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/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}))