ocaml: phase 6 Bool module + Option.equal/Option.compare (+5 tests, 584 total)

Bool module:
  equal a b      = a = b
  compare a b    = 0 if equal, 1 if a, -1 if b (false < true)
  to_string      'true' / 'false'
  of_string s    = s = 'true'
  not_           wraps host not
  to_int         true=1, false=0

Option additions (take eq/cmp parameter for the inner value):
  equal eq a b   None=None, otherwise eq the inner values
  compare cmp a b  None < Some _; otherwise cmp inner

  Option.equal (=) (Some 1) (Some 1)        = true
  Option.equal (=) (Some 1) None             = false
  Option.compare compare (Some 5) (Some 3)  = 1

lib/ocaml/runtime.sx

@@ -321,6 +321,18 @@
        | None -> Error none_v
        | Some x -> Ok x
 
+     let equal eq a b =
+       match a with
+       | None -> (match b with None -> true | Some _ -> false)
+       | Some x ->
+         (match b with None -> false | Some y -> eq x y)
+
+     let compare cmp a b =
+       match a with
+       | None -> (match b with None -> 0 | Some _ -> -1)
+       | Some x ->
+         (match b with None -> 1 | Some y -> cmp x y)
+
      let some x = Some x
      let none = None
    end ;;
@@ -464,6 +476,18 @@
      let sub s i n = String.sub s i n
    end ;;
 
+   module Bool = struct
+     let equal a b = a = b
+     let compare a b =
+       if a = b then 0
+       else if a then 1
+       else -1
+     let to_string b = if b then \"true\" else \"false\"
+     let of_string s = s = \"true\"
+     let not_ b = not b
+     let to_int b = if b then 1 else 0
+   end ;;
+
    module Char = struct
      let code c = _char_code c
      let chr n = _char_chr n

lib/ocaml/test.sh

@@ -1448,6 +1448,18 @@ cat > "$TMPFILE" << 'EPOCHS'
 (epoch 5202)
 (eval "(ocaml-run \"String.cat \\\"hello \\\" \\\"world\\\"\")")
 
+;; ── Bool module + Option.equal/compare ───────────────────────
+(epoch 5210)
+(eval "(ocaml-run \"Bool.to_string true ^ \\\"-\\\" ^ Bool.to_string false\")")
+(epoch 5211)
+(eval "(ocaml-run \"Bool.compare true false\")")
+(epoch 5212)
+(eval "(ocaml-run \"Option.equal (=) (Some 1) (Some 1)\")")
+(epoch 5213)
+(eval "(ocaml-run \"Option.equal (=) (Some 1) None\")")
+(epoch 5214)
+(eval "(ocaml-run \"Option.compare compare (Some 5) (Some 3)\")")
+
 EPOCHS
 
 OUTPUT=$(timeout 360 "$SX_SERVER" < "$TMPFILE" 2>/dev/null)
@@ -2303,6 +2315,13 @@ check 5200 "String.equal abc abc"         'true'
 check 5201 "String.compare banana apple"  '1'
 check 5202 "String.cat hello world"       '"hello world"'
 
+# ── Bool module + Option.equal/compare ─────────────────────────
+check 5210 "Bool.to_string true/false"    '"true-false"'
+check 5211 "Bool.compare true false"      '1'
+check 5212 "Option.equal Some 1 Some 1"   'true'
+check 5213 "Option.equal Some 1 None"     'false'
+check 5214 "Option.compare Some 5 Some 3" '1'
+
 TOTAL=$((PASS + FAIL))
 if [ $FAIL -eq 0 ]; then
   echo "ok $PASS/$TOTAL OCaml-on-SX tests passed"

plans/ocaml-on-sx.md

@@ -407,6 +407,12 @@ _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 — Bool module + Option.equal / Option.compare
+  (+5 tests, 584 total). Bool: equal, compare (false < true via if
+  ladder), to_string, of_string, not_, to_int. Option additions
+  take an `eq` or `cmp` parameter for the inner-value check, mirroring
+  real OCaml's signature: `Option.equal eq a b`, `Option.compare cmp
+  a b`. None < Some _ for compare.
 - 2026-05-09 Phase 5.1 — bag.ml baseline + String.equal/compare/cat/
   empty (+3 tests, 579 total). bag.ml: split a sentence on spaces,
   count word frequency in a Hashtbl, return the maximum count.