predsort/3, term_variables/2, arith: floor/ceiling/truncate/round/sign/sqrt/pow

- pl-eval-arith: add floor, ceiling, truncate, round, sqrt, sign, pow, integer,
  float, float_integer_part, float_fractional_part, **, ^ operators
- pl-collect-vars: helper that extracts unbound variables from a term (left-to-right,
  deduplicated by var id)
- term_variables/2: dispatches via pl-collect-vars, unifies second arg with var list
- pl-predsort-insert!: inserts one element into a sorted list using a 3-arg comparator
  predicate; deduplicates elements where comparator returns '='
- pl-predsort-build!: builds sorted list via fold over pl-predsort-insert!
- predsort/3: full ISO predsort — sorts and deduplicates a list using a caller-supplied
  predicate
- lib/prolog/tests/advanced.sx: 21 tests (12 arith, 5 term_variables, 4 predsort)
- conformance.sh: add advanced suite
- scoreboard: 517/517 (was 496/496)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

lib/prolog/conformance.sh

@@ -40,6 +40,7 @@ SUITES=(
   "io_predicates:lib/prolog/tests/io_predicates.sx:pl-io-predicates-tests-run!"
   "assert_rules:lib/prolog/tests/assert_rules.sx:pl-assert-rules-tests-run!"
   "string_agg:lib/prolog/tests/string_agg.sx:pl-string-agg-tests-run!"
+  "advanced:lib/prolog/tests/advanced.sx:pl-advanced-tests-run!"
 )
 
 SCRIPT='(epoch 1)

lib/prolog/runtime.sx

@@ -410,6 +410,72 @@
           ((sorted-keys (sort (keys kv))))
           (map (fn (k) (dict-get kv k)) sorted-keys))))))
 
+(define
+  pl-collect-vars
+  (fn
+    (term seen-ids)
+    (let
+      ((walked (pl-walk term)))
+      (cond
+        ((pl-var? walked)
+          (let
+            ((id (pl-var-id walked)))
+            (if
+              (some (fn (s) (= s id)) seen-ids)
+              (list seen-ids (list))
+              (list (cons id seen-ids) (list walked)))))
+        ((pl-compound? walked)
+          (reduce
+            (fn
+              (acc arg)
+              (let
+                ((result (pl-collect-vars arg (first acc))))
+                (list (first result) (append (nth acc 1) (nth result 1)))))
+            (list seen-ids (list))
+            (pl-args walked)))
+        (true (list seen-ids (list)))))))
+
+(define
+  pl-predsort-insert!
+  (fn
+    (db pred elem sorted trail)
+    (if
+      (empty? sorted)
+      (list elem)
+      (let
+        ((head (first sorted)) (order-var (pl-mk-rt-var "_PO")))
+        (let
+          ((call-goal (pl-apply-goal pred (list order-var elem head)))
+            (mark (pl-trail-mark trail)))
+          (let
+            ((ok (pl-solve-once! db call-goal trail)))
+            (if
+              ok
+              (let
+                ((order (pl-atom-name (pl-walk-deep order-var))))
+                (do
+                  (pl-trail-undo-to! trail mark)
+                  (cond
+                    ((= order "<") (cons elem sorted))
+                    ((= order "=") sorted)
+                    ((= order ">")
+                      (let
+                        ((rest-sorted (pl-predsort-insert! db pred elem (rest sorted) trail)))
+                        (if rest-sorted (cons head rest-sorted) false)))
+                    (true false))))
+              (begin (pl-trail-undo-to! trail mark) false))))))))
+
+(define
+  pl-predsort-build!
+  (fn
+    (db pred items trail)
+    (reduce
+      (fn
+        (sorted elem)
+        (if sorted (pl-predsort-insert! db pred elem sorted trail) false))
+      (list)
+      items)))
+
 (define
   pl-collect-solutions
   (fn
@@ -782,6 +848,7 @@
               false)))
         (true false)))))
 
+;; ── Structural equality helper (for ==/2, \==/2, delete/3) ────────
 (define
   pl-solve-atom-chars!
   (fn
@@ -820,6 +887,7 @@
             false))
         (true false)))))
 
