events: availability.sx — free/busy + conflict detection on Datalog + 16 tests

occurrence/booking EDB; rules busy/conflict (canonical pair, half-open
overlap)/busy_in. API ev-busy, ev-conflicts, ev-has-conflict?, ev-free?
(transient qwindow). Integrates with calendar expansion. 53/53 green.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

.claude/scheduled_tasks.lock

@@ -1 +1 @@
-{"sessionId":"bf20a443-9df8-4cb9-932e-8c6f4c4625c2","pid":1303602,"procStart":"253831081","acquiredAt":1779865895644}
+{"sessionId":"c4d97db1-361c-4a04-a99b-c838f9385469","pid":2426590,"procStart":"349789073","acquiredAt":1780789990975}

lib/events/availability.sx

@@ -0,0 +1,131 @@
+;; lib/events/availability.sx — free/busy + conflict detection on Datalog.
+;;
+;; Availability is per-actor and is forward-chained Datalog over two EDB
+;; relations:
+;;
+;;   (occurrence Key EventId Start End)   ; an expanded calendar occurrence
+;;   (booking    Actor Key)               ; actor attends/holds that occurrence
+;;
+;; The derived relations are the whole policy:
+;;
+;;   busy(A,S,E)        — A is committed for [S,E) (a booked occurrence)
+;;   conflict(A,O1,O2)  — A double-booked into two overlapping occurrences
+;;   busy_in(A,QS,QE)   — A is busy somewhere inside query window [QS,QE)
+;;
+;; Intervals are half-open [Start,End) in epoch minutes (see calendar.sx), so
+;; adjacent slots (E == next start) do NOT conflict. Conflict pairs are
+;; canonical (O1 < O2 by key) so each overlap is reported once. The same `busy`
+;; rule answers "is A free in [QS,QE)?" (busy_in is empty) and feeds "when is A
+;; next free?" — same rules, different bindings.
+
+;; A stable key for an occurrence dict {:id :start :end}.
+(define ev-occ-key (fn (occ) (str (get occ :id) "@" (get occ :start))))
+
+(define
+  ev-occurrence-fact
+  (fn
+    (occ)
+    (list
+      (quote occurrence)
+      (ev-occ-key occ)
+      (get occ :id)
+      (get occ :start)
+      (get occ :end))))
+
+(define ev-occurrence-facts (fn (occs) (map ev-occurrence-fact occs)))
+
+(define ev-booking-fact (fn (actor key) (list (quote booking) actor key)))
+
+(define ev-qwindow-fact (fn (qs qe) (list (quote qwindow) qs qe)))
+
+;; Range restriction: each comparison's variables are bound by an earlier
+;; positive literal (qwindow / busy precede the < tests). Conflict uses
+;; (< O1 O2) on the keys so each overlapping pair is reported once.
+(define
+  ev-avail-rules
+  (quote
+    ((busy A S E <- (booking A O) (occurrence O _ S E))
+      (conflict
+        A
+        O1
+        O2
+        <-
+        (booking A O1)
+        (booking A O2)
+        (occurrence O1 _ S1 E1)
+        (occurrence O2 _ S2 E2)
+        (< O1 O2)
+        (< S1 E2)
+        (< S2 E1))
+      (busy_in A QS QE <- (qwindow QS QE) (busy A S E) (< S QE) (< QS E)))))
+
+;; Build a Datalog db from EDB facts under the availability ruleset.
+(define ev-build-avail (fn (facts) (dl-program-data facts ev-avail-rules)))
+
+;; Convenience: build a db from occurrence dicts + booking pairs.
+;; bookings is a list of (actor key) pairs.
+(define
+  ev-avail-db
+  (fn
+    (occs bookings)
+    (ev-build-avail
+      (append
+        (ev-occurrence-facts occs)
+        (map
+          (fn (b) (ev-booking-fact (first b) (first (rest b))))
+          bookings)))))
+
+;; Helper: insertion sort a list of (S E ...) lists ascending by S then E.
+(define
+  ev-list-before?
+  (fn
+    (a b)
+    (cond
+      ((< (first a) (first b)) true)
+      ((> (first a) (first b)) false)
+      (else (< (first (rest a)) (first (rest b)))))))
+
+(define
+  ev-list-insert
+  (fn
+    (x sorted)
+    (cond
+      ((empty? sorted) (list x))
+      ((ev-list-before? x (first sorted)) (cons x sorted))
+      (else (cons (first sorted) (ev-list-insert x (rest sorted)))))))
+
+(define
+  ev-sort-lists
+  (fn (xs) (reduce (fn (acc x) (ev-list-insert x acc)) (list) xs)))
+
+;; All busy intervals (list S E) for an actor, ascending by start.
+(define
+  ev-busy
+  (fn
+    (db actor)
+    (let
+      ((rows (dl-query db (list (quote busy) actor (quote S) (quote E)))))
+      (ev-sort-lists (map (fn (b) (list (get b :S) (get b :E))) rows)))))
+
+;; Distinct conflicting occurrence-key pairs for an actor (each pair once).
+(define
+  ev-conflicts
+  (fn
+    (db actor)
+    (dl-query db (list (quote conflict) actor (quote O1) (quote O2)))))
+
+(define
+  ev-has-conflict?
+  (fn (db actor) (> (len (ev-conflicts db actor)) 0)))
+
+;; Is `actor` free across the whole window [qs,qe)? (no booked occurrence
+;; overlaps it). Asserts a transient qwindow fact, queries, retracts.
+(define
+  ev-free?
+  (fn
+    (db actor qs qe)
+    (do
+      (dl-assert! db (ev-qwindow-fact qs qe))
+      (let
+        ((rows (dl-query db (list (quote busy_in) actor (quote QS) (quote QE)))))
+        (begin (dl-retract! db (ev-qwindow-fact qs qe)) (empty? rows))))))

