zero? (list (? number? n))) (set (co σ k (zero? n)))]
         [('sub1 (list (? number? n))) (set (co σ k (widen (sub1 n))))]
         [('add1 (list (? number? n))) (set (co σ k (widen (add1 n))))]
         [('zero? (list 'number))
          (set (co σ k #t)
               (co σ k #f))]
         [('sub1 (list 'number)) (set (co σ k 'number))]
         [('* (list (? number? n) (? number? m)))
          (set (co σ k (widen (* m n))))]
         [('* (list (? number? n) 'number))
          (set (co σ k 'number))]
         [('* (list 'number 'number))
          (set (co σ k 'number))]
         [(_ _) (set state)])]

      [_ (set state)]))

  ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
  ;; 0CFA-style Abstract semantics

  (define (bind s)
    (match s
      [(ap σ (clos l x e ρ) v k)
       (values (extend ρ x x)
               (extend σ x (set v)))]
      [(ap σ (rlos l f x e ρ) v k)
       (values (extend (extend ρ x x) f f)
               (join (join σ x (set v)) f (set (rlos l f x e ρ))))]))

 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

  ;; Exp -> Set Val
  ;; 0CFA without store widening
  (define (aval e)
    (for/set ([s (fix step-compiled (inj e))]
              #:when (ans? s))
      (ans-v s)))

  ;; Exp -> Set Vlal
  ;; 0CFA with store widening
  (define (aval^ e)
    (for/fold ([vs (set)])
        ([s (fix wide-step (inj-wide e))])
      (set-union vs
                 (match s
                   [(cons cs σ)
                    (for/set ([c cs]
                              #:when (ans^? c))
                      (ans^-v c))]))))

  ;; Exp -> Set State
  (define (inj e)
    ((fcompile e) (hash) (hash) 'mt))

  ;; Exp -> Set State^
  (define (inj-wide e)
    (for/first ([s (inj e)])
      (set (cons (set (s->c s)) (state-σ s)))))

  ;; State^ -> { State^ }
  (define (wide-step state)
    (match state
      [(cons cs σ)
       (define ss (for/set ([c cs]) (c->s c σ)))
       (define ss* ((appl step-compiled) ss))
       (set (cons (for/set ([s ss*]) (s->c s))
                  (join-stores ss*)))]))

  (time (aval^ (parse P))))

 (module slow racket
  (require 'tweaks)
  ;; 0CFA in the AAM style on some hairy Church numeral churning

  (struct addr (a) #:transparent)
  ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
  ;; Lazy/non-lazy
  ;; XXX: Switch these for laziness
  #;(define-syntax-rule (deref ρ σ k x) (set (co σ k (addr (lookup-env ρ x)))))

  (define-syntax-rule (deref ρ σ k x)
    (do ([v (lookup ρ σ x)])
        (co σ k v)))

  ;; Store (Addr + Val) -> Set Val
  ;; XXX: Switch these for laziness
  #;(define-syntax-rule (get-val σ v) (match v [(addr loc) (hash-ref σ loc (λ () (error "~a ~a" loc σ)))] [_ (set v)]))
  (define-syntax-rule (get-val σ v) (set v))

  (define (scompile e)
    (compile (λ (x)
                (λ (σ ρ k) (deref ρ σ k x)))
             e))

  ;; State -> Set State
  (define (step-compiled state)
    (match state
      [(co σ k v)
       (match k
         ['mt (do ([v <- (σ v)])
                  (ans σ v))]
         [(ar c ρ l) (c σ ρ (fn v l))]
         [(fn f l)
          (do ([k (get-cont σ l)]
               [f <- (σ f)])
              (ap σ f v k))]
         [(ifk c a ρ l)
          (for*/union ([k (get-cont σ l)]
                       [v <- (σ v)])
            ((if v c a) σ ρ k))]
         [(1opk o l)
          (do ([k (get-cont σ l)]
               [v <- (σ v)])
              (ap-op σ o (list v) k))]
         [(2opak o c ρ l)
          (c σ ρ (2opfk o v l))]
         [(2opfk o u l)
          (do ([k (get-cont σ l)]
               [v <- (σ v)]
               [u <- (σ u)])
              (ap-op σ o (list v u) k))])]