+;; ── Flatten helper: collect all non-list leaves into SX list ───────
 (define
   pl-solve-atom-codes!
   (fn
@@ -864,6 +932,7 @@
             false))
         (true false)))))
 
+;; ── numlist helper: build SX list of ("num" i) for i in [lo..hi] ──
 (define
   pl-solve-char-code!
   (fn
@@ -886,7 +955,7 @@
             k))
         (true false)))))
 
-;; ── Structural equality helper (for ==/2, \==/2, delete/3) ────────
+;; ── atomic_list_concat helper: collect atom names / num vals ───────
 (define
   pl-struct-eq?
   (fn
@@ -896,19 +965,18 @@
         (= (dict-get a :id) (dict-get b :id)))
       ((and (pl-atom? a) (pl-atom? b))
         (= (pl-atom-name a) (pl-atom-name b)))
-      ((and (pl-num? a) (pl-num? b))
-        (= (pl-num-val a) (pl-num-val b)))
+      ((and (pl-num? a) (pl-num? b)) (= (pl-num-val a) (pl-num-val b)))
       ((and (pl-compound? a) (pl-compound? b))
         (if
           (and
             (= (pl-fun a) (pl-fun b))
             (= (len (pl-args a)) (len (pl-args b))))
           (let
-            ((all-eq true)
-              (i 0))
+            ((all-eq true) (i 0))
             (begin
               (for-each
-                (fn (ai)
+                (fn
+                  (ai)
                   (begin
                     (if
                       (not (pl-struct-eq? ai (nth (pl-args b) i)))
@@ -920,7 +988,7 @@
           false))
       (true false))))
 
-;; ── Flatten helper: collect all non-list leaves into SX list ───────
+;; ── sum_list helper ────────────────────────────────────────────────
 (define
   pl-flatten-prolog
   (fn
@@ -941,7 +1009,7 @@
               (cons h (pl-flatten-prolog tl)))))
         (true (list w))))))
 
-;; ── numlist helper: build SX list of ("num" i) for i in [lo..hi] ──
+;; ── max_list / min_list helpers ────────────────────────────────────
 (define
   pl-numlist-build
   (fn
@@ -951,7 +1019,6 @@
       (list)
       (cons (list "num" lo) (pl-numlist-build (+ lo 1) hi)))))
 
-;; ── atomic_list_concat helper: collect atom names / num vals ───────
 (define
   pl-atomic-list-collect
   (fn
@@ -959,7 +1026,8 @@
     (let
       ((items (pl-prolog-list-to-sx prolog-list)))
       (map
-        (fn (item)
+        (fn
+          (item)
           (let
             ((w (pl-walk-deep item)))
             (cond
@@ -968,7 +1036,7 @@
               (true ""))))
         items))))
 
-;; ── sum_list helper ────────────────────────────────────────────────
+;; ── delete/3 helper: remove elements struct-equal to elem ──────────
 (define
   pl-sum-list-sx
   (fn
@@ -976,12 +1044,11 @@
     (let
       ((items (pl-prolog-list-to-sx prolog-list)))
       (reduce
-        (fn (acc item)
-          (+ acc (pl-num-val (pl-walk-deep item))))
+        (fn (acc item) (+ acc (pl-num-val (pl-walk-deep item))))
         0
         items))))
 
-;; ── max_list / min_list helpers ────────────────────────────────────
+;; ── join string list with separator ────────────────────────────────
 (define
   pl-max-list-sx
   (fn
@@ -989,8 +1056,10 @@
     (let
       ((items (pl-prolog-list-to-sx prolog-list)))
       (reduce
-        (fn (acc item)
-          (let ((v (pl-num-val (pl-walk-deep item))))
+        (fn
+          (acc item)
+          (let
+            ((v (pl-num-val (pl-walk-deep item))))
             (if (> v acc) v acc)))
         (pl-num-val (pl-walk-deep (first items)))
         (rest items)))))
@@ -1002,26 +1071,24 @@
     (let
       ((items (pl-prolog-list-to-sx prolog-list)))
       (reduce
-        (fn (acc item)
-          (let ((v (pl-num-val (pl-walk-deep item))))
+        (fn
+          (acc item)
+          (let
+            ((v (pl-num-val (pl-walk-deep item))))
             (if (< v acc) v acc)))
         (pl-num-val (pl-walk-deep (first items)))
         (rest items)))))
 
