datalog: semi-naive saturator + delta sets (Phase 5, 114/114)

dl-saturate! is now semi-naive: tracks a per-relation delta dict,
and on each iteration walks every positive body-literal position,
substituting the delta of its relation while joining the rest
against the previous-iteration DB. Candidates are collected before
mutating the DB so the "full" sides see a consistent snapshot.
Rules with no positive body literal (e.g. (p X) :- (= X 5).)
fall back to a one-shot naive pass via dl-collect-rule-candidates.

dl-saturate-naive! retained as the reference implementation; 8
differential tests compare per-relation tuple counts on every
recursive program. Switched dl-tuple-member? to indexed iteration
instead of recursive rest (eliminates per-step list copy). Larger
chains under bundled conformance trip O(n) membership × CPU
sharing — added a Blocker to swap relations to hash-set membership.

lib/datalog/eval.sx

@@ -1,12 +1,17 @@
-;; lib/datalog/eval.sx — naive bottom-up fixpoint evaluator.
+;; lib/datalog/eval.sx — fixpoint evaluator (naive + semi-naive).
 ;;
-;; (dl-saturate! db) iterates rules until no new tuples are derived.
-;; The Herbrand base is finite (no function symbols) so termination is
-;; guaranteed by the language.
+;; Two saturators are exposed:
+;;   `dl-saturate-naive!` — re-joins each rule against the full DB every
+;;     iteration. Reference implementation; useful for differential tests.
+;;   `dl-saturate!`       — semi-naive default. Tracks per-relation delta
+;;     sets and substitutes one positive body literal per rule with the
+;;     delta of its relation, joining the rest against the previous-
+;;     iteration DB. Same fixpoint, dramatically less work on recursive
+;;     rules.
 ;;
-;; Body literal kinds handled here:
-;;   positive (rel arg ... arg)  → match against EDB+IDB tuples (dl-match-positive)
-;;   built-in (< X Y), (is X e)  → constraint via dl-eval-builtin (Phase 4)
+;; Body literal kinds:
+;;   positive (rel arg ... arg)  → match against EDB+IDB tuples
+;;   built-in (< X Y), (is X e)  → constraint via dl-eval-builtin
 ;;   negation {:neg lit}         → Phase 7
 
 (define
@@ -30,6 +35,26 @@
                 tuples)
               results)))))))
 
+;; Match a positive literal against the delta set for its relation only.
+(define
+  dl-match-positive-delta
+  (fn
+    (lit delta subst)
+    (let
+      ((rel (dl-rel-name lit)) (results (list)))
+      (let
+        ((tuples (if (has-key? delta rel) (get delta rel) (list))))
+        (do
+          (for-each
+            (fn
+              (tuple)
+              (let
+                ((s (dl-unify lit tuple subst)))
+                (when (not (nil? s)) (append! results s))))
+            tuples)
+          results)))))
+
+;; Naive matcher (for dl-saturate-naive! and dl-query post-saturation).
 (define
   dl-match-lit
   (fn
@@ -66,6 +91,7 @@
               options)
             results))))))
 
+;; Naive: apply each rule against full DB until no new tuples.
 (define
   dl-apply-rule!
   (fn
@@ -83,14 +109,14 @@
         new?))))
 
 (define
-  dl-saturate!
+  dl-saturate-naive!
   (fn
     (db)
     (let
       ((changed true))
       (do
         (define
-          dl-sat-loop
+          dl-snloop
           (fn
             ()
             (when
@@ -100,10 +126,190 @@
                 (for-each
                   (fn (r) (when (dl-apply-rule! db r) (set! changed true)))
                   (dl-rules db))
-                (dl-sat-loop)))))
-        (dl-sat-loop)
+                (dl-snloop)))))
+        (dl-snloop)
         db))))
 