      [(ap σ fun a k)
       (match fun
         [(clos l x c ρ) 
          (define-values (ρ* σ*) (bind state))
          (c σ* ρ* k)]
         [(rlos l f x c ρ)
          (define-values (ρ* σ*) (bind state))
          (c σ* ρ* k)]
         ;; stuck
         [_ (set state)])]

      [(ap-op σ o vs k)
       (match* (o vs)
         [('zero? (list (? number? n))) (set (co σ k (zero? n)))]
         [('sub1 (list (? number? n)))  (set (co σ k (widen (sub1 n))))]
         [('add1 (list (? number? n)))  (set (co σ k (widen (add1 n))))]
         [('zero? (list 'number))
          (set (co σ k #t)
               (co σ k #f))]
         [('sub1 (list 'number)) (set (co σ k 'number))]
         [('* (list (? number? n) (? number? m)))
          (set (co σ k (widen (* m n))))]
         [('* (list (? number? n) 'number))
          (set (co σ k 'number))]
         [('* (list 'number 'number))
          (set (co σ k 'number))]
         [(_ _) (set state)])]
      ;; stuck or an answer
      [_ (set state)]))

 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
  ;; 0CFA-style Abstract semantics

  (define (bind s)
    (match s
      [(ap σ (clos l x e ρ) v k)
       (values (extend ρ x x)
               (join σ x (get-val σ v)))]
      [(ap σ (rlos l f x e ρ) v k)
       (values (extend (extend ρ x x) f f)
               (join (join σ x (get-val σ v)) f (set (rlos l f x e ρ))))]))

 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

  ;; Exp -> Set Vlal
  ;; 0CFA with store widening
  (define (aval^-compiled e)
    (for/union ([s (fix wide-step-compiled (inj-wide-compiled e))])
      (match s
        [(cons cs σ)
         (for/set ([c cs]
                   #:when (ans^? c))
           (ans^-v c))])))

  ;; Exp -> Set State
  (define (inj-compiled e)
    ((scompile e) (hash) (hash) 'mt))

  ;; Exp -> Set State^
  (define (inj-wide-compiled e)
    (for/first ([s (inj-compiled e)])
      (set (cons (set (s->c s))
                 (state-σ s)))))

  ;; Exp -> Set State^
  (define (inj-wide e)
    (set (cons (set (ev^ e (hash) 'mt)) (hash))))

  ;; State^ -> { State^ }
  (define (wide-step-compiled state)
    (match state
      [(cons cs σ)
       (define ss (for/set ([c cs]) (c->s c σ)))
       (define ss* ((appl step-compiled) ss))
       (set (cons (for/set ([s ss*]) (s->c s))
                  (join-stores ss*)))]))

  (time (aval^-compiled (parse P))))
 (require 'fast 'slow)
	#lang racket/load

	(module tweaks racket
	(require (for-syntax syntax/parse))
	(provide <- for/union for/union for/set
	appl fix do join extend get-cont lookup-env lookup P parse
	compile widen push
	join-stores s->c c->s
	(struct-out ev^)
	(struct-out co^)
	(struct-out ap^)
	(struct-out ap-op^)
	(struct-out ans^)

	(struct-out exp)
	(struct-out var)
	(struct-out num)
	(struct-out bln)
	(struct-out lam)
	(struct-out app)
	(struct-out rec)
	(struct-out ife)
	(struct-out 1op)
	(struct-out 2op)

	(struct-out clos)
	(struct-out rlos)

	(struct-out ar)
	(struct-out fn)
	(struct-out ifk)
	(struct-out 1opk)
	(struct-out 2opak)
	(struct-out 2opfk)

