Replace the listy context API with indexed lookups and explicit scope invariants

Tests.lean

@@ -168,6 +168,41 @@ def runNeutralRepresentationChecks : IO Bool := do
     IO.println "fail  stuck eliminators stay in the neutral fragment"
     pure false
 
+def runContextInvariantChecks : IO Bool := do
+  let cxt :=
+    (Cxt.empty.bind "A" (.univ 0)).define "x" .zero .nat
+  let wfOk := Cxt.isWellFormed cxt
+  let lookupOk :=
+    match cxt.lookup "x", cxt.lookup "A" with
+    | some (ix, tx), some (iA, tA) =>
+        ix.val == 0 &&
+        iA.val == 1 &&
+        (match tx with | .nat => true | _ => false) &&
+        (match tA with | .univ 0 => true | _ => false)
+    | _, _ =>
+        false
+  let indexedOk :=
+    let latest : Fin cxt.lvl := ⟨0, by decide⟩
+    let outer : Fin cxt.lvl := ⟨1, by decide⟩
+    (match cxt.typeAt latest with
+     | ("x", .nat) => true
+     | _ => false) &&
+    (match cxt.typeAt outer with
+     | ("A", .univ 0) => true
+     | _ => false) &&
+    (match cxt.valueAt latest with
+     | .zero => true
+     | _ => false) &&
+    (match cxt.valueAt outer with
+     | .neu (.var 0) => true
+     | _ => false)
+  if wfOk && lookupOk && indexedOk then
+    IO.println "pass  context lookup is indexed and scope invariants hold"
+    pure true
+  else
+    IO.println "fail  context lookup is indexed and scope invariants hold"
+    pure false
+
 def runLevelSolverChecks : IO Bool := do
   let satOk :=
     match solveLevelConstraints [(.max 0 1, 1), (1, .succ 1)] with
@@ -212,9 +247,10 @@ def main : IO UInt32 := do
   let results ← cases.mapM runCase
   let safetyOk ← runInternalSafetyChecks
   let neutralOk ← runNeutralRepresentationChecks
+  let contextOk ← runContextInvariantChecks
   let levelOk ← runLevelSolverChecks
   let prettyOk ← runPrettyPrinterChecks
-  let allResults := results ++ [safetyOk, neutralOk, levelOk, prettyOk]
+  let allResults := results ++ [safetyOk, neutralOk, contextOk, levelOk, prettyOk]
   let failed := allResults.countP (· == false)
   if failed == 0 then
     IO.println s!"\n{allResults.length} passed, 0 failed"