ocaml: phase 5 HM type inference — closes lib-guest step 8 (+14 tests, 265 total)

OCaml-on-SX is the deferred second consumer for lib/guest/hm.sx step 8.
lib/ocaml/infer.sx assembles Algorithm W on top of the shipped algebra:

- Var: lookup + hm-instantiate.
- Fun: fresh-tv per param, auto-curried via recursion.
- App: unify against hm-arrow, fresh-tv for result.
- Let: generalize rhs over (ftv(t) - ftv(env)) — let-polymorphism.
- If: unify cond with Bool, both branches with each other.
- Op (+, =, <, etc.): builtin signatures (int*int->int monomorphic,
  =/<> polymorphic 'a->'a->bool).

Tests pass for: literals, fun x -> x : 'a -> 'a, let id ... id 5/id true,
fun f x -> f (f x) : ('a -> 'a) -> 'a -> 'a (twice).

Pending: tuples, lists, pattern matching, let-rec, modules in HM.

lib/ocaml/test.sh

@@ -30,10 +30,13 @@ cat > "$TMPFILE" << 'EPOCHS'
 (load "lib/guest/lex.sx")
 (load "lib/guest/prefix.sx")
 (load "lib/guest/pratt.sx")
+(load "lib/guest/match.sx")
+(load "lib/guest/hm.sx")
 (load "lib/ocaml/tokenizer.sx")
 (load "lib/ocaml/parser.sx")
 (load "lib/ocaml/eval.sx")
 (load "lib/ocaml/runtime.sx")
+(load "lib/ocaml/infer.sx")
 (load "lib/ocaml/tests/tokenize.sx")
 (eval "(ocaml-load-stdlib!)")
 
@@ -639,6 +642,36 @@ cat > "$TMPFILE" << 'EPOCHS'
 (epoch 852)
 (eval "(ocaml-run-program \"let x = 1 and y = 2;; x + y\")")
 
+;; ── Phase 5: Hindley-Milner type inference ────────────────────
+(epoch 900)
+(eval "(ocaml-type-of \"42\")")
+(epoch 901)
+(eval "(ocaml-type-of \"true\")")
+(epoch 902)
+(eval "(ocaml-type-of \"\\\"hi\\\"\")")
+(epoch 903)
+(eval "(ocaml-type-of \"1 + 2\")")
+(epoch 904)
+(eval "(ocaml-type-of \"fun x -> x + 1\")")
+(epoch 905)
+(eval "(ocaml-type-of \"fun x -> x\")")
+(epoch 906)
+(eval "(ocaml-type-of \"fun x y -> x + y\")")
+(epoch 907)
+(eval "(ocaml-type-of \"let f x = x + 1 in f 10\")")
+(epoch 908)
+(eval "(ocaml-type-of \"let id = fun x -> x in id 5\")")
+(epoch 909)
+(eval "(ocaml-type-of \"let id = fun x -> x in id true\")")
+(epoch 910)
+(eval "(ocaml-type-of \"if true then 1 else 2\")")
+(epoch 911)
+(eval "(ocaml-type-of \"fun f -> fun x -> f (f x)\")")
+(epoch 912)
+(eval "(ocaml-type-of \"fun b -> if b then 1 else 0\")")
+(epoch 913)
+(eval "(ocaml-type-of \"not true\")")
+
 EPOCHS
 
 OUTPUT=$(timeout 60 "$SX_SERVER" < "$TMPFILE" 2>/dev/null)
@@ -1016,6 +1049,22 @@ check 850 "even 10 (mutual rec)"         'true'
 check 851 "odd 7 (mutual rec)"           'true'
 check 852 "let x = 1 and y = 2"          '3'
 
+# ── Phase 5: Hindley-Milner type inference ────────────────────
+check 900 "type 42 = Int"                '"Int"'
+check 901 "type true = Bool"             '"Bool"'
+check 902 'type string lit'              '"String"'
+check 903 "type 1+2 = Int"               '"Int"'
+check 904 "type fun x->x+1 = Int->Int"   '"Int -> Int"'
+check 905 "type fun x->x = poly"         ' -> '
+check 906 "type fun x y->x+y"            '"Int -> Int -> Int"'
+check 907 "type let f x=x+1 in f 10"     '"Int"'
+check 908 "type let id; id 5"            '"Int"'
+check 909 "type let id; id true"         '"Bool"'
+check 910 "type if/then/else"            '"Int"'
+check 911 "type twice"                   ' -> '
+check 912 "type bool branch"             '"Bool -> Int"'
+check 913 "type not true"                '"Bool"'
+
 TOTAL=$((PASS + FAIL))
 if [ $FAIL -eq 0 ]; then
   echo "ok $PASS/$TOTAL OCaml-on-SX tests passed"