wip: stack frames

doc/liveness.org

@@ -0,0 +1,88 @@
+* 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
+

doc/make-vm-stackier.org

@@ -0,0 +1,68 @@
+* rationale?
+
+previously, the VM's stack was used for storing local variables across blocks; a Scheme procedure was split into several low-level routines (one for the procedure itself and one for each continuation), and the stack was used as a communication channel for these separate routines. in contrast, registers were local to each routine. this aligns with Wasm's model of functions pretty well, with Wasm /locals/ acting as the VM's /registers/, and a global mutable stack serving as fallback.
+
+this worked quite well until it became time to implement ~call/cc~.
+
+we are considering making the following alterations to the VM:
+- explicitly segment the stack into frames.
+- passing procedures and return addresses on the stack.
+
+* scratchpad
+
+** Scheme source
+
+#+begin_src scheme
+(* 2 (call/cc
+      (λ (cc)
+        (begin (cc 6)
+               3))))
+#+end_src
+
+** CPS
+
+#+begin_src scheme
+(λ (ktail0)
+  (letrec ((with-cc
+            (λ (cc ktail1)
+              (letrec ((k0 (κ (_)
+                              (continue ktail1 3))))
+                (cc 6 k0)))))
+    (prim (call/cc with-cc)
+          (κ (x1)
+             (prim (* 2 x1)
+                   (κ (x2) (continue ktail0 x2)))))))
+#+end_src
+
+** stack VM
+
+#+begin_src scheme
+;; (call n) expects `n' values on the stack as arguments. then the
+;; procedure is expected at index `n', and the return continuation
+;; should be at `n+1'.
+
+(define $k0
+  (pop! %_) ; [ _ ret ]
+  (push! 3) ; [ ret ]
+  (tail-call 1) ; [ 3 ret ]
+  )
+
+(define $with-cc
+  (pop! %cc) ; [ cc ret ]
+  (push! $k0) ; [ ret ]
+  (push! %cc) ; [ $k0 ret ]
+  (push! 6) ; [ cc $k0 ret ]
+  ;; call a procedure with one argument.
+  (call 1) ; [ 6 cc $k0 ret ]
+  )
+
+(define $main
+  (pop! %ktail0) ; [ ret ]
+  (prim %x1 (call/cc $with-cc)) ; []
+  (prim %x2 (* 2 %x1)) ; []
+  (push! %ktail0) ; []
+  (push! %x2) ; [ ret ]
+  (tail-call 1) ; [ %x2 ret ]
+  )
+#+end_src
+