feat(frontend-sql): recognize the SQL frequency L2 and entropy idioms

[zzylol]

Rebased on main d4869a7 (DF 54).

Wave 1 chain: #594 → #593 → #592 → #591 → #595 → #596 → #597 → #598 → #599 (on #589)

Why

#509 Example 2 writes two of its three statistics as SQL idioms:

-- Q2: Entropy(src_ip)
SELECT -SUM(p * LN(p)) FROM (SELECT COUNT(*) * 1.0 / SUM(COUNT(*)) OVER () AS p FROM flows WHERE ... GROUP BY src_ip);
-- Q3: L2(src_ip)
SELECT SQRT(SUM(c * c)) FROM (SELECT src_ip, COUNT(*) AS c FROM flows WHERE ... GROUP BY src_ip);

and says "The SQL frontend does not yet recognize the Q2 and Q3 forms as Entropy and L2. TODO: add this recognition to the per-language frontends." Without an Entropy/L2 intent, Pass 1 has nothing to attach the exact, summary and UnivMon candidates to, and Pass 2 cannot share a UnivMon with Q1.

The parked #562 (L2) and #564 (entropy) added these rules as a Pass 1 SemanticEquivalentRewriteStrategy in the old asap-aware-mapping. This PR ports them. Part of #509 / #580 (W8).

What

Before (Q2, lowered):

Project(-col0) ← Aggregate(SUM(p*LN(p))) ← Project(p = COUNT*1.0/total) ← SQLWindowFunc(SUM(COUNT) OVER ()) ← Aggregate(COUNT(*) GROUP BY src_ip) ← Scan(flows)

After:

Project(CASE WHEN population_count = 0 THEN NULL ELSE -(0.0 - frequency_entropy * LN 2) END)
└── Join(Cross)
    ├── Aggregate[FrequencyEntropy { col: src_ip, accuracy: <query target> }]
    └── Aggregate[Count { accuracy: Exact }]          (both read the filtered scan)

Q3 becomes the same shape with FrequencyL2 and no unit change. Stage 1 then offers PassThrough (the exact reducer from #597) and summary alternatives, including UnivMon, for each intent.

How

• Rules (verbatim from feat(planner): recognize floating SQL frequency L2 idioms #562 + feat(planner): recognize normalized SQL entropy in nats #564). crates/frontend-sql/src/frequency.rs: follow projections only; require a single-key unfiltered COUNT(*) over a non-nullable Bool/Int64/Utf8 key, no HAVING; for L2, SQRT(SUM(c*c)) with a product already typed Float64; for entropy, LN, p = COUNT(*)[*1.0] / SUM(COUNT(*)) OVER () over the complete unordered frame. The result converts bits to nats, keeps SQL's -0.0, and uses an exact population count for SQL's empty-input NULL, so an approximate estimate never decides NULL. The schema must equal the original.
• Adaptation: where the rule runs. The old rule was a Pass 1 replacement strategy used by the legacy search, which plan_stages does not run: Stage 1 only enumerates realizations of single-measure aggregates. Following the design doc's TODO ("per-language frontends"), lower_sql_dialect now applies the rule at the query root. So the original relational DAG is no longer kept as a separate candidate. The exact alternative is the native exact reducer, and the tests show that it agrees with the original SQL.
• SQL sqrt (from feat(planner): recognize floating SQL frequency L2 idioms #562). The executor's expression compiler accepts sqrt on Int64/Float64/NULL.

Refused, as before: the uncast integer product (which is the design's literal Q3, because SQL Int64 overflow is observable), nullable keys, HAVING, scaled probabilities, LOG2, and partitioned or ordered windows.

Tests

Ported from #562/#564: frontend-sql/tests/frequency_{l2,entropy}.rs (recognition, refusals, accuracy propagation, exact population guard) and integration-tests/tests/sql_frequency_{l2,entropy}.rs (original and recognized L2 agree; entropy in nats, -0.0, NULL on empty input). The legacy-search inventory tests become stage1_offers_exact_and_summary_l2_alternatives over enumerate_local_logical_candidates. Without the lower_sql call, the recognition and entropy execution tests fail.

Gate: fmt and clippy (-D warnings) pass. cargo test --workspace: 1,538 passed, 10 ignored (#589: 1,517 / 10).

Ports #562, #564. Stacked on #597. Next: #599.

[zzylol]

Superseded by #707 (merged): G5, Example 2 — Pass 2 summary-capability rule, UnivMon, SQL L2/entropy idioms.