	(struct-out state)
	(struct-out ev)
	(struct-out co)
	(struct-out ap)
	(struct-out ap-op)
	(struct-out ans))

	(define <- (case-lambda))
	(begin-for-syntax
	(define-syntax-class guards
	#:attributes ((guard-forms 1) (gv 1) (gfromv 1)) #:literals (<-)
	(pattern ((~and (~seq (~or [i:id e:expr]
	[(is:id ...) e0:expr]) ...)
	(~seq start:expr ...))
	(~optional (~seq [v:id <- (σ:expr fromv:expr)] ...)
	#:defaults ([(v 1) #'()]
	[(σ 1) #'()]
	[(fromv 1) #'()])))
	;; XXX: Switch these for laziness
	;;#:with (guard-forms ...) #'(start ... [v (get-val σ fromv)] ...)
	;;#:with (gv ...) #'() #:with (gfromv ...) #'()
	#:with (guard-forms ...) #'(start ...)
	#:with (gv ...) #'(v ...)
	#:with (gfromv ...) #'(fromv ...)
	)))
	(define-syntax (for/get-vals stx)
	(syntax-parse stx
	[(_ form:id targets:expr gs:guards body1:expr body:expr ...)
	(syntax/loc stx
	(form targets (gs.guard-forms ...)
	(let* ([gs.gv gs.gfromv] ...)
	body1 body ...)))]))

	(define-syntax-rule (for/union guards body1 body ...)
	(for/get-vals for/fold ([res (set)]) guards (set-union res (let () body1 body ...))))
	(define-syntax-rule (for*/union guards body1 body ...)
	(for/get-vals for*/fold ([res (set)]) guards (set-union res (let () body1 body ...))))

	(define-syntax-rule (for*/set guards body1 body ...)
	(for/get-vals for*/fold ([res (set)]) guards (set-add res (let () body1 body ...))))

	;; (X -> Set X) -> (Set X) -> (Set X)
	(define ((appl f) s)
	(for/union ([x (in-set s)]) (f x)))

	;; (X -> Set X) (Set X) -> (Set X)
	;; Calculate fixpoint of (appl f).
	(define (fix f s)
	(let loop ((accum (set)) (front s))
	(if (set-empty? front)
	accum
	(let ((new-front ((appl f) front)))
	(loop (set-union accum front)
	(set-subtract new-front accum))))))

	;; An Exp is one of:
	;; (var Lab Exp)
	;; (num Lab Number)
	;; (bln Lab Boolean)
	;; (lam Lab Sym Exp)
	;; (app Lab Exp Exp)
	;; (rec Sym Lam)
	;; (if Lab Exp Exp Exp)
	(struct exp (lab) #:transparent)
	(struct var exp (name) #:transparent)
	(struct num exp (val) #:transparent)
	(struct bln exp (b) #:transparent)
	(struct lam exp (var exp) #:transparent)
	(struct app exp (rator rand) #:transparent)
	(struct rec (name fun) #:transparent)
	(struct ife exp (t c a) #:transparent)
	(struct 1op exp (o a) #:transparent)
	(struct 2op exp (o a b) #:transparent)

	;; A Val is one of:
	;; - Number
	;; - Boolean
	;; - (clos Lab Sym Exp Env)
	;; - (rlos Lab Sym Sym Exp Env)
	(struct clos (l x e ρ) #:transparent)
	(struct rlos (l f x e ρ) #:transparent)

	;; A Cont is one of:
	;; - 'mt
	;; - (ar Exp Env Cont)
	;; - (fn Val Cont)
	;; - (ifk Exp Exp Env Cont)
	;; - (1opk Opr Cont)
	;; - (2opak Opr Exp Env Cont)
	;; - (2opfk Opr Val Cont)
	(struct ar (e ρ k) #:transparent)
	(struct fn (v k) #:transparent)
	(struct ifk (c a ρ k) #:transparent)
	(struct 1opk (o k) #:transparent)
	(struct 2opak (o e ρ k) #:transparent)
	(struct 2opfk (o v k) #:transparent)

