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/conformance.conf

@@ -8,6 +8,7 @@ PRELOADS=(
   lib/guest/pratt.sx
   lib/maude/term.sx
   lib/maude/parser.sx
+  lib/maude/sorts.sx
   lib/maude/reduce.sx
   lib/maude/matching.sx
   lib/maude/conditional.sx
@@ -27,6 +28,7 @@ SUITES=(
   "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!)"
+  "sorts:lib/maude/tests/sorts.sx:(mau-sorts-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/scoreboard.json

@@ -1,8 +1,8 @@
 {
   "lang": "maude",
-  "total_passed": 236,
+  "total_passed": 250,
   "total_failed": 0,
-  "total": 236,
+  "total": 250,
   "suites": [
     {"name":"parse","passed":65,"failed":0,"total":65},
     {"name":"reduce","passed":26,"failed":0,"total":26},
@@ -10,6 +10,7 @@
     {"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":"sorts","passed":14,"failed":0,"total":14},
     {"name":"rewrite","passed":21,"failed":0,"total":21},
     {"name":"searchpath","passed":8,"failed":0,"total":8},
     {"name":"strategy","passed":19,"failed":0,"total":19},
@@ -17,5 +18,5 @@
     {"name":"pretty","passed":11,"failed":0,"total":11},
     {"name":"run","passed":6,"failed":0,"total":6}
   ],
-  "generated": "2026-06-07T15:43:54+00:00"
+  "generated": "2026-06-07T15:46:14+00:00"
 }

lib/maude/scoreboard.md

@@ -1,6 +1,6 @@
 # maude scoreboard
 
-**236 / 236 passing** (0 failure(s)).
+**250 / 250 passing** (0 failure(s)).
 
 | Suite | Passed | Total | Status |
 |-------|--------|-------|--------|
@@ -10,6 +10,7 @@
 | conditional | 19 | 19 | ok |
 | owise | 8 | 8 | ok |
 | gather | 7 | 7 | ok |
+| sorts | 14 | 14 | ok |
 | rewrite | 21 | 21 | ok |
 | searchpath | 8 | 8 | ok |
 | strategy | 19 | 19 | ok |

lib/maude/sorts.sx

@@ -0,0 +1,87 @@
+;; lib/maude/sorts.sx — order-sorted least-sort inference.
+;;
+;; Order-sorted signatures: subsorts induce a partial order on sorts, and an
+;; overloaded operator can have several declarations. The LEAST SORT of a term
+;; is the smallest result sort among the operator declarations whose argument
+;; sorts the actual arguments satisfy (modulo subsorting). This is what lets
+;; `f(1)` be a NzNat while `f(s 0)` is only a Nat when f is declared at both.
+;;
+;;   mau/term-sort   M T        -> least sort of T (string, "?" if unknown)
+;;   mau/has-sort?   M T SORT   -> does T's least sort fit under SORT?
+
+(define
+  mau/arg-sorts-ok?
+  (fn
+    (m argsorts declared)
+    (cond
+      ((and (empty? argsorts) (empty? declared)) true)
+      ((or (empty? argsorts) (empty? declared)) false)
+      ((mau/sort<=? m (first argsorts) (first declared))
+        (mau/arg-sorts-ok? m (rest argsorts) (rest declared)))
+      (else false))))
+
+(define
+  mau/matching-ops
+  (fn
+    (m name argsorts)
+    (filter
+      (fn
+        (op)
+        (and
+          (= (len (get op :arity)) (len argsorts))
+          (mau/arg-sorts-ok? m argsorts (get op :arity))))
+      (mau/ops-named m name))))
+
+(define
+  mau/least-loop
+  (fn
+    (m best rst)
+    (cond
+      ((empty? rst) best)
+      ((mau/sort<=? m (first rst) best)
+        (mau/least-loop m (first rst) (rest rst)))
+      (else (mau/least-loop m best (rest rst))))))
+
+(define
+  mau/least-sort
+  (fn
+    (m sorts)
+    (if (empty? sorts) "?" (mau/least-loop m (first sorts) (rest sorts)))))
+
+(define
+  mau/result-sort
+  (fn
+    (m name argsorts)
+    (let
+      ((cands (mau/matching-ops m name argsorts)))
+      (if
+        (empty? cands)
+        (let
+          ((any (mau/ops-named m name)))
+          (if (empty? any) "?" (get (first any) :result)))
+        (mau/least-sort m (map (fn (op) (get op :result)) cands))))))
+
+(define
+  mau/term-sort
+  (fn
+    (m t)
+    (cond
+      ((mau/var? t) (mau/vsort t))
+      ((mau/app? t)
+        (mau/result-sort
+          m
+          (mau/op t)
+          (map (fn (a) (mau/term-sort m a)) (mau/args t))))
+      (else "?"))))
+
+(define
+  mau/term-sort-src
+  (fn (m src) (mau/term-sort m (mau/parse-term-in m src))))
+
+(define
+  mau/has-sort?
+  (fn (m t sort) (mau/sort<=? m (mau/term-sort m t) sort)))
+
+(define
+  mau/has-sort-src?
+  (fn (m src sort) (mau/has-sort? m (mau/parse-term-in m src) sort)))

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}))