-;; ── delete/3 helper: remove elements struct-equal to elem ──────────
 (define
   pl-delete-sx
   (fn
     (prolog-list elem)
     (let
-      ((items (pl-prolog-list-to-sx prolog-list))
-        (ew (pl-walk-deep elem)))
+      ((items (pl-prolog-list-to-sx prolog-list)) (ew (pl-walk-deep elem)))
       (filter
-        (fn (item)
-          (not (pl-struct-eq? (pl-walk-deep item) ew)))
+        (fn (item) (not (pl-struct-eq? (pl-walk-deep item) ew)))
         items))))
 
-;; ── join string list with separator ────────────────────────────────
 (define
   pl-join-strings
   (fn
@@ -1029,10 +1096,7 @@
     (if
       (empty? strs)
       ""
-      (reduce
-        (fn (acc s) (str acc sep s))
-        (first strs)
-        (rest strs)))))
+      (reduce (fn (acc s) (str acc sep s)) (first strs) (rest strs)))))
 
 (define
   pl-apply-goal
@@ -1433,14 +1497,7 @@
                 (let
                   ((clause (first parsed)))
                   (let
-                    ((actual-term
-                       (if
-                         (and
-                           (list? clause)
-                           (= (len clause) 3)
-                           (= (nth clause 0) "clause"))
-                         (nth clause 1)
-                         clause)))
+                    ((actual-term (if (and (list? clause) (= (len clause) 3) (= (nth clause 0) "clause")) (nth clause 1) clause)))
                     (let
                       ((fresh (pl-instantiate actual-term {})))
                       (if (pl-unify! term-arg fresh trail) (k) false))))
@@ -1473,10 +1530,14 @@
                   (set! pl-output-buffer saved-buffer)
                   (if
                     result
-                    (if (pl-unify! var (list "atom" captured) trail) (k) false)
+                    (if
+                      (pl-unify! var (list "atom" captured) trail)
+                      (k)
+                      false)
                     false))))))
         false))))
 
+
 (define
   pl-solve-writeln!
   (fn
@@ -1495,7 +1556,8 @@
       (if
         (pl-atom? fmt-walked)
         (do
-          (pl-output-write! (pl-format-process (pl-atom-name fmt-walked) (list)))
+          (pl-output-write!
+            (pl-format-process (pl-atom-name fmt-walked) (list)))
           (k))
         false))))
 
@@ -1516,7 +1578,6 @@
             (k)))
         false))))
 
-
 (define
   pl-substring
   (fn (s start sublen) (substring s start (+ start sublen))))
@@ -2407,6 +2468,32 @@
             (pl-walk (nth (pl-args g) 2))
             trail
             k))
+        ((and (pl-compound? g) (= (pl-fun g) "term_variables") (= (len (pl-args g)) 2))
+          (let
+            ((term (pl-walk (nth (pl-args g) 0)))
+              (vars-arg (pl-walk (nth (pl-args g) 1))))
+            (let
+              ((result (pl-collect-vars term (list))))
+              (let
+                ((var-list (nth result 1)))
+                (let
+                  ((prolog-vars (pl-list-to-prolog var-list)))
+                  (if (pl-unify! vars-arg prolog-vars trail) (k) false))))))
+        ((and (pl-compound? g) (= (pl-fun g) "predsort") (= (len (pl-args g)) 3))
+          (let
+            ((pred (pl-walk (nth (pl-args g) 0)))
+              (list-arg (pl-walk (nth (pl-args g) 1)))
+              (result-arg (pl-walk (nth (pl-args g) 2))))
+            (let
+              ((items (pl-prolog-list-to-sx (pl-walk-deep list-arg))))
+              (let
+                ((sorted (pl-predsort-build! db pred items trail)))
+                (if
+                  sorted
+                  (let
+                    ((prolog-sorted (pl-list-to-prolog sorted)))
+                    (if (pl-unify! result-arg prolog-sorted trail) (k) false))
+                  false)))))
         (true (pl-solve-user! db g trail cut-box k))))))
 
