Lottery — committed entries, a published seed, and a draw that closes forever

lottery.cell

// ============================================================================
// LOTTERY — committed entries, a published seed, and a draw that closes forever
// ============================================================================
// Public lotteries get rigged in two ways: officials slip entries in after
// seeing the pool (charter-school placement scandals), or they quietly
// "re-draw" until a favored name comes up — the 2017 HUD housing-voucher
// re-draws drew exactly this complaint. Both attacks die structurally here:
// an applicant's entry count cannot exceed 1 (memory wall), entries lock
// BEFORE the draw, the winner is a pure function of the locked pool and a
// pre-published seed, and `drawn` is a terminal state soma verify proves
// has no exit — there is no second draw.
// ============================================================================

cell HousingLottery {
    face {
        signal enter_pool(applicant: String) -> Map
        signal lock_entries() -> Map
        signal draw(seed: Int) -> Map
        signal pool_size() -> Int
        signal winner_name() -> String
        signal phase() -> String
    }

    memory {
        // applicant -> entries. A second entry is unrepresentable.
        entries: Map<String, Int> [persistent, consistent]
        invariant entries >= 0 && entries <= 1

        result: Map<String, String> [persistent, consistent]
    }

    // drawn has no outgoing edges: there is no re-draw.
    state lottery {
        initial: accepting
        accepting -> entries_locked
        entries_locked -> drawn
    }

    on phase() { return get_status("lottery") }

    on enter_pool(applicant: String) {
        if phase() != "accepting" {
            return map("ok", false, "reason", "pool is {phase()}")
        }
        let prior = entries.get(applicant) ?? 0
        let w = try { entries.set(applicant, prior + 1) }
        if w.error != () {
            return map("ok", false, "reason", "{applicant} already entered")
        }
        return map("ok", true, "pool", pool_size())
    }

    on pool_size() {
        let names = entries.keys()
        return len(names)
    }

    on lock_entries() {
        let r = try { transition("lottery", "entries_locked") }
        if r.error != () { return map("ok", false, "reason", "{r.error}") }
        return map("ok", true, "pool", pool_size())
    }

    // Deterministic: anyone can recompute the winner from the locked pool
    // and the seed the commission published before entries opened.
    on draw(seed: Int) {
        let r = try { transition("lottery", "drawn") }
        if r.error != () { return map("ok", false, "reason", "{r.error}") }
        let pool = sort(entries.keys())
        let idx = seed - idiv(seed, len(pool)) * len(pool)
        result.set("winner", pool[idx])
        return map("ok", true, "winner", pool[idx], "pool", len(pool))
    }

    on winner_name() { return result.get("winner") ?? "none" }
}

cell test LotteryTests {
    rules {
        assert enter_pool("ada").ok == true
        assert enter_pool("bob").ok == true
        assert enter_pool("eve").ok == true
        assert enter_pool("bob").ok == false            // double entry bounces
        assert_fails entries.set("bob", 2)              // unrepresentable
        assert draw(7).ok == false                      // no draw before lock
        assert lock_entries().ok == true
        assert enter_pool("late").ok == false           // pool locked
        assert pool_size() == 3
        assert draw(7).ok == true                       // 7 mod 3 = 1 -> "bob"
        assert winner_name() == "bob"
        assert draw(8).ok == false                      // NO re-draw, ever
        assert_fails transition("lottery", "entries_locked")
        assert_fails transition("lottery", "accepting")
    }
}