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wip: abstract stack/continuation machine
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msyds
2026-08-17 22:31:45 -06:00
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#+title: ABI
largely based on the Guile Hoot's [[https://codeberg.org/spritely/hoot/src/branch/main/design/ABI.md][ABI]].
* calling convention
** non-tail calls
- set the global variable ~$current-closure~ to the callee's closure.
- load arguments into globals ~$arg0~, ~$arg1~, ~$arg2~, …
- push return continuation onto ~$cont-stack~
* scratchpad
#+begin_src scheme
;; Scheme source
(define (silly f g h x)
(f (h x) (g x)))
;; continuation-passing style
(define (silly f g h x ktail)
(h x (κ (x0)
(g x (κ (x1)
(f x0 x1 ktail))))))
;; with explicit stacks
(define (silly)
(define f (pop!))
(define g (pop!))
(define h (pop!))
(define x (pop!))
(define ktail (pop-cont!))
(push-cont! (κ (x0)
(define x* (pop!))
(define g* (pop!))
(push-cont! (κ (x1)
(define f* (pop!))
(define x0* (pop!))
(push-cont! ktail)
(push! x0*)
(push! x1)
(call! f)))
(push! x*)
(call! g)))
(push! x)
(call! h))
#+end_src
** fac
*** Scheme source
#+begin_src scheme
(define fac
(λ (n)
(if (zero? n)
1
(* n (fac (- n 1))))))
(fac 3)
#+end_src
*** CPS
#+begin_src scheme
(define fac
(λ (n ktail)
(zero? n (κ (x0)
(if x0
1
(- n 1
(κ (x1)
(fac x1
(κ (x2)
(* n x2 ktail))))))))))
(fac 3 halt)
#+end_src
*** tailified
#+begin_src scheme
(define (fac-k1)
(define n (pop!))
(define x2 (pop!))
(define x3 (* n x2))
(define ktail (pop-cont!))
(push! x3)
(call! ktail))
(define (fac-k0)
(define x0 (pop!))
(define n (pop!))
(if x0
(begin (define ktail (pop-cont!))
(push! 1)
(call! ktail))
(begin (define x1 (- n 1))
(push! x1)
(push-cont! fac-k1)
(call! fac))))
(define (fac)
(define n (pop!))
(push! n)
(push-cont! fac-k0)
(push! n)
(call! zero?))
(push! 3)
(push-cont! halt)
(call! fac)
#+end_src
evaluation of ~(fac 0)~:
#+begin_src scheme
(push! 0) ; [] []
(push-cont! halt) ; [0] []
(call! fac) ; [0] [halt]
(define n (pop!)) ; [0] [halt]
(push! n) ; [] [halt]
(push-cont! fac-k0) ; [0] [halt]
(push! n) ; [0] [halt fac-k0]
(call! zero?) ; [0 0] [halt fac-k0]
#<internals of zero?> ; [0 0] [halt fac-k0]
(define x0 (pop!)) ; [0 #t] [halt]
(define n (pop!)) ; [0] [halt]
(define ktail (pop-cont!)) ; [] [halt]
(push! 1) ; [] []
(call! ktail) ; [1] []
#+end_src
evaluation of ~(fac 3)~
#+begin_src scheme
(push! 3) ; [] []
(push-cont! halt) ; [3] []
(call! fac) ; [3] [halt]
(define n (pop!)) ; [3] [halt]
(push! n) ; [] [halt]
(push-cont! fac-k0) ; [3] [halt]
(push! n) ; [3] [halt fac-k0]
(call! zero?) ; [3 3] [halt fac-k0]
#<internals of zero?> ; [3 3] [halt fac-k0]