+;; ── Semi-naive ───────────────────────────────────────────────────
+
+;; Take a snapshot dict {rel -> tuples} of every relation currently in
+;; the DB. Used as initial delta for the first iteration.
+(define
+  dl-snapshot-facts
+  (fn
+    (db)
+    (let
+      ((facts (get db :facts)) (out {}))
+      (do
+        (for-each
+          (fn (k) (dict-set! out k (dl-copy-list (get facts k))))
+          (keys facts))
+        out))))
+
+(define
+  dl-copy-list
+  (fn
+    (xs)
+    (let
+      ((out (list)))
+      (do (for-each (fn (x) (append! out x)) xs) out))))
+
+;; Does any relation in `delta` have ≥1 tuple?
+(define
+  dl-delta-empty?
+  (fn
+    (delta)
+    (let
+      ((ks (keys delta)) (any-non-empty false))
+      (do
+        (for-each
+          (fn
+            (k)
+            (when
+              (> (len (get delta k)) 0)
+              (set! any-non-empty true)))
+          ks)
+        (not any-non-empty)))))
+
+;; Find substitutions such that `lits` are all satisfied AND `delta-idx`
+;; is matched against the per-relation delta only. The other positive
+;; literals match against the snapshot DB (db.facts read at iteration
+;; start). Built-ins and negations behave as in `dl-match-lit`.
+(define
+  dl-find-bindings-semi
+  (fn
+    (lits db delta delta-idx subst)
+    (dl-fbs-aux lits db delta delta-idx 0 subst)))
+
+(define
+  dl-fbs-aux
+  (fn
+    (lits db delta delta-idx i subst)
+    (cond
+      ((nil? subst) (list))
+      ((>= i (len lits)) (list subst))
+      (else
+        (let
+          ((lit (nth lits i))
+            (options
+              (cond
+                ((and (dict? lit) (has-key? lit :neg))
+                  (error "datalog: negation in semi-naive (Phase 7)"))
+                ((dl-builtin? lit)
+                  (let
+                    ((s (dl-eval-builtin lit subst)))
+                    (if (nil? s) (list) (list s))))
+                ((and (list? lit) (> (len lit) 0))
+                  (if
+                    (= i delta-idx)
+                    (dl-match-positive-delta lit delta subst)
+                    (dl-match-positive lit db subst)))
+                (else (error (str "datalog: unknown body-lit: " lit)))))
+            (results (list)))
+          (do
+            (for-each
+              (fn
+                (s)
+                (for-each
+                  (fn (s2) (append! results s2))
+                  (dl-fbs-aux lits db delta delta-idx (+ i 1) s)))
+              options)
+            results))))))
+
+;; Collect candidate head tuples from a rule using delta. Walks every
+;; positive body position and unions the resulting heads. For rules
+;; with no positive body literal, falls back to a naive single-pass
+;; (so static facts like `(p X) :- (= X 5).` derive on iteration 1).
+(define
+  dl-collect-rule-candidates
+  (fn
+    (rule db delta)
+    (let
+      ((head (get rule :head))
+        (body (get rule :body))
+        (out (list))
+        (saw-pos false))
+      (do
+        (define
+          dl-cri
+          (fn
+            (i)
+            (when
+              (< i (len body))
+              (do
+                (let
+                  ((lit (nth body i)))
+                  (when
+                    (dl-positive-lit? lit)
+                    (do
+                      (set! saw-pos true)
+                      (for-each
+                        (fn (s) (append! out (dl-apply-subst head s)))
+                        (dl-find-bindings-semi
+                          body
+                          db
+                          delta
+                          i
+                          (dl-empty-subst))))))
+                (dl-cri (+ i 1))))))
+        (dl-cri 0)
+        (when
+          (not saw-pos)
+          (for-each
+            (fn (s) (append! out (dl-apply-subst head s)))
+            (dl-find-bindings body db (dl-empty-subst))))
+        out))))
+
+;; Add a list of candidate tuples to db; collect newly-added ones into
+;; the new-delta dict (keyed by relation name).
+(define
+  dl-commit-candidates!
+  (fn
+    (db candidates new-delta)
+    (for-each
+      (fn
+        (lit)
+        (when
+          (dl-add-fact! db lit)
+          (let
+            ((rel (dl-rel-name lit)))
+            (do
+              (when
+                (not (has-key? new-delta rel))
+                (dict-set! new-delta rel (list)))
+              (append! (get new-delta rel) lit)))))
+      candidates)))
+
+(define
+  dl-saturate!
+  (fn
+    (db)
+    (let
+      ((delta (dl-snapshot-facts db)))
+      (do
+        (define
+          dl-sn-step
+          (fn
+            ()
+            (let
+              ((pending (list)) (new-delta {}))
+              (do
+                (for-each
+                  (fn
+                    (rule)
+                    (for-each
+                      (fn (cand) (append! pending cand))
+                      (dl-collect-rule-candidates rule db delta)))
+                  (dl-rules db))
+                (dl-commit-candidates! db pending new-delta)
+                (cond
+                  ((dl-delta-empty? new-delta) nil)
+                  (else (do (set! delta new-delta) (dl-sn-step))))))))
+        (dl-sn-step)
+        db))))
+
+;; ── Querying ─────────────────────────────────────────────────────
+
 (define
   dl-query
   (fn