maude: order-sorted least-sort inference (14 tests, 250 total)

lib/maude/sorts.sx — mau/term-sort computes the least sort of a term (smallest
result sort among op declarations whose arg sorts the actuals satisfy modulo
subsorting); overloaded f(1)=NzNat vs f(s 0)=Nat. mau/has-sort? for
membership-style checks. Answers the plan's order-sorted substrate question.

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

lib/maude/tests/sorts.sx

@@ -0,0 +1,53 @@
+;; lib/maude/tests/sorts.sx — order-sorted least-sort inference.
+
+(define mso-pass 0)
+(define mso-fail 0)
+(define mso-failures (list))
+
+(define
+  mso-check!
+  (fn
+    (name got expected)
+    (if
+      (= got expected)
+      (set! mso-pass (+ mso-pass 1))
+      (do
+        (set! mso-fail (+ mso-fail 1))
+        (append!
+          mso-failures
+          (str name "  expected: " expected "  got: " got))))))
+
+(define
+  mso-m
+  (mau/parse-module
+    "fmod NUMS is\n  sorts Zero NzNat Nat .\n  subsort Zero < Nat .\n  subsort NzNat < Nat .\n  op 0 : -> Zero .\n  op 1 : -> NzNat .\n  op s_ : Nat -> Nat .\n  op _+_ : Nat Nat -> Nat .\n  op p : NzNat -> NzNat .\n  op f : Nat -> Nat .\n  op f : NzNat -> NzNat .\nendfm"))
+
+;; constants take their declared result sort
+(mso-check! "sort-zero" (mau/term-sort-src mso-m "0") "Zero")
+(mso-check! "sort-one" (mau/term-sort-src mso-m "1") "NzNat")
+
+;; application: arg subsort of declared domain
+(mso-check! "sort-s0" (mau/term-sort-src mso-m "s 0") "Nat")
+(mso-check! "sort-plus" (mau/term-sort-src mso-m "0 + 1") "Nat")
+(mso-check! "sort-p" (mau/term-sort-src mso-m "p(1)") "NzNat")
+
+;; variable keeps its sort
+(mso-check! "sort-var" (mau/term-sort mso-m (mau/var "X" "Nat")) "Nat")
+
+;; LEAST sort under overloading: f(1) fits both f decls -> the smaller, NzNat
+(mso-check! "least-f-1" (mau/term-sort-src mso-m "f(1)") "NzNat")
+;; f(s 0): s 0 is Nat, only fits f : Nat -> Nat
+(mso-check! "least-f-s0" (mau/term-sort-src mso-m "f(s 0)") "Nat")
+;; nested: f(f(1)) -> f(NzNat) -> NzNat
+(mso-check! "least-nested" (mau/term-sort-src mso-m "f(f(1))") "NzNat")
+
+;; membership-style sort checks
+(mso-check! "has-zero-nat" (mau/has-sort-src? mso-m "0" "Nat") true)
+(mso-check! "has-one-nat" (mau/has-sort-src? mso-m "1" "Nat") true)
+(mso-check! "has-zero-not-nznat" (mau/has-sort-src? mso-m "0" "NzNat") false)
+(mso-check! "has-refl" (mau/has-sort-src? mso-m "1" "NzNat") true)
+
+;; unknown operator -> "?"
+(mso-check! "sort-unknown" (mau/term-sort mso-m (mau/const "ghost")) "?")
+
+(define mau-sorts-tests-run! (fn () {:failures mso-failures :total (+ mso-pass mso-fail) :passed mso-pass :failed mso-fail}))