datalog-plan: align roadmap with briefing — insert built-ins (P4) and magic sets (P6)

plans/datalog-on-sx.md

@@ -103,23 +103,59 @@ Key differences from Prolog:
       sibling, same-generation, grandparent, cyclic graph reach, six
       safety cases. 87 / 87 conformance.
 
-### Phase 4 — semi-naive evaluation (performance)
+### Phase 4 — built-in predicates + body arithmetic
+Almost every real query needs `<`, `=`, simple arithmetic, and string
+comparisons in body position. These are not EDB lookups — they're
+constraints that filter bindings.
+- [ ] Recognise built-in predicates in body: `(< X Y)`, `(<= X Y)`, `(> X Y)`,
+      `(>= X Y)`, `(= X Y)`, `(!= X Y)` and arithmetic forms `(is Z (+ X Y))`,
+      `(is Z (- X Y))`, `(is Z (* X Y))`, `(is Z (/ X Y))`.
+- [ ] Built-in evaluation: at the join step, after binding variables from
+      EDB lookups, evaluate built-ins as constraints. If any built-in fails
+      or has unbound inputs, drop the candidate substitution.
+- [ ] **Safety extension**: `is` binds its left operand iff right operand is
+      fully ground. `(< X Y)` requires both X and Y bound by some prior body
+      literal — reject unsafe at `dl-add-rule!` time.
+- [ ] Wire arithmetic operators through to SX numeric primitives — no
+      separate Datalog number tower.
+- [ ] Tests: range filters, arithmetic derivations, comparison-based
+      queries, safety violation on `(p X) :- (< X 5).`
+
+### Phase 5 — semi-naive evaluation (performance)
 - [ ] Delta sets: track newly derived tuples per iteration
 - [ ] Semi-naive rule: only join against delta tuples from last iteration, not full relation
 - [ ] Significant speedup for recursive rules — avoids re-deriving known tuples
-- [ ] `dl-stratify` `db` → dependency graph + SCC analysis → stratum ordering
 - [ ] Tests: verify semi-naive produces same results as naive; benchmark on large ancestor chain
 
-### Phase 5 — stratified negation
+### Phase 6 — magic sets (goal-directed bottom-up, opt-in)
+Naive bottom-up derives **all** consequences before answering. Magic sets
+rewrite the program so the fixpoint only derives tuples relevant to the
+goal — a major perf win for "what's reachable from node X" queries on
+large graphs.
+- [ ] Adornments: annotate rule predicates with bound (`b`) / free (`f`)
+      patterns based on how they're called.
+- [ ] Magic transformation: for each adorned predicate, generate a
+      `magic_<pred>` relation and rewrite rule bodies to filter through it.
+- [ ] Sideways information passing strategy (SIPS): left-to-right by
+      default; pluggable.
+- [ ] Optional pass — `(dl-set-strategy! db :magic)`; default semi-naive.
+- [ ] Tests: equivalence vs naive on small inputs; perf win on a 10k-node
+      reachability query from a single root.
+
+### Phase 7 — stratified negation
 - [ ] Dependency graph analysis: which relations depend on which (positively or negatively)
 - [ ] Stratification check: error if negation is in a cycle (non-stratifiable program)
-- [ ] Evaluation: process strata in order — lower stratum fully computed before using its
-      complement in a higher stratum
-- [ ] `not(P)` in rule body: at evaluation time, check P is NOT in the derived EDB
-- [ ] Tests: non-member (`not(member(X,L))`), colored-graph (`not(same-color(X,Y))`),
-      stratification error detection
+- [ ] `dl-stratify db` → SCC analysis → stratum ordering
+- [ ] Evaluation: process strata in order — lower stratum fully computed
+      before using its complement in a higher stratum
+- [ ] `not(P)` in rule body: at evaluation time, check P is NOT in the
+      derived EDB
+- [ ] Safety extension: head vars in negative literals must also appear in
+      some positive body literal of the same rule
+- [ ] Tests: non-member (`not(member(X,L))`), colored-graph
+      (`not(same-color(X,Y))`), stratification error detection
 
-### Phase 6 — aggregation (Datalog+)
+### Phase 8 — aggregation (Datalog+)
 - [ ] `count(X, Goal)` → number of distinct X satisfying Goal
 - [ ] `sum(X, Goal)` → sum of X values satisfying Goal
 - [ ] `min(X, Goal)` / `max(X, Goal)` → min/max of X satisfying Goal
@@ -127,7 +163,7 @@ Key differences from Prolog:
 - [ ] Aggregation breaks stratification — evaluate in a separate post-fixpoint pass
 - [ ] Tests: social network statistics, grade aggregation, inventory sums
 
-### Phase 7 — SX embedding API
+### Phase 9 — SX embedding API
 - [ ] `(dl-program facts rules)` → database from SX data directly (no parsing required)
       ```
       (dl-program
@@ -141,7 +177,7 @@ Key differences from Prolog:
 - [ ] Integration demo: federation graph query — `(ancestor actor1 actor2)` over
       rose-ash ActivityPub follow relationships
 
-### Phase 8 — Datalog as a query language for rose-ash
+### Phase 10 — Datalog as a query language for rose-ash
 - [ ] Schema: map SQLAlchemy model relationships to Datalog EDB facts
       (e.g. `(follows user1 user2)`, `(authored user post)`, `(tagged post tag)`)
 - [ ] Loader: `dl-load-from-db!` — query PostgreSQL, populate Datalog EDB