	;; State
	(struct state (σ) #:transparent)
	(struct ev state (e ρ k) #:transparent)
	(struct co state (k v) #:transparent)
	(struct ap state (f a k) #:transparent)
	(struct ap-op state (o vs k) #:transparent)
	(struct ans state (v) #:transparent)

	(define (lookup ρ σ x)
	(hash-ref σ (hash-ref ρ x)))
	(define (lookup-env ρ x)
	(hash-ref ρ x))
	(define (get-cont σ l)
	(hash-ref σ l))
	(define (extend ρ x v)
	(hash-set ρ x v))
	(define (join σ a s)
	(hash-set σ a
	(set-union s (hash-ref σ a (set)))))

	(define-syntax-rule (do guards e)
	(for*/set guards e))
	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	;; Widening State to State^

	;; State^ = (cons (Set Conf) Store)

	;; Conf
	(struct ev^ (e ρ k) #:transparent)
	(struct co^ (k v) #:transparent)
	(struct ap^ (f a k) #:transparent)
	(struct ap-op^ (o vs k) #:transparent)
	(struct ans^ (v) #:transparent)

	;; The following "functions" are called in hot loops,
	;; so make them macros instead to inline them across the module boundary.
	;; Conf Store -> State
	(define-syntax-rule (c->s c σ)
	(match c
	[(ev^ e ρ k) (ev σ e ρ k)]
	[(co^ k v) (co σ k v)]
	[(ap^ f a k) (ap σ f a k)]
	[(ap-op^ o vs k) (ap-op σ o vs k)]
	[(ans^ v) (ans σ v)]))

	;; State -> Conf
	(define-syntax-rule (s->c s)
	(match s
	[(ev _ e ρ k) (ev^ e ρ k)]
	[(co _ k v) (co^ k v)]
	[(ap _ f a k) (ap^ f a k)]
	[(ap-op _ o vs k) (ap-op^ o vs k)]
	[(ans _ v) (ans^ v)]))

	;; Set State -> Store
	(define-syntax-rule (join-stores ss)
	(letrec ([join-store (λ (σ1 σ2)
	(for/fold ([σ σ1])
	([k×v (in-hash-pairs σ2)])
	(hash-set σ (car k×v)
	(set-union (cdr k×v)
	(hash-ref σ (car k×v) (set))))))])
	(for/fold ([σ (hash)])
	([s ss])
	(join-store σ (state-σ s)))))

	(define-syntax-rule (widen b)
	(cond [(number? b) 'number]
	[else (error "Unknown base value" b)]))

	(define-syntax-rule (push s)
	(match s
	[(ev σ e ρ k)
	(define a (exp-lab e))
	(values (join σ a (set k))
	a)]))

	(define (parse sexp)
	(match sexp
	[`(let* () ,e) (parse e)]
	[`(let* ((,x ,e) . ,r) ,b)
	(app (gensym)
	(lam (gensym) x (parse `(let* ,r ,b)))
	(parse e))]
	[`(lambda (,x) ,e)
	(lam (gensym) x (parse e))]
	[`(if ,e0 ,e1 ,e2)
	(ife (gensym) (parse e0) (parse e1) (parse e2))]
	[`(rec ,f ,e)
	(rec f (parse e))]
	[`(sub1 ,e)
	(1op (gensym) 'sub1 (parse e))]
	[`(add1 ,e)
	(1op (gensym) 'add1 (parse e))]
	[`(zero? ,e)
	(1op (gensym) 'zero? (parse e))]
	[`(* ,e0 ,e1)
	(2op (gensym) '* (parse e0) (parse e1))]
	[`(,e0 ,e1)
	(app (gensym)
	(parse e0)
	(parse e1))]
	[(? boolean? b) (bln (gensym) b)]
	[(? number? n) (num (gensym) n)]
	[(? symbol? s) (var (gensym) s)]))