 (define
@@ -2543,6 +2630,42 @@
                   ((va (pl-eval-arith (first args)))
                     (vb (pl-eval-arith (nth args 1))))
                   (cond ((< va vb) va) (true vb))))
+              ((and (= f "floor") (= (len args) 1))
+                (floor (pl-eval-arith (first args))))
+              ((and (= f "ceiling") (= (len args) 1))
+                (ceil (pl-eval-arith (first args))))
+              ((and (= f "truncate") (= (len args) 1))
+                (truncate (pl-eval-arith (first args))))
+              ((and (= f "round") (= (len args) 1))
+                (round (pl-eval-arith (first args))))
+              ((and (= f "sqrt") (= (len args) 1))
+                (sqrt (pl-eval-arith (first args))))
+              ((and (= f "sign") (= (len args) 1))
+                (let
+                  ((v (pl-eval-arith (first args))))
+                  (cond ((< v 0) -1) ((> v 0) 1) (true 0))))
+              ((and (= f "integer") (= (len args) 1))
+                (truncate (pl-eval-arith (first args))))
+              ((and (= f "float") (= (len args) 1))
+                (pl-eval-arith (first args)))
+              ((and (= f "float_integer_part") (= (len args) 1))
+                (truncate (pl-eval-arith (first args))))
+              ((and (= f "float_fractional_part") (= (len args) 1))
+                (let
+                  ((v (pl-eval-arith (first args))))
+                  (- v (truncate v))))
+              ((and (= f "**") (= (len args) 2))
+                (pow
+                  (pl-eval-arith (first args))
+                  (pl-eval-arith (nth args 1))))
+              ((and (= f "^") (= (len args) 2))
+                (pow
+                  (pl-eval-arith (first args))
+                  (pl-eval-arith (nth args 1))))
+              ((and (= f "pow") (= (len args) 2))
+                (pow
+                  (pl-eval-arith (first args))
+                  (pl-eval-arith (nth args 1))))
               (true 0))))
         (true 0)))))
 

lib/prolog/scoreboard.json

@@ -1,7 +1,7 @@
 {
-  "total_passed": 496,
+  "total_passed": 517,
   "total_failed": 0,
-  "total": 496,
-  "suites": {"parse":{"passed":25,"total":25,"failed":0},"unify":{"passed":47,"total":47,"failed":0},"clausedb":{"passed":14,"total":14,"failed":0},"solve":{"passed":62,"total":62,"failed":0},"operators":{"passed":19,"total":19,"failed":0},"dynamic":{"passed":11,"total":11,"failed":0},"findall":{"passed":11,"total":11,"failed":0},"term_inspect":{"passed":14,"total":14,"failed":0},"append":{"passed":6,"total":6,"failed":0},"reverse":{"passed":6,"total":6,"failed":0},"member":{"passed":7,"total":7,"failed":0},"nqueens":{"passed":6,"total":6,"failed":0},"family":{"passed":10,"total":10,"failed":0},"atoms":{"passed":34,"total":34,"failed":0},"query_api":{"passed":16,"total":16,"failed":0},"iso_predicates":{"passed":29,"total":29,"failed":0},"meta_predicates":{"passed":25,"total":25,"failed":0},"list_predicates":{"passed":33,"total":33,"failed":0},"meta_call":{"passed":15,"total":15,"failed":0},"set_predicates":{"passed":15,"total":15,"failed":0},"char_predicates":{"passed":27,"total":27,"failed":0},"io_predicates":{"passed":24,"total":24,"failed":0},"assert_rules":{"passed":15,"total":15,"failed":0},"string_agg":{"passed":25,"total":25,"failed":0}},
-  "generated": "2026-04-25T13:49:43+00:00"
+  "total": 517,
+  "suites": {"parse":{"passed":25,"total":25,"failed":0},"unify":{"passed":47,"total":47,"failed":0},"clausedb":{"passed":14,"total":14,"failed":0},"solve":{"passed":62,"total":62,"failed":0},"operators":{"passed":19,"total":19,"failed":0},"dynamic":{"passed":11,"total":11,"failed":0},"findall":{"passed":11,"total":11,"failed":0},"term_inspect":{"passed":14,"total":14,"failed":0},"append":{"passed":6,"total":6,"failed":0},"reverse":{"passed":6,"total":6,"failed":0},"member":{"passed":7,"total":7,"failed":0},"nqueens":{"passed":6,"total":6,"failed":0},"family":{"passed":10,"total":10,"failed":0},"atoms":{"passed":34,"total":34,"failed":0},"query_api":{"passed":16,"total":16,"failed":0},"iso_predicates":{"passed":29,"total":29,"failed":0},"meta_predicates":{"passed":25,"total":25,"failed":0},"list_predicates":{"passed":33,"total":33,"failed":0},"meta_call":{"passed":15,"total":15,"failed":0},"set_predicates":{"passed":15,"total":15,"failed":0},"char_predicates":{"passed":27,"total":27,"failed":0},"io_predicates":{"passed":24,"total":24,"failed":0},"assert_rules":{"passed":15,"total":15,"failed":0},"string_agg":{"passed":25,"total":25,"failed":0},"advanced":{"passed":21,"total":21,"failed":0}},
+  "generated": "2026-04-25T14:12:52+00:00"
 }

