diff --git a/lib/guest/pratt.sx b/lib/guest/pratt.sx
new file mode 100644
index 00000000..24138697
--- /dev/null
+++ b/lib/guest/pratt.sx
@@ -0,0 +1,28 @@
+;; lib/guest/pratt.sx — operator-table format + lookup for Pratt-style
+;; precedence climbing.
+;;
+;; The climbing loop stays per-language because the two canaries use
+;; opposite conventions (Lua: higher prec = tighter; Prolog: lower prec =
+;; tighter, with xfx/xfy/yfx assoc tags). Forcing a single loop adds
+;; callback indirection that obscures more than it shares.
+;;
+;; What IS shared and gets extracted: the operator-table format and lookup.
+;; "Grammar is a dict, not hardcoded cond."
+;;
+;; Entry shape: (NAME PREC ASSOC).
+;;   NAME   — string, the operator's source token.
+;;   PREC   — integer, in the host's own convention.
+;;   ASSOC  — :left | :right | :none for languages with traditional
+;;            associativity, or "xfx" / "xfy" / "yfx" for Prolog-style.
+
+(define
+  pratt-op-lookup
+  (fn (table name)
+    (cond
+      ((empty? table) nil)
+      ((= (first (first table)) name) (first table))
+      (:else (pratt-op-lookup (rest table) name)))))
+
+(define pratt-op-name  (fn (entry) (first entry)))
+(define pratt-op-prec  (fn (entry) (nth entry 1)))
+(define pratt-op-assoc (fn (entry) (nth entry 2)))
diff --git a/lib/lua/parser.sx b/lib/lua/parser.sx
index d604224b..1993294a 100644
--- a/lib/lua/parser.sx
+++ b/lib/lua/parser.sx
@@ -3,28 +3,33 @@
 (define lua-tok-value (fn (t) (if (= t nil) nil (get t :value))))
 
 (define
-  lua-binop-prec
-  (fn
-    (op)
-    (cond
-      ((= op "or") 1)
-      ((= op "and") 2)
-      ((= op "<") 3)
-      ((= op ">") 3)
-      ((= op "<=") 3)
-      ((= op ">=") 3)
-      ((= op "==") 3)
-      ((= op "~=") 3)
-      ((= op "..") 5)
-      ((= op "+") 6)
-      ((= op "-") 6)
-      ((= op "*") 7)
-      ((= op "/") 7)
-      ((= op "%") 7)
-      ((= op "^") 10)
-      (else 0))))
+  lua-op-table
+  (list
+    (list "or"  1 :left)
+    (list "and" 2 :left)
+    (list "<"   3 :left)
+    (list ">"   3 :left)
+    (list "<="  3 :left)
+    (list ">="  3 :left)
+    (list "=="  3 :left)
+    (list "~="  3 :left)
+    (list ".."  5 :right)
+    (list "+"   6 :left)
+    (list "-"   6 :left)
+    (list "*"   7 :left)
+    (list "/"   7 :left)
+    (list "%"   7 :left)
+    (list "^"  10 :right)))
 
-(define lua-binop-right? (fn (op) (or (= op "..") (= op "^"))))
+(define lua-binop-prec
+  (fn (op)
+    (let ((entry (pratt-op-lookup lua-op-table op)))
+      (if (= entry nil) 0 (pratt-op-prec entry)))))
+
+(define lua-binop-right?
+  (fn (op)
+    (let ((entry (pratt-op-lookup lua-op-table op)))
+      (and (not (= entry nil)) (= (pratt-op-assoc entry) :right)))))
 
 (define
   lua-parse
diff --git a/lib/lua/test.sh b/lib/lua/test.sh
index 13dabffc..ed7daa60 100755
--- a/lib/lua/test.sh
+++ b/lib/lua/test.sh
@@ -30,6 +30,7 @@ cat > "$TMPFILE" << 'EPOCHS'
 (epoch 1)
 (load "lib/guest/lex.sx")
 (load "lib/guest/prefix.sx")
+(load "lib/guest/pratt.sx")
 (load "lib/lua/tokenizer.sx")
 (epoch 2)
 (load "lib/lua/parser.sx")
diff --git a/lib/prolog/conformance.conf b/lib/prolog/conformance.conf
index e31e74f0..6b1a542a 100644
--- a/lib/prolog/conformance.conf
+++ b/lib/prolog/conformance.conf
@@ -4,6 +4,7 @@ LANG_NAME=prolog
 MODE=dict
 
 PRELOADS=(
+  lib/guest/pratt.sx
   lib/prolog/tokenizer.sx
   lib/prolog/parser.sx
   lib/prolog/runtime.sx
diff --git a/lib/prolog/parser.sx b/lib/prolog/parser.sx
index d6ee00b7..aab0f159 100644
--- a/lib/prolog/parser.sx
+++ b/lib/prolog/parser.sx
@@ -104,18 +104,9 @@
     (list ":-" 1200 "xfx")
     (list "mod" 400 "yfx")))
 
-(define
-  pl-op-find
-  (fn
-    (name table)
-    (cond
-      ((empty? table) nil)
-      ((= (first (first table)) name) (rest (first table)))
-      (true (pl-op-find name (rest table))))))
+(define pl-op-lookup (fn (name) (pratt-op-lookup pl-op-table name)))
 
-(define pl-op-lookup (fn (name) (pl-op-find name pl-op-table)))
-
-;; Token → (name prec type) for known infix ops, else nil.
+;; Token → entry (name prec type) for known infix ops, else nil.
 (define
   pl-token-op
   (fn
@@ -123,14 +114,8 @@
     (let
       ((ty (get t :type)) (vv (get t :value)))
       (cond
-        ((and (= ty "punct") (= vv ","))
-          (let
-            ((info (pl-op-lookup ",")))
-            (if (nil? info) nil (cons "," info))))
-        ((or (= ty "atom") (= ty "op"))
-          (let
-            ((info (pl-op-lookup vv)))
-            (if (nil? info) nil (cons vv info))))
+        ((and (= ty "punct") (= vv ",")) (pl-op-lookup ","))
+        ((or (= ty "atom") (= ty "op")) (pl-op-lookup vv))
         (true nil)))))
 
 ;; ── Term parser ─────────────────────────────────────────────────────
diff --git a/lib/prolog/scoreboard.json b/lib/prolog/scoreboard.json
index 2c1d47ab..b03f44b7 100644
--- a/lib/prolog/scoreboard.json
+++ b/lib/prolog/scoreboard.json
@@ -3,5 +3,5 @@
   "total_failed": 0,
   "total": 590,
   "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},"compiler":{"passed":17,"total":17,"failed":0},"cross_validate":{"passed":17,"total":17,"failed":0},"integration":{"passed":20,"total":20,"failed":0},"hs_bridge":{"passed":19,"total":19,"failed":0}},
-  "generated": "2026-05-06T22:23:38+00:00"
+  "generated": "2026-05-07T17:07:57+00:00"
 }
diff --git a/lib/prolog/scoreboard.md b/lib/prolog/scoreboard.md
index d0d4d3c5..b83007bb 100644
--- a/lib/prolog/scoreboard.md
+++ b/lib/prolog/scoreboard.md
@@ -1,7 +1,7 @@
 # Prolog scoreboard
 
 **590 / 590 passing** (0 failure(s)).
-Generated 2026-05-06T22:23:38+00:00.
+Generated 2026-05-07T17:07:57+00:00.
 
 | Suite | Passed | Total | Status |
 |-------|--------|-------|--------|