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/conformance.sh

@@ -13,7 +13,7 @@ if [ ! -x "$SX_SERVER" ]; then
   exit 1
 fi
 
-SUITES=(dag analyze plan execute optimize fed cost serialize stats fault maude-optimize)
+SUITES=(dag analyze plan execute optimize fed cost serialize stats fault maude-optimize schedule)
 
 OUT_JSON="lib/artdag/scoreboard.json"
 OUT_MD="lib/artdag/scoreboard.md"
@@ -25,6 +25,27 @@ run_suite() {
   TMP=$(mktemp)
   local MAUDE_LOADS=""
   local BRIDGE_LOAD=""
+  local MK_LOADS=""
+  local SCHED_LOAD=""
+  if [ "$suite" = "schedule" ]; then
+    MK_LOADS='(load "lib/guest/match.sx")
+(load "lib/minikanren/unify.sx")
+(load "lib/minikanren/stream.sx")
+(load "lib/minikanren/goals.sx")
+(load "lib/minikanren/fresh.sx")
+(load "lib/minikanren/conde.sx")
+(load "lib/minikanren/run.sx")
+(load "lib/minikanren/relations.sx")
+(load "lib/minikanren/project.sx")
+(load "lib/minikanren/diseq.sx")
+(load "lib/minikanren/intarith.sx")
+(load "lib/minikanren/matche.sx")
+(load "lib/minikanren/defrel.sx")
+(load "lib/minikanren/nafc.sx")
+(load "lib/minikanren/fd.sx")
+(load "lib/minikanren/clpfd.sx")'
+    SCHED_LOAD='(load "lib/artdag/schedule.sx")'
+  fi
   if [ "$suite" = "maude-optimize" ]; then
     MAUDE_LOADS='(load "lib/guest/lex.sx")
 (load "lib/guest/pratt.sx")
@@ -64,6 +85,7 @@ run_suite() {
 (load "lib/persist/kv.sx")
 (load "lib/persist/api.sx")
 ${MAUDE_LOADS}
+${MK_LOADS}
 (load "lib/artdag/dag.sx")
 (load "lib/artdag/analyze.sx")
 (load "lib/artdag/plan.sx")
@@ -76,6 +98,7 @@ ${MAUDE_LOADS}
 (load "lib/artdag/fault.sx")
 (load "lib/artdag/api.sx")
 ${BRIDGE_LOAD}
+${SCHED_LOAD}
 (epoch 2)
 (eval "(define artdag-test-pass 0)")
 (eval "(define artdag-test-fail 0)")

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))))

lib/artdag/scoreboard.json

@@ -10,9 +10,10 @@
     "serialize": {"pass": 13, "fail": 0},
     "stats": {"pass": 12, "fail": 0},
     "fault": {"pass": 14, "fail": 0},
-    "maude-optimize": {"pass": 40, "fail": 0}
+    "maude-optimize": {"pass": 40, "fail": 0},
+    "schedule": {"pass": 15, "fail": 0}
   },
-  "total_pass": 198,
+  "total_pass": 213,
   "total_fail": 0,
-  "total": 198
+  "total": 213
 }

lib/artdag/scoreboard.md

@@ -15,4 +15,5 @@ _Generated by `lib/artdag/conformance.sh`_
 | stats | 12 | 0 | 12 |
 | fault | 14 | 0 | 14 |
 | maude-optimize | 40 | 0 | 40 |
-| **Total** | **198** | **0** | **198** |
+| schedule | 15 | 0 | 15 |
+| **Total** | **213** | **0** | **213** |

