ocaml: phase 6 Printf.sprintf %d/%s/%f/%c/%b/%% + global string_of_* (+5 tests, 492 total)

Replaces the stub sprintf in runtime.sx with a real implementation:
walk fmt char-by-char accumulating a prefix; on recognised %X return a
one-arg fn that formats the arg and recurses on the rest of fmt. The
function self-curries to the spec count — there's no separate arity
machinery, just a closure chain.

Specs: %d (int), %s (string), %f (float), %c (char/string in our model),
%b (bool), %% (literal). Unknown specs pass through.

Same expression returns a string (no specs) or a function (>=1 spec) —
OCaml proper would reject this; works fine in OCaml-on-SX's dynamic
runtime.

Also adds top-level aliases:
  string_of_int   = _string_of_int
  string_of_float = _string_of_float
  string_of_bool  = if b then "true" else "false"
  int_of_string   = _int_of_string

  Printf.sprintf "x=%d" 42              = "x=42"
  Printf.sprintf "%s = %d" "answer" 42  = "answer = 42"
  Printf.sprintf "%d%%" 50               = "50%"

lib/ocaml/runtime.sx

@@ -424,8 +424,35 @@
    end ;;
 
    module Printf = struct
-     let sprintf fmt = fmt
-     let printf fmt = print_string fmt
+     (* sprintf walks fmt, accumulating prefix. When it sees a %X
+        spec, it returns a function of one arg that substitutes the
+        arg and recurses on the rest of fmt. With no specs, returns
+        the bare format string. Specs supported: %d %s %f %c %b
+        (and %% as a literal). Unknown specs are passed through. *)
+     let sprintf fmt =
+       let n = _string_length fmt in
+       let rec walk pos prefix =
+         if pos >= n then prefix
+         else if pos + 1 < n && _string_get fmt pos = \"%\" then
+           let spec = _string_get fmt (pos + 1) in
+           if spec = \"%\" then walk (pos + 2) (prefix ^ \"%\")
+           else if spec = \"d\" || spec = \"s\" || spec = \"f\"
+                || spec = \"c\" || spec = \"b\" then
+             (fun arg ->
+                let s =
+                  if spec = \"d\" then _string_of_int arg
+                  else if spec = \"f\" then _string_of_float arg
+                  else if spec = \"b\" then
+                    (if arg then \"true\" else \"false\")
+                  else arg
+                in
+                walk (pos + 2) (prefix ^ s))
+           else walk (pos + 1) (prefix ^ _string_get fmt pos)
+         else walk (pos + 1) (prefix ^ _string_get fmt pos)
+       in
+       walk 0 \"\"
+
+     let printf fmt = sprintf fmt
    end ;;
 
    module Stack = struct
@@ -643,7 +670,13 @@
          | [] -> []
          | h :: t -> if mem h b then h :: inter t b else inter t b
      end
-   end")
+   end ;;
+
+   let string_of_int n = _string_of_int n
+   let string_of_float f = _string_of_float f
+   let string_of_bool b = if b then \"true\" else \"false\"
+   let int_of_string s = _int_of_string s
+   ")
 
 (define ocaml-stdlib-loaded false)
 (define ocaml-stdlib-env nil)

lib/ocaml/test.sh

@@ -1210,6 +1210,18 @@ cat > "$TMPFILE" << 'EPOCHS'
 (epoch 4932)
 (eval "(ocaml-run \"try (assert false; 0) with _ -> 99\")")
 
+;; ── Printf.sprintf + global string_of_* ──────────────────────
+(epoch 4940)
+(eval "(ocaml-run \"Printf.sprintf \\\"hello\\\"\")")
+(epoch 4941)
+(eval "(ocaml-run \"Printf.sprintf \\\"x=%d\\\" 42\")")
+(epoch 4942)
+(eval "(ocaml-run \"Printf.sprintf \\\"%s = %d\\\" \\\"answer\\\" 42\")")
+(epoch 4943)
+(eval "(ocaml-run \"Printf.sprintf \\\"%d%%\\\" 50\")")
+(epoch 4944)
+(eval "(ocaml-run \"string_of_int 7 ^ \\\"-\\\" ^ string_of_bool true\")")
+
 EPOCHS
 
 OUTPUT=$(timeout 360 "$SX_SERVER" < "$TMPFILE" 2>/dev/null)
@@ -1919,6 +1931,13 @@ check 4930 "assert true; 42"              '42'
 check 4931 "assert (x = 5); x + 1"        '6'
 check 4932 "try (assert false; ...) with" '99'
 
+# ── Printf.sprintf ───────────────────────────────────────────────
+check 4940 "sprintf no args"              '"hello"'
+check 4941 "sprintf one %d"               '"x=42"'
+check 4942 "sprintf %s = %d"              '"answer = 42"'
+check 4943 "sprintf %d%% literal percent" '"50%"'
+check 4944 "string_of_int + string_of_b"  '"7-true"'
+
 TOTAL=$((PASS + FAIL))
 if [ $FAIL -eq 0 ]; then
   echo "ok $PASS/$TOTAL OCaml-on-SX tests passed"

plans/ocaml-on-sx.md

@@ -407,6 +407,18 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-09 Phase 6 — Printf.sprintf with %d/%s/%f/%c/%b/%% (+4
+  tests) and global `string_of_int`/`string_of_float`/`string_of_bool`
+  (+1 test). 492 total. sprintf walks fmt char-by-char accumulating
+  a prefix; on a recognised spec it returns a one-arg fn that formats
+  the arg and recurses on the rest of fmt — naturally curries to the
+  right arity since the spec count drives the chain. Dynamic typing
+  lets us return either a string (no specs) or a function (≥1 spec)
+  from the same expression, which OCaml proper would reject.
+  Examples:
+    Printf.sprintf "x=%d" 42                = "x=42"
+    Printf.sprintf "%s = %d" "answer" 42    = "answer = 42"
+    Printf.sprintf "%d%%" 50                 = "50%"
 - 2026-05-09 Phase 4 — `assert EXPR` (+3 tests, 487 total). Tokenizer
   already classified `assert` as a keyword; parse-prefix now handles
   it like `not` (advance, recur, wrap). Eval evaluates the operand and