plans: tick sieve.hs, progress log 2026-04-25

plans/haskell-on-sx.md

@@ -83,7 +83,7 @@ Key mappings:
 - [x] Do-notation for a stub `IO` monad (just threading, no real side effects yet)
 - [ ] Classic programs in `lib/haskell/tests/programs/`:
   - [x] `fib.hs` — infinite Fibonacci stream
-  - [ ] `sieve.hs` — lazy sieve of Eratosthenes
+  - [x] `sieve.hs` — lazy sieve of Eratosthenes
   - [ ] `quicksort.hs` — naive QS
   - [ ] `nqueens.hs`
   - [ ] `calculator.hs` — parser combinator style expression evaluator
@@ -114,6 +114,14 @@ Key mappings:
 
 _Newest first._
 
+- **2026-04-25** — Classic program `sieve.hs`: lazy sieve of Eratosthenes.
+  Added `mod`, `div`, `rem`, `quot` to `hk-binop` (and as first-class
+  values in `hk-init-env`), enabling backtick operator use. The filter-based
+  sieve `sieve (p:xs) = p : sieve (filter (\x -> x \`mod\` p /= 0) xs)` works
+  with the existing lazy cons + Prelude `filter`. 2 new tests in
+  `lib/haskell/tests/program-sieve.sx` (first 10 primes, 20th prime = 71).
+  390/390 green.
+
 - **2026-04-25** — First classic program: `fib.hs`. Canonical Haskell
   source lives at `lib/haskell/tests/programs/fib.hs` (the
   two-cons-cell self-referential fibs definition plus a hand-rolled