test(of): prove the Tabula is total over 1583-9999

A hand-transcribed 13-entry table is only trustworthy if nothing the engine
constructs falls through it. Sampled property plus an exhaustive sweep behind
COLITUR_EXHAUSTIVE_SWEEP, matching the claim Precedence_ef.band already
carries for RG 91's 28 entries.

Mutation-proved rather than assumed: deleting the entry-13 branch reddens it
on a named date.

1 files changed, 40 insertions, 1 deletions

diff --git a/test/test_precedence_of.ml b/test/test_precedence_of.ml
index 8817fa8..64b182c 100644
--- a/test/test_precedence_of.ml
+++ b/test/test_precedence_of.ml
@@ -225,8 +225,47 @@ let test_part3 () =
       Alcotest.(check int) label expected (Rite_of.Precedence_of.band c cand))
     part3_cases
 
+(* The temporal candidate Temporal_of produces for [d], as Precedence.resolve
+   would build it. *)
+let temporal_candidate d =
+  let t = Rite_of.Temporal_of.temporal d in
+  { Precedence.cel = t.Temporal.office; origin = Precedence.Temporal }
+
+let ctx_of_date d =
+  let t = Rite_of.Temporal_of.temporal d in
+  { Precedence.date = d; season = t.Temporal.season; weekday = Date.weekday d }
+
+let band_of_date d = Rite_of.Precedence_of.band (ctx_of_date d) (temporal_candidate d)
+
+(* Every day of a year: the temporal candidate must land on a real table
+   entry, never [unclassified]. *)
+let check_year y =
+  let mk_date y m dd =
+    Date.make ~year:y ~month:m ~day:dd |> Result.get_ok in
+  let d = ref (mk_date y 1 1) in
+  let last = mk_date y 12 31 in
+  while Date.compare !d last <= 0 do
+    let b = band_of_date !d in
+    if b = Rite_of.Precedence_of.unclassified then
+      Alcotest.failf "%s: temporal candidate is unclassified"
+        (Date.to_iso8601 !d);
+    d := Date.add_days !d 1
+  done
+
+let prop_band_total =
+  QCheck.Test.make ~count:200 ~name:"band classifies every temporal candidate"
+    (QCheck.int_range 1583 9999)
+    (fun y -> check_year y; true)
+
+let test_exhaustive_band_total () =
+  if Sys.getenv_opt "COLITUR_EXHAUSTIVE_SWEEP" = None then
+    Alcotest.skip ()
+  else for y = 1583 to 9999 do check_year y done
+
 let suite =
   ( "precedence-of",
     [ Alcotest.test_case "Tabula part I (entries 1-4)" `Quick test_part1;
       Alcotest.test_case "Tabula part II (entries 5-9)" `Quick test_part2;
-      Alcotest.test_case "Tabula part III (entries 10-13)" `Quick test_part3 ] )
+      Alcotest.test_case "Tabula part III (entries 10-13)" `Quick test_part3;
+      Alcotest.test_case "band is total over the domain" `Slow test_exhaustive_band_total ]
+    @ List.map QCheck_alcotest.to_alcotest [ prop_band_total ] )