	(define (compile var-case e)
	(let compile ([e e])
	(match e
	[(var l x) (var-case x)]
	[(num l n) (λ (σ ρ k) (set (co σ k n)))]
	[(bln l b) (λ (σ ρ k) (set (co σ k b)))]
	[(lam l x e)
	(define c (compile e))
	(λ (σ ρ k) (set (co σ k (clos l x c ρ))))]
	[(rec f (lam l x e))
	(define c (compile e))
	(λ (σ ρ k) (set (co σ k (rlos l f x c ρ))))]
	[(app l e0 e1)
	(define c0 (compile e0))
	(define c1 (compile e1))
	(λ (σ ρ k)
	;; "ev" simulated for push's sake.
	(define-values (σ* a) (push (ev σ (app l e0 e1) ρ k)))
	(c0 σ* ρ (ar c1 ρ a)))]
	[(ife l e0 e1 e2)
	(define c0 (compile e0))
	(define c1 (compile e1))
	(define c2 (compile e2))
	(λ (σ ρ k)
	(define-values (σ* a) (push (ev σ (ife l e0 e1 e2) ρ k)))
	(c0 σ* ρ (ifk c1 c2 ρ a)))]
	[(1op l o e)
	(define c (compile e))
	(λ (σ ρ k)
	(define-values (σ* a) (push (ev σ (1op l o e) ρ k)))
	(c σ* ρ (1opk o a)))]
	[(2op l o e0 e1)
	(define c0 (compile e0))
	(define c1 (compile e1))
	(λ (σ ρ k)
	(define-values (σ* a) (push (ev σ (2op l o e0 e1) ρ k)))
	(c0 σ* ρ (2opak o c1 ρ a)))])))

	(define P
	;; Ian's example, curried, alpha renamed and
	;; let* in place of define where possible.
	'(let* ((plus (lambda (p1)
	(lambda (p2)
	(lambda (pf)
	(lambda (x) ((p1 pf) ((p2 pf) x)))))))
	(mult (lambda (m1)
	(lambda (m2)
	(lambda (mf) (m2 (m1 mf))))))
	(pred (lambda (n)
	(lambda (rf)
	(lambda (rx)
	(((n (lambda (g) (lambda (h) (h (g rf)))))
	(lambda (ignored) rx))
	(lambda (id) id))))))
	(sub (lambda (s1)
	(lambda (s2)
	((s2 pred) s1))))

	(church0 (lambda (f0) (lambda (x0) x0)))
	(church1 (lambda (f1) (lambda (x1) (f1 x1))))
	(church2 (lambda (f2) (lambda (x2) (f2 (f2 x2)))))
	(church3 (lambda (f3) (lambda (x3) (f3 (f3 (f3 x3))))))
	(church0? (lambda (z) ((z (lambda (zx) #f)) #t)))
	(c->n (lambda (cn) ((cn (lambda (u) (add1 u))) 0)))
	(church=? (rec c=?
	(lambda (e1)
	(lambda (e2)
	(if (church0? e1)
	(church0? e2)
	(if (church0? e2)
	#f
	((c=? ((sub e1) church1)) ((sub e2) church1)))))))))
	;; multiplication distributes over addition
	((church=? ((mult church2) ((plus church1) church3)))
	((plus ((mult church2) church1)) ((mult church2) church3))))))

	(module fast racket
	(require 'tweaks)

	;; Expr -> (Store Env Cont -> State)
	(define (fcompile e)
	(compile (λ (x)
	(λ (σ ρ k)
	(do ([v (lookup ρ σ x)])
	(co σ k v))))
	e))

