implement closures

tests/sex-programs/fixpoint.sex

@@ -0,0 +1,55 @@
+(input)
+(output "direct: 120"
+        "fac: 120 3628800"
+        "fib: 55 6765")
+(return 0)
+
+;;; A fixed point built out of closures, which is the hardest thing to
+;;; ask of them: recursion with no recursive function anywhere, only
+;;; self-application.
+;;;
+;;; Self-application needs `x x' and so a recursive type, which is
+;;; spelled here by routing it through a named struct whose field is a
+;;; closure whose own signature mentions that struct. The generated
+;;; closure struct is written before `struct rec' is, so this only
+;;; compiles because a forward declaration is emitted ahead of both.
+;;;
+;;; Note what `fix' captures: a *pointer* to the knot, not the knot. A
+;;; closure is a code pointer beside N bytes of environment, so
+;;; capturing one by value would need N >= 8 + N. No budget makes that
+;;; true, and the static assertion says so rather than letting it
+;;; corrupt anything.
+
+(include stdio.h)
+
+(struct rec ((f (closure (((* (struct rec))) (int)) int))))
+
+;;; Takes a step that expects itself, returns an ordinary closure with
+;;; the self-application hidden inside
+(fn fix ((step (* (struct rec)))) (closure ((int)) int)
+  (return (closure ((n int)) int (step)
+            (return ((-> step f) step n)))))
+
+(pub fn main () int
+  (var fac-knot (struct rec))
+  (= (. fac-knot f)
+     (closure ((self (* (struct rec))) (n int)) int ()
+       (if (<= n 1) (return 1))
+       (return (* n ((-> self f) self (- n 1))))))
+
+  ;; the knot applied to itself directly, without fix
+  (printf "direct: %d\n" ((. fac-knot f) (& fac-knot) 5))
+
+  (var fib-knot (struct rec))
+  (= (. fib-knot f)
+     (closure ((self (* (struct rec))) (n int)) int ()
+       (if (< n 2) (return n))
+       (return (+ ((-> self f) self (- n 1))
+                  ((-> self f) self (- n 2))))))
+
+  ;; one combinator, two different recursions
+  (var fac (closure ((int)) int) (fix (& fac-knot)))
+  (var fib (closure ((int)) int) (fix (& fib-knot)))
+  (printf "fac: %d %d\n" (fac 5) (fac 10))
+  (printf "fib: %d %d\n" (fib 10) (fib 20))
+  (return 0))