lib/prolog/scoreboard.md

@@ -1,7 +1,7 @@
 # Prolog scoreboard
 
-**496 / 496 passing** (0 failure(s)).
-Generated 2026-04-25T13:49:43+00:00.
+**517 / 517 passing** (0 failure(s)).
+Generated 2026-04-25T14:12:52+00:00.
 
 | Suite | Passed | Total | Status |
 |-------|--------|-------|--------|
@@ -29,6 +29,7 @@ Generated 2026-04-25T13:49:43+00:00.
 | io_predicates | 24 | 24 | ok |
 | assert_rules | 15 | 15 | ok |
 | string_agg | 25 | 25 | ok |
+| advanced | 21 | 21 | ok |
 
 Run `bash lib/prolog/conformance.sh` to refresh. Override the binary
 with `SX_SERVER=path/to/sx_server.exe bash …`.

lib/prolog/tests/advanced.sx

@@ -0,0 +1,254 @@
+;; lib/prolog/tests/advanced.sx — predsort/3, term_variables/2, arith extensions
+
+(define pl-adv-test-count 0)
+(define pl-adv-test-pass 0)
+(define pl-adv-test-fail 0)
+(define pl-adv-test-failures (list))
+
+(define
+  pl-adv-test!
+  (fn
+    (name got expected)
+    (begin
+      (set! pl-adv-test-count (+ pl-adv-test-count 1))
+      (if
+        (= got expected)
+        (set! pl-adv-test-pass (+ pl-adv-test-pass 1))
+        (begin
+          (set! pl-adv-test-fail (+ pl-adv-test-fail 1))
+          (append!
+            pl-adv-test-failures
+            (str name "\n    expected: " expected "\n    got:      " got)))))))
+
+(define
+  pl-adv-goal
+  (fn
+    (src env)
+    (pl-instantiate (nth (first (pl-parse (str "g :- " src "."))) 2) env)))
+
+(define pl-adv-db (pl-mk-db))
+;; Load a numeric comparator for predsort tests
+(pl-db-load!
+  pl-adv-db
+  (pl-parse
+    "cmp_num(Order, X, Y) :- (X < Y -> Order = '<' ; (X > Y -> Order = '>' ; Order = '='))."))
+
+;; ── Arithmetic extensions ──────────────────────────────────────────
+
+(define pl-adv-arith-env-1 {:X (pl-mk-rt-var "X")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "X is floor(3.7)" pl-adv-arith-env-1)
+  (pl-mk-trail))
+(pl-adv-test!
+  "floor(3.7) = 3"
+  (pl-num-val (pl-walk-deep (dict-get pl-adv-arith-env-1 "X")))
+  3)
+
+(define pl-adv-arith-env-2 {:X (pl-mk-rt-var "X")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "X is ceiling(3.2)" pl-adv-arith-env-2)
+  (pl-mk-trail))
+(pl-adv-test!
+  "ceiling(3.2) = 4"
+  (pl-num-val (pl-walk-deep (dict-get pl-adv-arith-env-2 "X")))
+  4)
+
+(define pl-adv-arith-env-3 {:X (pl-mk-rt-var "X")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "X is truncate(3.9)" pl-adv-arith-env-3)
+  (pl-mk-trail))
+(pl-adv-test!
+  "truncate(3.9) = 3"
+  (pl-num-val (pl-walk-deep (dict-get pl-adv-arith-env-3 "X")))
+  3)
+
+(define pl-adv-arith-env-4 {:X (pl-mk-rt-var "X")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "X is truncate(0 - 3.9)" pl-adv-arith-env-4)
+  (pl-mk-trail))
+(pl-adv-test!