lib/artdag/tests/schedule.sx

@@ -0,0 +1,127 @@
+; Phase 3/7 (optional) — relational scheduling on lib/minikanren CLP(FD).
+; Each node gets a slot var; edges impose fd-lt; fd-label searches. The ASAP solution
+; agrees with plan.sx's greedy Kahn waves; enumerating all solutions is the extra.
+
+; ---- linear chain a -> b -> c: exactly one minimal schedule ----
+
+(define
+  sc-chain
+  (artdag/build
+    (list
+      (list "a" "src" (list) {})
+      (list "b" "blur" (list "a") {:radius 1})
+      (list "c" "blur" (list "b") {:radius 2}))))
+(define sc-chain-a (artdag/dag-id sc-chain "a"))
+(define sc-chain-b (artdag/dag-id sc-chain "b"))
+(define sc-chain-c (artdag/dag-id sc-chain "c"))
+(define sc-chain-asap (artdag/schedule-asap sc-chain))
+
+(artdag-test "chain: ASAP schedule exists" (nil? sc-chain-asap) false)
+
+(artdag-test
+  "chain: slots are strictly increasing along the chain"
+  (list
+    (get sc-chain-asap sc-chain-a)
+    (get sc-chain-asap sc-chain-b)
+    (get sc-chain-asap sc-chain-c))
+  (list 1 2 3))
+
+(artdag-test
+  "chain: makespan equals chain length"
+  (artdag/schedule-makespan sc-chain-asap)
+  3)
+
+(artdag-test
+  "chain: exactly one schedule when slots = node count (no slack)"
+  (len (artdag/schedules sc-chain 3))
+  1)
+
+(artdag-test
+  "chain: ASAP batches are one node per slot"
+  (map len (artdag/schedule->batches sc-chain sc-chain-asap))
+  (list 1 1 1))
+
+(artdag-test
+  "chain: ASAP schedule is valid (deps respected)"
+  (artdag/schedule-valid? sc-chain sc-chain-asap)
+  true)
+
+; ---- diamond a -> b,c -> d: b and c are parallel ----
+
+(define
+  sc-dia
+  (artdag/build
+    (list
+      (list "a" "src" (list) {})
+      (list "b" "blur" (list "a") {:radius 1})
+      (list "c" "bright" (list "a") {:radius 1})
+      (list "d" "over" (list "b" "c") {} true))))
+(define sc-dia-asap (artdag/schedule-asap sc-dia))
+
+(artdag-test
+  "diamond: ASAP makespan is 3 (a | b,c | d)"
+  (artdag/schedule-makespan sc-dia-asap)
+  3)
+
+(artdag-test
+  "diamond: ASAP batch sizes are 1,2,1"
+  (map len (artdag/schedule->batches sc-dia sc-dia-asap))
+  (list 1 2 1))
+
+(artdag-test
+  "diamond: FD ASAP batches agree with plan.sx greedy waves"
+  (=
+    (artdag/schedule->batches sc-dia sc-dia-asap)
+    (map artdag/sort-strings (artdag/plan sc-dia 0)))
+  true)
+
+(artdag-test
+  "diamond: every enumerated schedule is valid"
+  (every?
+    (fn (asn) (artdag/schedule-valid? sc-dia asn))
+    (artdag/schedules sc-dia 4))
+  true)
+
+(artdag-test
+  "diamond: b and c share a slot in the ASAP schedule"
+  (=
+    (get sc-dia-asap (artdag/dag-id sc-dia "b"))
+    (get sc-dia-asap (artdag/dag-id sc-dia "c")))
+  true)
+
+; ---- parallelism cap: filter schedules to <= cap nodes per slot ----
+
+(artdag-test
+  "cap 1: the ASAP (b,c parallel) schedule is excluded, serial ones remain"
+  (every?
+    (fn
+      (asn)
+      (every?
+        (fn (b) (<= (len b) 1))
+        (artdag/schedule->batches sc-dia asn)))
+    (artdag/schedules-capped sc-dia 4 1))
+  true)
+
+(artdag-test
+  "cap 1: at least one serial schedule exists within 4 slots"
+  (> (len (artdag/schedules-capped sc-dia 4 1)) 0)
+  true)
+
+(artdag-test
+  "cap 2: admits the parallel ASAP schedule"
+  (if
+    (some
+      (fn (shape) (= shape (list 1 2 1)))
+      (map
+        (fn (asn) (map len (artdag/schedule->batches sc-dia asn)))
+        (artdag/schedules-capped sc-dia 4 2)))
+    true
+    false)
+  true)
+
+; ---- unsatisfiable: too few slots for the chain ----
+
+(artdag-test
+  "chain: no schedule when slots < chain length"
+  (nil? (artdag/schedule sc-chain 2))
+  true)