[AdaWorldAPI]

Implements the first architecture PR named by ADR-2026-10-20-SIX §2 (entries/2026-10-20-six-decisions.md, on main via #1640). The single-table rewrites move into the contract, independent of any physical layout. relalg becomes a consumer.

Dependency diagram

Before

lance-graph-relalg ── owns normalize (Rel rewrites) ──► lowers to r2il / mask-risc
lance-graph-contract   (no set algebra)

After

lance-graph-contract::set_algebra        (zero deps: SetExpr, Res, Runs, normalize)
        ▲  path dep, new
lance-graph-relalg ── Rel ⇄ SetExpr, then delegates ──► lowers to r2il / mask-risc (unchanged)
        (Quack, crepe / R2IL: later consumers via D-CMR-6; not touched here)

The contract's Cargo.toml is unchanged; it still has no dependencies.

What is in the contract

• SetExpr: All | Empty | Sym(u32) | Res(Res) | And | Or | Not.
  • Sym is an opaque two-valued set. It does not name a plane or a bitset; relalg maps Plane(i) onto it.
  • Res is a residual predicate on one lane, with the same fields as relalg's Atom.
• normalize: relalg's rules, ported unchanged except for absorption.

  • Rules: De Morgan, associative flattening, idempotence, complement pairs, per-lane interval fusion and merge.

  • Absorption is matched against flattened sibling sets, in two forms:

    1. A dual child And(ms) inside an Or is dropped when some member m is already covered by the siblings: m is a sibling, or an Or whose members are all siblings.
    2. It is also dropped when a sibling And(ks) has every k among ms. This is x ∨ (x ∧ y) with x itself a conjunction.

    Both have duals inside an And. Children are dropped one at a time, each checked only against the children still kept. This closes N17 (ISS-RELALG-ABSORPTION-AFTER-DE-MORGAN): ¬(x ∧ (x ∨ y)) now reduces to ¬x when x is a leaf, an And or an Or.

  • Flattening happens before relalg's slot admission.

  • No rule distributes, so normalization never grows an expression; a test checks this.

• Runs: sorted, disjoint, half-open intervals.
  • ∩, ∪ and ∖ are each a single merge pass, O(n + m).
  • complement(universe) returns Err(OutOfUniverse) when the set reaches past the given universe.

relalg

normalize converts Rel to SetExpr, calls the contract and converts back. symbolic, run, lowering and the public API are unchanged.

Regression results (relalg, before vs after)

target	before	after
tests/rewrites.rs	14 passed	14 passed (identical names)
lib unit tests	2 passed	3 passed (+conversion_round_trips)
tests/absorption_n17.rs (new)	—	2 passed

• cargo test -p lance-graph-contract --lib set_algebra: 10 passed.
• Consumers: cargo check --all-targets passes for holo-h14d-probe, lance-graph-metta and crepe-plan-probe.
• Clippy -D warnings is clean on the contract and on relalg.

crepe-plan-probe: its test m_the_known_absorption_gap_is_untouched_and_not_produced pinned N17 as unfixed and asked to be updated when that changed. CI probe caught it. The test is renamed ..._is_closed_and_not_produced and now asserts that both compound cases reduce. Its Or case also exposed absorption form 2, which was added with a red-first test.

Algebra-law tests (contract)

• Differential. normalize(e) is compared against e over materialized bitsets with an explicit universe (N = 97), for 3,000 random nested expressions. The test also checks idempotence and that the rewrites fired on most inputs (anti-vacuity).
• Runs laws. ∩, ∪, ∖ and complement are compared with bitsets, together with canonical form, De Morgan, distributivity, identities and double complement. Universes tested: 0, 1, 2, 63, 64, 65 and 100.
• Single cases. N17, its dual, the sub-conjunction case, a silence twin, flattening before depth, and complement pairs.

Disable probes (each restored afterwards)

probe	effect
contract normalize returns its input	relalg: 10 of 14 rewrites.rs tests and both N17 tests fail, so relalg really exercises the contract
absorption form 1 off	only the N17 tests fail (1 in relalg, 2 in the contract)
absorption form 2 off	only absorption_of_a_superset_conjunction fails
absorption on a partial cover (all → any)	the silence twin fails, and so does the bitset differential (the rule becomes unsound)
max dropped in the union merge	runs_obey_the_set_laws_against_bitsets fails

Scope held

No joins, positional gathers, relational AST ownership, recursion, D-MPS-8 or graph_hop. Measures on Runs (Count, Sum) are not in this PR.

Board updates:

• LATEST_STATE: contract inventory.
• STATUS_BOARD: D-CMR-1 and D-RA-2.
• ISSUES: N17.
• New entry 2026-10-20-d-cmr-1-set-algebra.md, plus the entries index.

main is merged in (#1641); its conflicts were in board files only.

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