η for box

fixes #27

tests/Tests/Equal.idr

@@ -48,6 +48,7 @@ tests : Test
 tests = "equality & subtyping" :- [
   note #""s{t,…}" for term substs; "s‹p,…›" for dim substs"#,
   note #""0=1 ⊢ 𝒥" means that 𝒥 holds in an inconsistent dim context"#,
+  note "binds before ∥ are globals, after it are BVs",
 
   "universes" :- [
     testEq "★₀ = ★₀" $
@@ -165,7 +166,6 @@ tests = "equality & subtyping" :- [
       refl a x = ^Ann (^DLam (SN x)) (^Eq0 a x x)
   in
   [
-    note "binds before ∥ are globals, after it are BVs",
     note #"refl A x is an abbreviation for "(δ i ⇒ x) ∷ (x ≡ x : A)""#,
     testEq "refl A a = refl A a" $
       equalE empty
@@ -523,9 +523,51 @@ tests = "equality & subtyping" :- [
   todo "enum",
   todo "enum elim",
 
-  todo "box types",
-  todo "boxes",
-  todo "box elim",
+  "box types" :- [
+    testEq "[1.A] = [1.A] : ★" $
+      equalT empty
+        (^TYPE 0)
+        (^BOX One (^FT "A" 0))
+        (^BOX One (^FT "A" 0)),
+    testNeq "[1.A] ≠ [ω.A] : ★" $
+      equalT empty
+        (^TYPE 0)
+        (^BOX One (^FT "A" 0))
+        (^BOX Any (^FT "A" 0)),
+    testNeq "[1.A] ≠ [1.B] : ★" $
+      equalT empty
+        (^TYPE 0)
+        (^BOX One (^FT "A" 0))
+        (^BOX One (^FT "B" 0)),
+    testNeq "[1.A] ≠ A : ★" $
+      equalT empty
+        (^TYPE 0)
+        (^BOX One (^FT "A" 0))
+        (^FT "A" 0),
+    testEq "0=1 ⊢ [1.A] = [1.B] : ★" $
+      equalT empty01
+        (^TYPE 0)
+        (^BOX One (^FT "A" 0))
+        (^BOX One (^FT "B" 0))
+  ],
+
+  "boxes" :- [
+    testEq "[a] = [a] : [ω.A]" $
+      equalT empty
+        (^BOX Any (^FT "A" 0))
+        (^Box (^FT "a" 0))
+        (^Box (^FT "a" 0)),
+    testNeq "[a] ≠ [a'] : [ω.A]" $
+      equalT empty
+        (^BOX Any (^FT "A" 0))
+        (^Box (^FT "a" 0))
+        (^Box (^FT "a'" 0)),
+    testEq "ω.x : [ω.A] ⊢ x = [case1 b return A of {[y] ⇒ y}] : [ω.A]" $
+      equalT (ctx [< ("x", ^BOX Any (^FT "A" 0))])
+        (^BOX Any (^FT "A" 0))
+        (^BVT 0)
+        (^Box (E $ ^CaseBox One (^BV 0) (SN $ ^FT "A" 0) (SY [< "y"] (^BVT 0))))
+  ],
 
   "elim closure" :- [
     note "bold numbers for de bruijn indices",