artdag: miniKanren CLP(FD) scheduler (schedule.sx) + 15 tests

lib/artdag/schedule.sx on lib/minikanren: slot var per node, fd-lt per edge, fd-label
search. schedule-asap (smallest-first labeling) agrees exactly with plan.sx greedy Kahn
waves (cross-validated); schedules enumerates all valid schedules; schedules-capped
filters to <=cap per slot; schedule-valid? independent dep check. Adds a 'schedule' suite
to conformance.sh loading the minikanren CLP(FD) stack. Completes the optional Phase 3/7
miniKanren box. schedule 15/15, total 213/213.

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

lib/artdag/schedule.sx

@@ -0,0 +1,139 @@
+; lib/artdag/schedule.sx — relational scheduling on lib/minikanren CLP(FD).
+; Each node gets a slot var in [1..max-slots]; every edge (input->node) imposes
+; `fd-lt slot(input) slot(node)`. `fd-label` searches the finite domains; a solution
+; is a {node-id -> slot} assignment respecting all dependencies. Grouping by slot
+; gives parallel batches (plan.sx's batch shape). Labeling picks smallest slots
+; first, so the FIRST solution is the ASAP leveling — it agrees with plan.sx's greedy
+; Kahn waves; the relational extra is enumerating EVERY valid schedule. The
+; parallelism cap is a cardinality property, enforced by filtering labeled solutions
+; (the FD core handles precedence only). lib/minikanren is a READ-ONLY consumed
+; substrate: make-var, fd-in, fd-lt, fd-label, mk-conj, reify, stream-take, empty-s.
+
+(define
+  artdag/range1
+  (fn (n) (map (fn (i) (+ i 1)) (range 0 n))))
+
+(define
+  artdag/-zip-assoc
+  (fn
+    (ids vals)
+    (reduce
+      (fn (m p) (assoc m (first p) (nth p 1)))
+      {}
+      (zip ids vals))))
+
+; build the constraint goal + the ordered slot vars for a dag over domain 1..maxslots.
+(define
+  artdag/sched-goal-and-vars
+  (fn
+    (dag maxslots)
+    (let
+      ((ids (artdag/dag-order dag)))
+      (let
+        ((vars (map (fn (id) (make-var)) ids)))
+        (let
+          ((id->var (artdag/-zip-assoc ids vars))
+            (dom (artdag/range1 maxslots)))
+          (let
+            ((in-goals (map (fn (v) (fd-in v dom)) vars))
+              (lt-goals
+                (reduce
+                  (fn
+                    (acc id)
+                    (concat
+                      acc
+                      (map
+                        (fn
+                          (inp)
+                          (fd-lt (get id->var inp) (get id->var id)))
+                        (artdag/node-inputs (artdag/dag-get dag id)))))
+                  (list)
+                  ids)))
+            {:goal (apply mk-conj (concat in-goals lt-goals (list (fd-label vars)))) :vars vars :ids ids}))))))
+
+(define
+  artdag/-sched-solutions
+  (fn
+    (g limit)
+    (map
+      (fn (sol) (artdag/-zip-assoc (get g :ids) sol))
+      (map
+        (fn (s) (reify (get g :vars) s))
+        (stream-take limit ((get g :goal) empty-s))))))
+
+; all valid dependency-respecting slot assignments within 1..maxslots.
+(define
+  artdag/schedules
+  (fn
+    (dag maxslots)
+    (artdag/-sched-solutions
+      (artdag/sched-goal-and-vars dag maxslots)
+      -1)))
+
+; one valid assignment (ASAP within the bound), or nil if maxslots is too small.
+(define
+  artdag/schedule
+  (fn
+    (dag maxslots)
+    (let
+      ((ss (artdag/-sched-solutions (artdag/sched-goal-and-vars dag maxslots) 1)))
+      (if (empty? ss) nil (first ss)))))
+
+; ASAP schedule: node-count slots are always sufficient (a linear chain is the worst
+; case), and smallest-first labeling yields the tightest leveling.
+(define
+  artdag/schedule-asap
+  (fn (dag) (artdag/schedule dag (artdag/node-count dag))))
+
+(define
+  artdag/schedule-makespan
+  (fn
+    (assignment)
+    (reduce
+      (fn (m id) (max m (get assignment id)))
+      0
+      (keys assignment))))
+
+; group node-ids by slot (ascending), each batch id-sorted for determinism.
+(define
+  artdag/schedule->batches
+  (fn
+    (dag assignment)
+    (let
+      ((mx (artdag/schedule-makespan assignment)))
+      (filter
+        (fn (b) (not (empty? b)))
+        (map
+          (fn
+            (slot)
+            (artdag/sort-strings
+              (filter
+                (fn (id) (= (get assignment id) slot))
+                (keys assignment))))
+          (artdag/range1 mx))))))
+
+; independent check: every input is scheduled strictly before its consumer.
+(define
+  artdag/schedule-valid?
+  (fn
+    (dag assignment)
+    (every?
+      (fn
+        (id)
+        (every?
+          (fn (inp) (< (get assignment inp) (get assignment id)))
+          (artdag/node-inputs (artdag/dag-get dag id))))
+      (artdag/dag-order dag))))
+
+; schedules whose every slot holds <= cap nodes (parallelism cap as a post-filter).
+(define
+  artdag/schedules-capped
+  (fn
+    (dag maxslots cap)
+    (filter
+      (fn
+        (asn)
+        (every?
+          (fn (b) (<= (len b) cap))
+          (artdag/schedule->batches dag asn)))
+      (artdag/schedules dag maxslots))))