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gyehoek-hs/doc/liveness.org
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2026-08-28 11:39:37 -06:00

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* example
#+begin_src scheme
(letrec ((fac (λ (n)
(if (zero? n)
1
(* n (fac (- n 1)))))))
(fac 3))
#+end_src
#+begin_src scheme
(λ (ktail0)
(letrec ((fac
(λ (n ktail1)
(zero?
n
(κ (x0)
(if x0
(continue ktail1 1)
(- n 1
(κ (x1)
(fac x1
(κ (x2)
(* n x2 ktail1)))))))))))
(fac 3)))
#+end_src
#+begin_example
n ktail1
| |
| | x0
| | |
| | ^
| |
| | x1
| | |
| | ^
| |
| | x2
| | |
^ ^ ^
#+end_example
#+begin_src scheme
(define $fac-c0
(pop! %x0 0) ; [ x0 $fac-c0 n $fac ktail1 ]
(if %x0 ; [ $fac-c0 n $fac ktail1 ]
;; every variable but `ktail1' is dead so we pop them all.
;; this probably means that `if' should take two continuations
;; rather than two blocks.
(then (pop! %_) ; [ $fac-c0 n $fac ktail1 ]
(pop! %_) ; [ n $fac ktail1 ]
(pop! %_) ; [ $fac ktail1 ]
(push! 1) ; [ ktail1 ]
(return 1)) ; [ 1 ktail1 ]
(else (load! %n 1) ; [ $fac-c0 n $fac ktail1 ]
(prim %x1 (- %n 1)) ; [ $fac-c0 n $fac ktail1 ]
(push! $fac-c1) ; [ $fac-c0 n $fac ktail1 ]
(push! $fac) ; [ $fac-c1 $fac-c0 n $fac ktail1 ]
(push! %x1) ; [ $fac $fac-c1 $fac-c0 n $fac ktail1 ]
(call 1) ; [ x1 $fac $fac-c1 $fac-c0 n $fac ktail1 ]
)))
(define $fac-c1
(pop! %x2) ; [ x2 $fac-c1 $fac-c0 n $fac ktail1 ]
(load! %n 3) ; [ $fac-c1 $fac-c0 n $fac ktail1 ]
(prim %x3 (* %n %x2))
(push! %x3) ; [ $fac-c1 $fac-c0 n $fac ktail1 ]
(return 1) ; [ x3 $fac-c1 $fac-c0 n $fac ktail1 ]
)
(define $fac
(load! %ktail1 2) ; [ n $fac ktail1 ]
(load! %n 0) ; [ n $fac ktail1 ]
(push! $fac-c0) ; [ n $fac ktail1 ]
(push! $zero?) ; [ $fac-c0 n $fac ktail1 ]
(push! %n) ; [ $zero? $fac-c0 n $fac ktail1 ]
(call 1) ; [ n $zero? $fac-c0 n $fac ktail1 ]
)
(define $start
(push! $fac) ; [ $start ktail0 ]
(push! 3) ; [ $fac $start ktail0 ]
(tail-call 1) ; [ 3 $fac $start ktail0 ]
;; ↑ `tail-call' knows how to dispose of the caller's stack frame.
)
#+end_src