	;; "Bytecode" interpreter
	;; State -> State
	(define (step-compiled state)
	(match state
	[(co σ k v)
	(match k
	['mt (set (ans σ v))]
	[(ar c ρ l) (c σ ρ (fn v l))]
	[(fn f l) (do ([k (get-cont σ l)])
	(ap σ f v k))]
	[(ifk c a ρ l)
	(for/union ([k (get-cont σ l)])
	((if v c a) σ ρ k))]
	[(1opk o l)
	(do ([k (get-cont σ l)])
	(ap-op σ o (list v) k))]
	[(2opak o c ρ l)
	(c σ ρ (2opfk o v l))]
	[(2opfk o u l)
	(do ([k (get-cont σ l)])
	(ap-op σ o (list v u) k))])]

	[(ap σ fun a k)
	(match fun
	[(clos l x c ρ)
	(define-values (ρ* σ*) (bind state))
	(c σ* ρ* k)]
	[(rlos l f x c ρ)
	(define-values (ρ* σ*) (bind state))
	(c σ* ρ* k)]
	[_ (set state)])]

	[(ap-op σ o vs k)
	(match* (o vs)
	[('zero? (list (? number? n))) (set (co σ k (zero? n)))]
	[('sub1 (list (? number? n))) (set (co σ k (widen (sub1 n))))]
	[('add1 (list (? number? n))) (set (co σ k (widen (add1 n))))]
	[('zero? (list 'number))
	(set (co σ k #t)
	(co σ k #f))]
	[('sub1 (list 'number)) (set (co σ k 'number))]
	[('* (list (? number? n) (? number? m)))
	(set (co σ k (widen (* m n))))]
	[('* (list (? number? n) 'number))
	(set (co σ k 'number))]
	[('* (list 'number 'number))
	(set (co σ k 'number))]
	[(_ _) (set state)])]

	[_ (set state)]))

	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	;; 0CFA-style Abstract semantics

	(define (bind s)
	(match s
	[(ap σ (clos l x e ρ) v k)
	(values (extend ρ x x)
	(extend σ x (set v)))]
	[(ap σ (rlos l f x e ρ) v k)
	(values (extend (extend ρ x x) f f)
	(join (join σ x (set v)) f (set (rlos l f x e ρ))))]))

	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

	;; Exp -> Set Val
	;; 0CFA without store widening
	(define (aval e)
	(for/set ([s (fix step-compiled (inj e))]
	#:when (ans? s))
	(ans-v s)))

	;; Exp -> Set Vlal
	;; 0CFA with store widening
	(define (aval^ e)
	(for/fold ([vs (set)])
	([s (fix wide-step (inj-wide e))])
	(set-union vs
	(match s
	[(cons cs σ)
	(for/set ([c cs]
	#:when (ans^? c))
	(ans^-v c))]))))

	;; Exp -> Set State
	(define (inj e)
	((fcompile e) (hash) (hash) 'mt))

	;; Exp -> Set State^
	(define (inj-wide e)
	(for/first ([s (inj e)])
	(set (cons (set (s->c s)) (state-σ s)))))

	;; State^ -> { State^ }
	(define (wide-step state)
	(match state
	[(cons cs σ)
	(define ss (for/set ([c cs]) (c->s c σ)))
	(define ss* ((appl step-compiled) ss))
	(set (cons (for/set ([s ss*]) (s->c s))
	(join-stores ss*)))]))

	(time (aval^ (parse P))))

	(module slow racket
	(require 'tweaks)
	;; 0CFA in the AAM style on some hairy Church numeral churning

	(struct addr (a) #:transparent)
	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	;; Lazy/non-lazy
	;; XXX: Switch these for laziness
	#;(define-syntax-rule (deref ρ σ k x) (set (co σ k (addr (lookup-env ρ x)))))

	(define-syntax-rule (deref ρ σ k x)
	(do ([v (lookup ρ σ x)])
	(co σ k v)))

	;; Store (Addr + Val) -> Set Val
	;; XXX: Switch these for laziness
	#;(define-syntax-rule (get-val σ v) (match v [(addr loc) (hash-ref σ loc (λ () (error "~a ~a" loc σ)))] [_ (set v)]))
	(define-syntax-rule (get-val σ v) (set v))

