haskell: Phase 10 — math builtins (sqrt/floor/ceiling/round/truncate) (+6 tests, 28/28)

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

lib/haskell/eval.sx

@@ -789,6 +789,26 @@
                 (dict-set! hk-vfs (hk-force path) (hk-force contents))
                 (list "IO" (list "Tuple"))))
             2))
+        (dict-set! env "sqrt" (hk-mk-builtin "sqrt" (fn (x) (sqrt x)) 1))
+        (dict-set!
+          env
+          "floor"
+          (hk-mk-builtin "floor" (fn (x) (floor x)) 1))
+        (dict-set!
+          env
+          "ceiling"
+          (hk-mk-builtin
+            "ceiling"
+            (fn (x) (let ((f (floor x))) (if (= x f) f (+ f 1))))
+            1))
+        (dict-set!
+          env
+          "round"
+          (hk-mk-builtin "round" (fn (x) (round x)) 1))
+        (dict-set!
+          env
+          "truncate"
+          (hk-mk-builtin "truncate" (fn (x) (truncate x)) 1))
         (let
           ((--sx-to-hk-- (fn (lst) (if (empty? lst) (list "[]") (list ":" (first lst) (--sx-to-hk-- (rest lst))))))
             (--words--

lib/haskell/tests/numerics.sx

@@ -138,4 +138,22 @@
   (hk-deep-force (hk-run "main = show (negate 3.14)"))
   "-3.14")
 
+(hk-test "sqrt 16 = 4" (hk-deep-force (hk-run "main = sqrt 16")) 4)
+
+(hk-test "floor 3.7 = 3" (hk-deep-force (hk-run "main = floor 3.7")) 3)
+
+(hk-test "ceiling 3.2 = 4" (hk-deep-force (hk-run "main = ceiling 3.2")) 4)
+
+(hk-test
+  "ceiling on whole = self"
+  (hk-deep-force (hk-run "main = ceiling 4"))
+  4)
+
+(hk-test "round 2.6 = 3" (hk-deep-force (hk-run "main = round 2.6")) 3)
+
+(hk-test
+  "truncate -3.7 = -3"
+  (hk-deep-force (hk-run "main = truncate (negate 3.7)"))
+  -3)
+
 {:fails hk-test-fails :pass hk-test-pass :fail hk-test-fail}

plans/haskell-completeness.md

@@ -160,7 +160,7 @@ No OCaml changes are needed. The view type is fully representable as an SX dict.
   ints (`1.0e10` → `"10000000000"`) because our system can't distinguish
   `42` from `42.0` — both are SX numbers where `integer?` is true. Existing
   tests like `show 42 = "42"` rely on this rendering. Documented in `numerics.sx`._
-- [ ] Math builtins: `sqrt`, `floor`, `ceiling`, `round`, `truncate` — call
+- [x] Math builtins: `sqrt`, `floor`, `ceiling`, `round`, `truncate` — call
   the corresponding SX numeric primitives.
 - [ ] `Fractional` typeclass stub: `(/)`, `recip`, `fromRational`.
 - [ ] `Floating` typeclass stub: `pi`, `exp`, `log`, `sin`, `cos`, `(**)`
@@ -301,6 +301,12 @@ No OCaml changes are needed. The view type is fully representable as an SX dict.
 
 _Newest first._
 
+**2026-05-07** — Phase 10 math builtins (sqrt/floor/ceiling/round/truncate):
+- Inserted in the post-prelude `begin` block so they override the prelude's
+  identity stubs. `ceiling` is the only one needing a definition (SX doesn't
+  ship one — derived from `floor`). `sqrt`, `floor`, `round`, `truncate`
+  thunk through to SX primitives. 6 new tests in `numerics.sx` (now 28/28).
+
 **2026-05-07** — Phase 10 Float display through `hk-show-val`:
 - Added `hk-show-num` and `hk-show-float-sci` helpers in `eval.sx`. Number
   formatting: `integer?` → decimal (covers all whole-valued numbers, both ints