lib/events/conformance.conf

@@ -16,8 +16,10 @@ PRELOADS=(
   lib/datalog/api.sx
   lib/datalog/magic.sx
   lib/events/calendar.sx
+  lib/events/availability.sx
 )
 
 SUITES=(
   "calendar:lib/events/tests/calendar.sx:(ev-calendar-tests-run!)"
+  "availability:lib/events/tests/availability.sx:(ev-availability-tests-run!)"
 )

lib/events/scoreboard.json

@@ -1,10 +1,11 @@
 {
   "lang": "events",
-  "total_passed": 37,
+  "total_passed": 53,
   "total_failed": 0,
-  "total": 37,
+  "total": 53,
   "suites": [
-    {"name":"calendar","passed":37,"failed":0,"total":37}
+    {"name":"calendar","passed":37,"failed":0,"total":37},
+    {"name":"availability","passed":16,"failed":0,"total":16}
   ],
-  "generated": "2026-06-06T23:52:14+00:00"
+  "generated": "2026-06-07T00:21:06+00:00"
 }

lib/events/scoreboard.md

@@ -1,7 +1,8 @@
 # events scoreboard
 
-**37 / 37 passing** (0 failure(s)).
+**53 / 53 passing** (0 failure(s)).
 
 | Suite | Passed | Total | Status |
 |-------|--------|-------|--------|
 | calendar | 37 | 37 | ok |
+| availability | 16 | 16 | ok |

