maude: gather / parse-time associativity for cons lists (7 tests, 236 total)

Infix ops parse left (default / gather (E e)) or right (gather (e E)) per the
gather attribute, so _:_ [gather (e E)] reads a : b : c as right-nested. Full
insertion sort now runs over bare cons lists with no parentheses.

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

lib/maude/conformance.conf

@@ -26,6 +26,7 @@ SUITES=(
   "matching:lib/maude/tests/matching.sx:(mau-matching-tests-run!)"
   "conditional:lib/maude/tests/conditional.sx:(mau-conditional-tests-run!)"
   "owise:lib/maude/tests/owise.sx:(mau-owise-tests-run!)"
+  "gather:lib/maude/tests/gather.sx:(mau-gather-tests-run!)"
   "rewrite:lib/maude/tests/rewrite.sx:(mau-rewrite-tests-run!)"
   "searchpath:lib/maude/tests/searchpath.sx:(mau-searchpath-tests-run!)"
   "strategy:lib/maude/tests/strategy.sx:(mau-strategy-tests-run!)"

lib/maude/parser.sx

@@ -19,7 +19,8 @@
 ;; Terms: prefix application f(a,b) (op name may contain underscores, e.g.
 ;; the prefix form _+_(2,3)); mixfix prefix s_ written `s X`; mixfix infix
 ;; _+_ written `X + Y`, parsed by precedence climbing over a table built
-;; from the op declarations.
+;; from the op declarations. Infix associativity follows `gather`: (E e)=left
+;; (default), (e E)=right (e.g. cons _:_), so `a : b : c` parses right-nested.
 
 ;; ---------- tokenizer ----------
 
@@ -173,6 +174,21 @@
       ((p (get (get op :attrs) :prec)))
       (if (= p nil) (mau/default-prec (get form :kind)) p))))
 
+;; parse associativity from a gather spec: (E e)=left, (e E)=right.
+(define
+  mau/gather-assoc
+  (fn
+    (attrs)
+    (let
+      ((g (get attrs :gather)))
+      (if
+        (or (= g nil) (< (len g) 2))
+        "left"
+        (cond
+          ((= (nth g 1) "E") "right")
+          ((= (nth g 0) "E") "left")
+          (else "left"))))))
+
 (define
   mau/build-infix-table
   (fn
@@ -187,7 +203,11 @@
           (if
             (= (get form :kind) "infix")
             (cons
-              (list (get form :token) (mau/op-prec op form) (get op :name))
+              (list
+                (get form :token)
+                (mau/op-prec op form)
+                (get op :name)
+                (mau/gather-assoc (get op :attrs)))
               rest-tbl)
             rest-tbl))))))
 
@@ -310,11 +330,13 @@
                           (do
                             (tadv!)
                             (let
-                              ((rhs (parse-expr (+ lbp 1))))
-                              (climb
-                                (mau/app
-                                  (nth entry 2)
-                                  (list acc rhs))))))))))))
+                              ((rbp (if (= (nth entry 3) "right") lbp (+ lbp 1))))
+                              (let
+                                ((rhs (parse-expr rbp)))
+                                (climb
+                                  (mau/app
+                                    (nth entry 2)
+                                    (list acc rhs)))))))))))))
             (climb lhs))))
       (parse-expr 0))))
 
@@ -398,6 +420,12 @@
               (do
                 (dict-set! acc :label (nth ts 1))
                 (loop (mau/drop ts 2))))
+            ((= (first ts) "gather")
+              (let
+                ((after2 (mau/drop ts 2)))
+                (do
+                  (dict-set! acc :gather (mau/take-until after2 ")"))
+                  (loop (rest (mau/drop-until after2 ")"))))))
             (else (loop (rest ts))))))
       (do (loop toks) acc))))
 

lib/maude/scoreboard.json

@@ -1,14 +1,15 @@
 {
   "lang": "maude",
-  "total_passed": 229,
+  "total_passed": 236,
   "total_failed": 0,
-  "total": 229,
+  "total": 236,
   "suites": [
     {"name":"parse","passed":65,"failed":0,"total":65},
     {"name":"reduce","passed":26,"failed":0,"total":26},
     {"name":"matching","passed":28,"failed":0,"total":28},
     {"name":"conditional","passed":19,"failed":0,"total":19},
     {"name":"owise","passed":8,"failed":0,"total":8},
+    {"name":"gather","passed":7,"failed":0,"total":7},
     {"name":"rewrite","passed":21,"failed":0,"total":21},
     {"name":"searchpath","passed":8,"failed":0,"total":8},
     {"name":"strategy","passed":19,"failed":0,"total":19},
@@ -16,5 +17,5 @@
     {"name":"pretty","passed":11,"failed":0,"total":11},
     {"name":"run","passed":6,"failed":0,"total":6}
   ],
-  "generated": "2026-06-07T15:39:50+00:00"
+  "generated": "2026-06-07T15:43:54+00:00"
 }

lib/maude/scoreboard.md

@@ -1,6 +1,6 @@
 # maude scoreboard
 
-**229 / 229 passing** (0 failure(s)).
+**236 / 236 passing** (0 failure(s)).
 