+  "truncate(0-3.9) = -3"
+  (pl-num-val (pl-walk-deep (dict-get pl-adv-arith-env-4 "X")))
+  -3)
+
+(define pl-adv-arith-env-5 {:X (pl-mk-rt-var "X")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "X is round(3.5)" pl-adv-arith-env-5)
+  (pl-mk-trail))
+(pl-adv-test!
+  "round(3.5) = 4"
+  (pl-num-val (pl-walk-deep (dict-get pl-adv-arith-env-5 "X")))
+  4)
+
+(define pl-adv-arith-env-6 {:X (pl-mk-rt-var "X")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "X is sqrt(4.0)" pl-adv-arith-env-6)
+  (pl-mk-trail))
+(pl-adv-test!
+  "sqrt(4.0) = 2"
+  (pl-num-val (pl-walk-deep (dict-get pl-adv-arith-env-6 "X")))
+  2)
+
+(define pl-adv-arith-env-7 {:X (pl-mk-rt-var "X")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "X is sign(0 - 5)" pl-adv-arith-env-7)
+  (pl-mk-trail))
+(pl-adv-test!
+  "sign(0-5) = -1"
+  (pl-num-val (pl-walk-deep (dict-get pl-adv-arith-env-7 "X")))
+  -1)
+
+(define pl-adv-arith-env-8 {:X (pl-mk-rt-var "X")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "X is sign(0)" pl-adv-arith-env-8)
+  (pl-mk-trail))
+(pl-adv-test!
+  "sign(0) = 0"
+  (pl-num-val (pl-walk-deep (dict-get pl-adv-arith-env-8 "X")))
+  0)
+
+(define pl-adv-arith-env-9 {:X (pl-mk-rt-var "X")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "X is sign(3)" pl-adv-arith-env-9)
+  (pl-mk-trail))
+(pl-adv-test!
+  "sign(3) = 1"
+  (pl-num-val (pl-walk-deep (dict-get pl-adv-arith-env-9 "X")))
+  1)
+
+(define pl-adv-arith-env-10 {:X (pl-mk-rt-var "X")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "X is pow(2, 3)" pl-adv-arith-env-10)
+  (pl-mk-trail))
+(pl-adv-test!
+  "pow(2,3) = 8"
+  (pl-num-val (pl-walk-deep (dict-get pl-adv-arith-env-10 "X")))
+  8)
+
+(define pl-adv-arith-env-11 {:X (pl-mk-rt-var "X")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "X is floor(0 - 3.7)" pl-adv-arith-env-11)
+  (pl-mk-trail))
+(pl-adv-test!
+  "floor(0-3.7) = -4"
+  (pl-num-val (pl-walk-deep (dict-get pl-adv-arith-env-11 "X")))
+  -4)
+
+(define pl-adv-arith-env-12 {:X (pl-mk-rt-var "X")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "X is ceiling(0 - 3.2)" pl-adv-arith-env-12)
+  (pl-mk-trail))
+(pl-adv-test!
+  "ceiling(0-3.2) = -3"
+  (pl-num-val (pl-walk-deep (dict-get pl-adv-arith-env-12 "X")))
+  -3)
+
+;; ── term_variables/2 ──────────────────────────────────────────────
+
+(define pl-adv-tv-env-1 {:Vs (pl-mk-rt-var "Vs")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "term_variables(hello, Vs)" pl-adv-tv-env-1)
+  (pl-mk-trail))
+(pl-adv-test!
+  "term_variables(hello,Vs) -> []"
+  (pl-format-term (pl-walk-deep (dict-get pl-adv-tv-env-1 "Vs")))
+  "[]")
+
+(define pl-adv-tv-env-2 {:Vs (pl-mk-rt-var "Vs")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "term_variables(f(a, g(b)), Vs)" pl-adv-tv-env-2)
