haskell: Phase 10 conformance — statistics.hs (5/5) + newton.hs (5/5), Phase 10 complete

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

lib/haskell/tests/program-newton.sx

@@ -0,0 +1,49 @@
+;; newton.hs — Newton's method for square root.
+;; Source: classic numerical analysis exercise.
+;;
+;; Exercises Phase 10: `Float`, `abs`, `/`, iteration via `until`.
+
+(define
+  hk-prog-val
+  (fn
+    (src name)
+    (hk-deep-force (get (hk-eval-program (hk-core src)) name))))
+
+(define
+  hk-newton-source
+  "improve x guess = (guess + x / guess) / 2\n\ngoodEnough x guess = abs (guess * guess - x) < 0.0001\n\nnewtonSqrt x = newtonHelp x 1.0\n\nnewtonHelp x guess = if goodEnough x guess\n                       then guess\n                       else newtonHelp x (improve x guess)\n")
+
+(hk-test
+  "newton.hs — newtonSqrt 4 ≈ 2"
+  (hk-prog-val
+    (str hk-newton-source "r = abs (newtonSqrt 4.0 - 2.0) < 0.001\n")
+    "r")
+  (list "True"))
+
+(hk-test
+  "newton.hs — newtonSqrt 9 ≈ 3"
+  (hk-prog-val
+    (str hk-newton-source "r = abs (newtonSqrt 9.0 - 3.0) < 0.001\n")
+    "r")
+  (list "True"))
+
+(hk-test
+  "newton.hs — newtonSqrt 2 ≈ 1.41421"
+  (hk-prog-val
+    (str hk-newton-source "r = abs (newtonSqrt 2.0 - 1.41421) < 0.001\n")
+    "r")
+  (list "True"))
+
+(hk-test
+  "newton.hs — improve converges (one step)"
+  (hk-prog-val (str hk-newton-source "r = improve 4.0 1.0\n") "r")
+  2.5)
+
+(hk-test
+  "newton.hs — newtonSqrt 100 ≈ 10"
+  (hk-prog-val
+    (str hk-newton-source "r = abs (newtonSqrt 100.0 - 10.0) < 0.001\n")
+    "r")
+  (list "True"))
+
+{:fails hk-test-fails :pass hk-test-pass :fail hk-test-fail}