 | Suite | Passed | Total | Status |
 |-------|--------|-------|--------|
@@ -9,6 +9,7 @@
 | matching | 28 | 28 | ok |
 | conditional | 19 | 19 | ok |
 | owise | 8 | 8 | ok |
+| gather | 7 | 7 | ok |
 | rewrite | 21 | 21 | ok |
 | searchpath | 8 | 8 | ok |
 | strategy | 19 | 19 | ok |

lib/maude/tests/gather.sx

@@ -0,0 +1,66 @@
+;; lib/maude/tests/gather.sx — gather / parse-time associativity.
+
+(define mga-pass 0)
+(define mga-fail 0)
+(define mga-failures (list))
+
+(define
+  mga-check!
+  (fn
+    (name got expected)
+    (if
+      (= got expected)
+      (set! mga-pass (+ mga-pass 1))
+      (do
+        (set! mga-fail (+ mga-fail 1))
+        (append!
+          mga-failures
+          (str name "  expected: " expected "  got: " got))))))
+
+(define
+  mga-m
+  (mau/parse-module
+    "fmod L is\n  sorts Nat List .\n  op 0 : -> Nat .\n  op s_ : Nat -> Nat .\n  op nil : -> List .\n  op _:_ : Nat List -> List [gather (e E)] .\n  op _+_ : Nat Nat -> Nat .\n  op _-_ : Nat Nat -> Nat [gather (E e)] .\n  vars X Y : Nat .\nendfm"))
+
+;; cons is right-associative: a : b : c  ==  a : (b : c)
+(mga-check!
+  "cons-right"
+  (mau/term->str (mau/parse-term-in mga-m "0 : s 0 : nil"))
+  "_:_(0, _:_(s_(0), nil))")
+;; + has no gather -> default left-assoc
+(mga-check!
+  "plus-left"
+  (mau/term->str (mau/parse-term-in mga-m "X + Y + X"))
+  "_+_(_+_(X, Y), X)")
+;; explicit (E e) is left
+(mga-check!
+  "minus-left"
+  (mau/term->str (mau/parse-term-in mga-m "X - Y - X"))
+  "_-_(_-_(X, Y), X)")
+;; gather attr recorded
+(mga-check!
+  "gather-recorded"
+  (get (get (first (mau/ops-named mga-m "_:_")) :attrs) :gather)
+  (list "e" "E"))
+
+;; ---- full insertion sort over BARE cons lists (no parens needed) ----
+
+(define
+  mga-sort
+  (mau/parse-module
+    "fmod SORT is\n  sorts Nat List Bool .\n  op 0 : -> Nat .\n  op s_ : Nat -> Nat .\n  op true : -> Bool .\n  op false : -> Bool .\n  op _<=_ : Nat Nat -> Bool .\n  op nil : -> List .\n  op _:_ : Nat List -> List [gather (e E)] .\n  op insert : Nat List -> List .\n  op sort : List -> List .\n  vars M N : Nat .\n  var L : List .\n  eq 0 <= N = true .\n  eq s M <= 0 = false .\n  eq s M <= s N = M <= N .\n  eq insert(N, nil) = N : nil .\n  ceq insert(N, M : L) = N : M : L if N <= M = true .\n  ceq insert(N, M : L) = M : insert(N, L) if N <= M = false .\n  eq sort(nil) = nil .\n  eq sort(N : L) = insert(N, sort(L)) .\nendfm"))
+
+(mga-check!
+  "sort-bare"
+  (mau/creduce->str mga-sort "sort(s s s 0 : s 0 : s s 0 : nil)")
+  "_:_(s_(0), _:_(s_(s_(0)), _:_(s_(s_(s_(0))), nil)))")
+(mga-check!
+  "sort-bare-5"
+  (mau/creduce->str mga-sort "sort(s s 0 : 0 : s 0 : nil)")
+  "_:_(0, _:_(s_(0), _:_(s_(s_(0)), nil)))")
+(mga-check!
+  "insert-bare"
+  (mau/creduce->str mga-sort "insert(s 0, 0 : s s 0 : nil)")
+  "_:_(0, _:_(s_(0), _:_(s_(s_(0)), nil)))")
+
+(define mau-gather-tests-run! (fn () {:failures mga-failures :total (+ mga-pass mga-fail) :passed mga-pass :failed mga-fail}))

plans/maude-on-sx.md

@@ -112,6 +112,10 @@ The novel substrate stress: equational matching. Pattern `X + Y` against `1 + 2
 - [x] Witness-path search (`lib/maude/searchpath.sx`) — `mau/search-path` /
   `mau/search-length` return the shortest sequence of states start..goal (the
   solution moves), not just yes/no. 8 tests.
+- [x] `gather` / parse-time associativity — infix ops parse left (default,
+  `(E e)`) or right (`(e E)`) per the gather attr, so cons `_:_ [gather (e E)]`
+  reads `a : b : c` as right-nested. Full insertion sort now runs over BARE cons
+  lists (no parens). 7 tests.
 - [x] `owise` equations — parser now reads trailing eq attributes
   (`eq L = R [owise] .`), `mau/split-attrs`; `mau/crewrite-top` is two-pass
   (ordinary equations first, owise last), so an owise catch-all fires only when