+  (pl-mk-trail))
+(pl-adv-test!
+  "term_variables(f(a,g(b)),Vs) -> []"
+  (pl-format-term (pl-walk-deep (dict-get pl-adv-tv-env-2 "Vs")))
+  "[]")
+
+(define pl-adv-tv-env-3 {:Y (pl-mk-rt-var "Y") :Vs (pl-mk-rt-var "Vs") :X (pl-mk-rt-var "X")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "term_variables(f(X, Y), Vs)" pl-adv-tv-env-3)
+  (pl-mk-trail))
+(pl-adv-test!
+  "term_variables(f(X,Y),Vs) has 2 vars"
+  (pl-list-length (pl-walk-deep (dict-get pl-adv-tv-env-3 "Vs")))
+  2)
+
+(define pl-adv-tv-env-4 {:Vs (pl-mk-rt-var "Vs") :X (pl-mk-rt-var "X")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "term_variables(X, Vs)" pl-adv-tv-env-4)
+  (pl-mk-trail))
+(pl-adv-test!
+  "term_variables(X,Vs) has 1 var"
+  (pl-list-length (pl-walk-deep (dict-get pl-adv-tv-env-4 "Vs")))
+  1)
+
+(define pl-adv-tv-env-5 {:Y (pl-mk-rt-var "Y") :Vs (pl-mk-rt-var "Vs") :X (pl-mk-rt-var "X")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "term_variables(foo(X, Y, X), Vs)" pl-adv-tv-env-5)
+  (pl-mk-trail))
+(pl-adv-test!
+  "term_variables(foo(X,Y,X),Vs) deduplicates X -> 2 vars"
+  (pl-list-length (pl-walk-deep (dict-get pl-adv-tv-env-5 "Vs")))
+  2)
+
+;; ── predsort/3 ────────────────────────────────────────────────────
+
+(define pl-adv-ps-env-1 {:R (pl-mk-rt-var "R")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "predsort(cmp_num, [], R)" pl-adv-ps-env-1)
+  (pl-mk-trail))
+(pl-adv-test!
+  "predsort([]) -> []"
+  (pl-format-term (pl-walk-deep (dict-get pl-adv-ps-env-1 "R")))
+  "[]")
+
+(define pl-adv-ps-env-2 {:R (pl-mk-rt-var "R")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "predsort(cmp_num, [1], R)" pl-adv-ps-env-2)
+  (pl-mk-trail))
+(pl-adv-test!
+  "predsort([1]) -> [1]"
+  (pl-format-term (pl-walk-deep (dict-get pl-adv-ps-env-2 "R")))
+  ".(1, [])")
+
+(define pl-adv-ps-env-3 {:R (pl-mk-rt-var "R")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "predsort(cmp_num, [3,1,2], R)" pl-adv-ps-env-3)
+  (pl-mk-trail))
+(pl-adv-test!
+  "predsort([3,1,2]) -> [1,2,3]"
+  (pl-format-term (pl-walk-deep (dict-get pl-adv-ps-env-3 "R")))
+  ".(1, .(2, .(3, [])))")
+
+(define pl-adv-ps-env-4 {:R (pl-mk-rt-var "R")})
+(pl-solve-once!
+  pl-adv-db
+  (pl-adv-goal "predsort(cmp_num, [3,1,2,1,3], R)" pl-adv-ps-env-4)
+  (pl-mk-trail))
+(pl-adv-test!
+  "predsort([3,1,2,1,3]) dedup -> [1,2,3]"
+  (pl-format-term (pl-walk-deep (dict-get pl-adv-ps-env-4 "R")))
+  ".(1, .(2, .(3, [])))")
+
+;; ── Runner ─────────────────────────────────────────────────────────
+
+(define pl-advanced-tests-run! (fn () {:failed pl-adv-test-fail :passed pl-adv-test-pass :total pl-adv-test-count :failures pl-adv-test-failures}))