	(define (scompile e)
	(compile (λ (x)
	(λ (σ ρ k) (deref ρ σ k x)))
	e))

	;; State -> Set State
	(define (step-compiled state)
	(match state
	[(co σ k v)
	(match k
	['mt (do ([v <- (σ v)])
	(ans σ v))]
	[(ar c ρ l) (c σ ρ (fn v l))]
	[(fn f l)
	(do ([k (get-cont σ l)]
	[f <- (σ f)])
	(ap σ f v k))]
	[(ifk c a ρ l)
	(for*/union ([k (get-cont σ l)]
	[v <- (σ v)])
	((if v c a) σ ρ k))]
	[(1opk o l)
	(do ([k (get-cont σ l)]
	[v <- (σ v)])
	(ap-op σ o (list v) k))]
	[(2opak o c ρ l)
	(c σ ρ (2opfk o v l))]
	[(2opfk o u l)
	(do ([k (get-cont σ l)]
	[v <- (σ v)]
	[u <- (σ u)])
	(ap-op σ o (list v u) k))])]

	[(ap σ fun a k)
	(match fun
	[(clos l x c ρ)
	(define-values (ρ* σ*) (bind state))
	(c σ* ρ* k)]
	[(rlos l f x c ρ)
	(define-values (ρ* σ*) (bind state))
	(c σ* ρ* k)]
	;; stuck
	[_ (set state)])]

	[(ap-op σ o vs k)
	(match* (o vs)
	[('zero? (list (? number? n))) (set (co σ k (zero? n)))]
	[('sub1 (list (? number? n))) (set (co σ k (widen (sub1 n))))]
	[('add1 (list (? number? n))) (set (co σ k (widen (add1 n))))]
	[('zero? (list 'number))
	(set (co σ k #t)
	(co σ k #f))]
	[('sub1 (list 'number)) (set (co σ k 'number))]
	[('* (list (? number? n) (? number? m)))
	(set (co σ k (widen (* m n))))]
	[('* (list (? number? n) 'number))
	(set (co σ k 'number))]
	[('* (list 'number 'number))
	(set (co σ k 'number))]
	[(_ _) (set state)])]
	;; stuck or an answer
	[_ (set state)]))

	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	;; 0CFA-style Abstract semantics

	(define (bind s)
	(match s
	[(ap σ (clos l x e ρ) v k)
	(values (extend ρ x x)
	(join σ x (get-val σ v)))]
	[(ap σ (rlos l f x e ρ) v k)
	(values (extend (extend ρ x x) f f)
	(join (join σ x (get-val σ v)) f (set (rlos l f x e ρ))))]))

	;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

	;; Exp -> Set Vlal
	;; 0CFA with store widening
	(define (aval^-compiled e)
	(for/union ([s (fix wide-step-compiled (inj-wide-compiled e))])
	(match s
	[(cons cs σ)
	(for/set ([c cs]
	#:when (ans^? c))
	(ans^-v c))])))

	;; Exp -> Set State
	(define (inj-compiled e)
	((scompile e) (hash) (hash) 'mt))

	;; Exp -> Set State^
	(define (inj-wide-compiled e)
	(for/first ([s (inj-compiled e)])
	(set (cons (set (s->c s))
	(state-σ s)))))

	;; Exp -> Set State^
	(define (inj-wide e)
	(set (cons (set (ev^ e (hash) 'mt)) (hash))))

	;; State^ -> { State^ }
	(define (wide-step-compiled state)
	(match state
	[(cons cs σ)
	(define ss (for/set ([c cs]) (c->s c σ)))
	(define ss* ((appl step-compiled) ss))
	(set (cons (for/set ([s ss*]) (s->c s))
	(join-stores ss*)))]))

	(time (aval^-compiled (parse P))))
	(require 'fast 'slow)