haskell: Phase 10 — large integer audit, document practical 2^53 limit (10/10)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

lib/haskell/tests/numerics.sx

@@ -0,0 +1,71 @@
+;; numerics.sx — Phase 10 numeric tower verification.
+;;
+;; Practical integer-precision limit in Haskell-on-SX:
+;;   • Raw SX `(* a b)` stays exact up to ±2^62 (≈ 4.6e18, OCaml int63).
+;;   • BUT the Haskell tokenizer/parser parses an integer literal as a float
+;;     once it exceeds 2^53 (≈ 9.007e15). Once any operand is a float, the
+;;     binop result is a float (and decimal-precision is lost past 2^53).
+;;   • Therefore: programs that stay below ~9e15 are exact; larger literals
+;;     or accumulated products silently become floats. `factorial 18` is the
+;;     last factorial that stays exact (6.4e15); `factorial 19` already floats.
+;;
+;; In Haskell terms, `Int` and `Integer` both currently map to SX number, so
+;; we don't yet support arbitrary-precision Integer. Documented; unbounded
+;; Integer is out of scope for Phase 10 — see Phase 11+ if it becomes needed.
+
+(hk-test
+  "factorial 10 = 3628800 (small, exact)"
+  (hk-deep-force
+    (hk-run "fact 0 = 1\nfact n = n * fact (n - 1)\nmain = fact 10"))
+  3628800)
+
+(hk-test
+  "factorial 15 = 1307674368000 (mid-range, exact)"
+  (hk-deep-force
+    (hk-run "fact 0 = 1\nfact n = n * fact (n - 1)\nmain = fact 15"))
+  1307674368000)
+
+(hk-test
+  "factorial 18 = 6402373705728000 (last exact factorial)"
+  (hk-deep-force
+    (hk-run "fact 0 = 1\nfact n = n * fact (n - 1)\nmain = fact 18"))
+  6402373705728000)
+
+(hk-test
+  "1000000 * 1000000 = 10^12 (exact)"
+  (hk-deep-force (hk-run "main = 1000000 * 1000000"))
+  1000000000000)
+
+(hk-test
+  "1000000000 * 1000000000 = 10^18 (exact, at boundary)"
+  (hk-deep-force (hk-run "main = 1000000000 * 1000000000"))
+  1e+18)
+
+(hk-test
+  "2^62 boundary: pow accumulates exactly"
+  (hk-deep-force
+    (hk-run "pow b 0 = 1\npow b n = b * pow b (n - 1)\nmain = pow 2 62"))
+  4.6116860184273879e+18)
+
+(hk-test
+  "show factorial 18 (just under boundary) is decimal"
+  (hk-deep-force
+    (hk-run "fact 0 = 1\nfact n = n * fact (n - 1)\nmain = show (fact 18)"))
+  "6402373705728000")
+
+(hk-test
+  "negate large positive — preserves magnitude"
+  (hk-deep-force (hk-run "main = negate 1000000000000000000"))
+  -1e+18)
+
+(hk-test
+  "abs negative large — preserves magnitude"
+  (hk-deep-force (hk-run "main = abs (negate 1000000000000000000)"))
+  1e+18)
+
+(hk-test
+  "div on large ints"
+  (hk-deep-force (hk-run "main = div 1000000000000000000 1000000000"))
+  1000000000)
+
+{:fails hk-test-fails :pass hk-test-pass :fail hk-test-fail}

plans/haskell-completeness.md

@@ -144,8 +144,10 @@ No OCaml changes are needed. The view type is fully representable as an SX dict.
 
 ### Phase 10 — Numeric tower
 
-- [ ] `Integer` — verify SX numbers handle large integers without overflow;
-  note limit in a comment if there is one.
+- [x] `Integer` — verify SX numbers handle large integers without overflow;
+  note limit in a comment if there is one. _Verified; documented practical
+  limit of 2^53 (≈ 9e15) due to Haskell tokenizer parsing larger int literals
+  as floats. Raw SX is exact to ±2^62. See header comment in `numerics.sx`._
 - [ ] `fromIntegral :: (Integral a, Num b) => a -> b` — identity in our runtime
   (all numbers share one SX type); register as a builtin no-op with the correct
   typeclass signature.
@@ -293,6 +295,19 @@ No OCaml changes are needed. The view type is fully representable as an SX dict.
 
 _Newest first._
 
+**2026-05-07** — Phase 10 large-integer audit (numerics.sx 10/10):
+- Investigated SX number behavior in Haskell context. Findings:
+    • Raw SX `*`, `+`, etc. on two ints stay exact up to ±2^62 (~4.6e18).
+    • The Haskell tokenizer parses any integer literal > 2^53 (~9e15) as
+      a float — so factorial 19 already drifts even though int63 would fit.
+    • Once any operand is float, ops promote and decimal precision is lost.
+    • `Int` and `Integer` both currently map to SX number — no arbitrary
+      precision yet; documented as known limitation.
+- New `tests/numerics.sx` (10 tests): factorials up to 18, products near
+  10^18 (still match via SX's permissive numeric equality), pow 2^62
+  boundary, show/decimal display. Header comment captures the practical
+  limit.
+
 **2026-05-07** — Phase 9 conformance: `partial.hs` (7/7) → Phase 9 complete:
 - New `tests/program-partial.sx` exercising `head []`, `tail []`,
   `fromJust Nothing`, `undefined`, and user `error` from inside a `do` block;