[frankmcsherry]

The follow-up to #1023 and #1024 for the half join, now that it is a proxy tactic (#1022) and DDIR's half join is a backend under it (#1021).

differential: what an outside wrapper needed

Two additions to int_proxy::frontier, the only things dogs3 needed in order to implement its own backend trait for BackendFrontier:

• BackendFrontier::inner_mut(), so the wrapper can drive the inner backend;
• read_as_of, now public and re-exported from int_proxy, so an outside wrapper reads a bridge as of since the same way the join and reduce wrappers do. It advances only times not already beyond since, and consolidates only if any moved.

dogs3: BackendFrontier as a proxy half-join backend

operators/half_join/frontier.rs implements ProxyHalfJoinBackend for BackendFrontier<Bk, T>:

• stage and cross pass through, so cross sees the advanced times;
• advance calls the inner backend, then reads the arranged side as of since;
• the stream side is untouched;
• no key intersection is needed, because the tactic skips keys that only one side holds.

Unlike the join and reduce wrappers, it has no unit-level shortcut. The half join compares times in the total order, and advancing an arranged time can change that comparison even against stream times beyond since: stored (0, 5) precedes (1, 0), but advanced to {(1, 0)} it is (1, 5) and does not. The check is per row instead. It is one comparison, and at a program time it moves nothing.

Tests in tests/proxy_half_join.rs:

• that flip;
• a random oracle over Product times, with arranged rows on both sides of since;
• every one- or two-element frontier of the pentagon lattice N5, which is not distributive.

DDIR

CorgiBackend::half_join wraps its backend with the arrangement's since, as join and reduce do. Every half join is wrapped, so each call site compiles to one operator.

In a delta join, an import's rows arrive twice: once arranged, and once lifted as a stream read as of since. Each pair meets exactly once only if both paths compare the same times. So imports feeding half joins no longer rely on published traces carrying root times, and the comment arguing they could be read as stored is replaced.

server_late_import.rs gains a delta join of an import with itself, installed early and late, checked against the join's result. It passes without the wrapper too, and has to: published traces carry root times today, where stored and as-of readings agree. The dogs3 tests are the ones that tell the wrapper from no wrapper.

Checks

• All test binaries of differential, dogs3, interactive and ddir-server pass.
• cargo check --all-targets: no warnings. Clippy: nothing new in the files touched.
• Release difftest, 1,000 cases with all nine oracles: all passed. Late-install sweep, 2,000 seeds of split,bind,reinstall: all passed.
• Cost at since = {minimum}, measured with a half-join probe kept out of the tree: wrapped and unwrapped were within run-to-run spread, in both directions, for integer and hashed keys.

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