(define x0 (pop!)) ; [3 #f] [halt]
(define n (pop!)) ; [3] [halt]
(define x1 (- n 1)) ; [] [halt]
(push! n) ; [] [halt]
(push! x1) ; [3] [halt]
(push-cont! fac-k1) ; [3 2] [halt]
(call! fac) ; [3 2] [halt fac-k1]
(define n (pop!)) ; [3 2] [halt fac-k1]
(push! n) ; [3 ] [halt fac-k1]
(push-cont! fac-k0) ; [3 2] [halt fac-k1]
(push! n) ; [3 2] [halt fac-k1 fac-k0]
(call! zero?) ; [3 2 2] [halt fac-k1 fac-k0]
#<internals of zero?> ; [3 2 2] [halt fac-k1 fac-k0]
(define x0 (pop!)) ; [3 2 #f] [halt fac-k1]
(define n (pop!)) ; [3 2] [halt fac-k1]
(define x1 (- n 1)) ; [3] [halt fac-k1]
(push! n) ; [3] [halt fac-k1]
(push! x1) ; [3 2] [halt fac-k1]
(push-cont! fac-k1) ; [3 2 1] [halt fac-k1]
(call! fac) ; [3 2 1] [halt fac-k1 fac-k1]
(define n (pop!)) ; [3 2 1] [halt fac-k1 fac-k1]
(push! n) ; [3 2] [halt fac-k1 fac-k1]
(push-cont! fac-k0) ; [3 2 1] [halt fac-k1 fac-k1]
(push! n) ; [3 2 1] [halt fac-k1 fac-k1 fac-k0]
(call! zero?) ; [3 2 1 1] [halt fac-k1 fac-k1 fac-k0]
#<internals of zero?> ; [3 2 1 1] [halt fac-k1 fac-k1 fac-k0]
(define x0 (pop!)) ; [3 2 1 #f] [halt fac-k1 fac-k1]
(define n (pop!)) ; [3 2 1] [halt fac-k1 fac-k1]
(define x1 (- n 1)) ; [3 2] [halt fac-k1 fac-k1]
(push! n) ; [3 2] [halt fac-k1]
(push! x1) ; [3 2 1] [halt fac-k1 fac-k1]
(push-cont! fac-k1) ; [3 2 1 0] [halt fac-k1 fac-k1]
(call! fac) ; [3 2 1 0] [halt fac-k1 fac-k1 fac-k1]
(define n (pop!)) ; [3 2 1 0] [halt fac-k1 fac-k1 fac-k1]
(push! n) ; [3 2 1] [halt fac-k1 fac-k1 fac-k1]
(push-cont! fac-k0) ; [3 2 1 0] [halt fac-k1 fac-k1 fac-k1]
(push! n) ; [3 2 1 0] [halt fac-k1 fac-k1 fac-k1 fac-k0]
(call! zero?) ; [3 2 1 0 0] [halt fac-k1 fac-k1 fac-k1 fac-k0]
#<internals of zero?> ; [3 2 1 0 0] [halt fac-k1 fac-k1 fac-k1 fac-k0]
(define x0 (pop!)) ; [3 2 1 0 #t] [halt fac-k1 fac-k1 fac-k1]
(define n (pop!)) ; [3 2 1 0] [halt fac-k1 fac-k1 fac-k1]
(define ktail (pop-cont!)) ; [3 2 1] [halt fac-k1 fac-k1 fac-k1]
(push! 1) ; [3 2 1 1] [halt fac-k1 fac-k1]
(call! ktail) ; [3 2 1 1] [halt fac-k1 fac-k1]
(define n (pop!)) ; [3 2 1 1] [halt fac-k1 fac-k1]
(define x2 (pop!)) ; [3 2 1] [halt fac-k1 fac-k1]
(define x3 (* n x2)) ; [3 2] [halt fac-k1 fac-k1]
(define ktail (pop-cont!)) ; [3 2] [halt fac-k1 fac-k1]
(push! x3) ; [3 2] [halt fac-k1]
(call! ktail) ; [3 2 1] [halt fac-k1]
(define n (pop!)) ; [3 2 1] [halt fac-k1]
(define x2 (pop!)) ; [3 2] [halt fac-k1]
(define x3 (* n x2)) ; [3] [halt fac-k1]
(define ktail (pop-cont!)) ; [3] [halt fac-k1]
(push! x3) ; [3] [halt]
(call! ktail) ; [3 2] [halt]
(define n (pop!)) ; [3 2] [halt]
(define x2 (pop!)) ; [3] [halt]
(define x3 (* n x2)) ; [] [halt]
(define ktail (pop-cont!)) ; [] [halt]
(push! x3) ; [] []
(call! ktail) ; [6] []
;; => (halt 6)
#+end_src