lib/events/tests/availability.sx

@@ -0,0 +1,247 @@
+;; lib/events/tests/availability.sx — free/busy + conflict rules on Datalog.
+
+(define ev-av-pass 0)
+(define ev-av-fail 0)
+(define ev-av-failures (list))
+
+(define
+  ev-av-check!
+  (fn
+    (name got expected)
+    (if
+      (= got expected)
+      (set! ev-av-pass (+ ev-av-pass 1))
+      (do
+        (set! ev-av-fail (+ ev-av-fail 1))
+        (append!
+          ev-av-failures
+          (str name "\n    expected: " expected "\n    got:      " got))))))
+
+;; Fixture: three occurrences on 2026-06-01.
+;;   standup  09:00–09:30   review 09:15–10:15 (overlaps standup)
+;;   lunch    12:00–13:00
+(define
+  ev-av-occs
+  (fn
+    ()
+    (list
+      (ev-occ
+        (quote standup)
+        (ev-dt 2026 6 1 9 0)
+        30)
+      (ev-occ
+        (quote review)
+        (ev-dt 2026 6 1 9 15)
+        60)
+      (ev-occ
+        (quote lunch)
+        (ev-dt 2026 6 1 12 0)
+        60))))
+
+(define ev-av-key (fn (id start) (str id "@" start)))
+
+;; alice: standup + review (overlap → conflict). bob: lunch only.
+(define
+  ev-av-db
+  (fn
+    ()
+    (ev-avail-db
+      (ev-av-occs)
+      (list
+        (list
+          (quote alice)
+          (ev-av-key
+            (quote standup)
+            (ev-dt 2026 6 1 9 0)))
+        (list
+          (quote alice)
+          (ev-av-key
+            (quote review)
+            (ev-dt 2026 6 1 9 15)))
+        (list
+          (quote bob)
+          (ev-av-key
+            (quote lunch)
+            (ev-dt 2026 6 1 12 0)))))))
+
+(define
+  ev-av-run-all!
+  (fn
+    ()
+    (let
+      ((db (ev-av-db)))
+      (do
+        (ev-av-check!
+          "busy lists alice committed intervals ascending"
+          (ev-busy db (quote alice))
+          (list
+            (list
+              (ev-dt 2026 6 1 9 0)
+              (ev-dt 2026 6 1 9 30))
+            (list
+              (ev-dt 2026 6 1 9 15)
+              (ev-dt 2026 6 1 10 15))))
+        (ev-av-check!
+          "busy lists bob single interval"
+          (ev-busy db (quote bob))
+          (list
+            (list
+              (ev-dt 2026 6 1 12 0)
+              (ev-dt 2026 6 1 13 0))))
+        (ev-av-check!
+          "busy empty for unknown actor"
+          (ev-busy db (quote carol))
+          (list))
+        (ev-av-check!
+          "alice has an overlap conflict"
+          (ev-has-conflict? db (quote alice))
+          true)
+        (ev-av-check!
+          "alice conflict reported once (canonical pair)"
+          (len (ev-conflicts db (quote alice)))
+          1)
+        (ev-av-check!
+          "bob has no conflict"
+          (ev-has-conflict? db (quote bob))
+          false)
+        (ev-av-check!
+          "non-overlapping bookings do not conflict"
+          (ev-has-conflict?
+            (ev-avail-db
+              (list
+                (ev-occ
+                  (quote a)
+                  (ev-dt
+                    2026
+                    6
+                    1
+                    9
+                    0)
+                  30)
+                (ev-occ
+                  (quote b)
+                  (ev-dt
+                    2026
+                    6
+                    1
+                    9
+                    30)
+                  30))
+              (list
+                (list
+                  (quote dave)
+                  (ev-av-key
+                    (quote a)
+                    (ev-dt
+                      2026
+                      6
+                      1
+                      9
+                      0)))
+                (list
+                  (quote dave)
+                  (ev-av-key
+                    (quote b)
+                    (ev-dt
+                      2026
+                      6
+                      1
+                      9
+                      30)))))
+            (quote dave))
+          false)
+        (ev-av-check!
+          "alice free in an empty window"
+          (ev-free?
+            db
+            (quote alice)
+            (ev-dt 2026 6 1 13 0)
+            (ev-dt 2026 6 1 14 0))
+          true)
+        (ev-av-check!
+          "alice not free overlapping a booking"
+          (ev-free?
+            db
+            (quote alice)
+            (ev-dt 2026 6 1 9 20)
+            (ev-dt 2026 6 1 9 40))
+          false)
+        (ev-av-check!
+          "free? is half-open at the trailing edge"
+          (ev-free?
+            db
+            (quote alice)
+            (ev-dt 2026 6 1 10 15)
+            (ev-dt 2026 6 1 11 0))
+          true)
+        (ev-av-check!
+          "free? is half-open at the leading edge"
+          (ev-free?
+            db
+            (quote bob)
+            (ev-dt 2026 6 1 11 0)
+            (ev-dt 2026 6 1 12 0))
+          true)
+        (ev-av-check!
+          "free? false when window straddles a booking edge"
+          (ev-free?
+            db
+            (quote bob)
+            (ev-dt 2026 6 1 11 0)
+            (ev-dt 2026 6 1 12 1))
+          false)
+        (ev-av-check!
+          "free? query leaves db reusable (no leaked qwindow)"
+          (do
+            (ev-free?
+              db
+              (quote alice)
+              (ev-dt 2026 6 1 9 0)
+              (ev-dt 2026 6 1 9 30))
+            (ev-busy db (quote bob)))
+          (list
+            (list
+              (ev-dt 2026 6 1 12 0)
+              (ev-dt 2026 6 1 13 0))))
+        (let
+          ((daily (ev-expand (ev-event (quote class) (ev-dt 2026 6 1 9 0) 60 {:freq :daily :count 3} 1) (ev-date 2026 6 1) (ev-date 2026 7 1))))
+          (let
+            ((db2 (ev-avail-db daily (map (fn (o) (list (quote sam) (ev-occ-key o))) daily))))
+            (do
+              (ev-av-check!
+                "expanded daily occurrences become busy intervals"
+                (len (ev-busy db2 (quote sam)))
+                3)
+              (ev-av-check!
+                "no conflicts among disjoint daily occurrences"
+                (ev-has-conflict? db2 (quote sam))
+                false)
+              (ev-av-check!
+                "busy on day two of the series"
+                (ev-free?
+                  db2
+                  (quote sam)
+                  (ev-dt
+                    2026
+                    6
+                    2
+                    9
+                    30)
+                  (ev-dt
+                    2026
+                    6
+                    2
+                    9
+                    45))
+                false))))))))
+
+(define
+  ev-availability-tests-run!
+  (fn
+    ()
+    (do
+      (set! ev-av-pass 0)
+      (set! ev-av-fail 0)
+      (set! ev-av-failures (list))
+      (ev-av-run-all!)
+      {:failures ev-av-failures :total (+ ev-av-pass ev-av-fail) :passed ev-av-pass :failed ev-av-fail})))

plans/events-on-sx.md

@@ -18,7 +18,7 @@ capacity rules, transactional booking, and a flow-driven notification dispatcher
 
 ## Status (rolling)
 
-`bash lib/events/conformance.sh` → **37/37** (Phase 1: calendar recurrence)
+`bash lib/events/conformance.sh` → **53/53** (Phase 1: calendar + availability)
 
 ## Ground rules
 
@@ -56,7 +56,8 @@ lib/events/api.sx ── (events/schedule) (events/book) (events/agenda) ──
 ## Phase 1 — Calendar + recurrence
 - [x] `calendar.sx` — event facts, RRULE expansion in a window (DAILY/WEEKLY)
 - [x] `calendar.sx` — MONTHLY (bymonthday + nth-weekday byday)
-- [ ] `availability.sx` — free/busy rules
+- [x] `availability.sx` — free/busy rules (busy/conflict/busy_in on Datalog)
+- [ ] `availability.sx` — next-free slot search (same rules, different bindings)
 - [ ] `api.sx` + tests + scoreboard + conformance.sh
 
 ## Phase 2 — Ticketing + booking
@@ -77,6 +78,12 @@ lib/events/api.sx ── (events/schedule) (events/book) (events/agenda) ──
 
 ## Progress log
 
+- 2026-06-07 — `availability.sx`: free/busy + conflict detection as forward-
+  chained Datalog over `occurrence`/`booking` EDB. Rules `busy(A,S,E)`,
+  `conflict(A,O1,O2)` (canonical `O1<O2`, half-open overlap `S1<E2 ∧ S2<E1`),
+  `busy_in(A,QS,QE)` for window queries. API: `ev-busy`, `ev-conflicts`,
+  `ev-has-conflict?`, `ev-free?` (transient qwindow assert/retract). Integrates
+  with calendar expansion (book expanded occurrences). 16 tests, 53/53 green.
 - 2026-06-06 — MONTHLY recurrence. `ev-days-in-month`, `ev-add-months`,
   BYMONTHDAY (incl. negative = from month end), ordinal BYDAY (`{:ord N :wd W}`,
   ord<0 = nth-from-last), default day-of-month (skips months too short, e.g.