put names into contexts, and contexts into errors
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13 changed files with 520 additions and 324 deletions
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@ -98,9 +98,12 @@ parameters (label : String) (act : Lazy (M ()))
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testTCFail = testThrows label (const True) $ runReaderT globals act
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ctx, ctx01 : TContext Three 0 n -> TyContext Three 0 n
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ctx = MkTyContext new
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ctx01 = MkTyContext ZeroIsOne
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ctx, ctx01 : Context (\n => (BaseName, Term Three 0 n)) n -> TyContext Three 0 n
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ctx tel = MkTyContext new [<] (map snd tel) (map fst tel)
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ctx01 tel = MkTyContext ZeroIsOne [<] (map snd tel) (map fst tel)
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empty01 : TyContext Three 0 0
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empty01 = {dctx := ZeroIsOne} empty
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inferredTypeEq : TyContext Three d n -> (exp, got : Term Three d n) -> M ()
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inferredTypeEq ctx exp got =
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@ -159,184 +162,184 @@ tests : Test
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tests = "typechecker" :- [
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"universes" :- [
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testTC "0 · ★₀ ⇐ ★₁ # by checkType" $
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checkType_ (ctx [<]) (TYPE 0) (Just 1),
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checkType_ empty (TYPE 0) (Just 1),
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testTC "0 · ★₀ ⇐ ★₁ # by check" $
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check_ (ctx [<]) szero (TYPE 0) (TYPE 1),
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check_ empty szero (TYPE 0) (TYPE 1),
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testTC "0 · ★₀ ⇐ ★₂" $
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checkType_ (ctx [<]) (TYPE 0) (Just 2),
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checkType_ empty (TYPE 0) (Just 2),
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testTC "0 · ★₀ ⇐ ★_" $
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checkType_ (ctx [<]) (TYPE 0) Nothing,
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checkType_ empty (TYPE 0) Nothing,
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testTCFail "0 · ★₁ ⇍ ★₀" $
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checkType_ (ctx [<]) (TYPE 1) (Just 0),
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checkType_ empty (TYPE 1) (Just 0),
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testTCFail "0 · ★₀ ⇍ ★₀" $
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checkType_ (ctx [<]) (TYPE 0) (Just 0),
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checkType_ empty (TYPE 0) (Just 0),
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testTC "0=1 ⊢ 0 · ★₁ ⇐ ★₀" $
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checkType_ (ctx01 [<]) (TYPE 1) (Just 0),
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checkType_ empty01 (TYPE 1) (Just 0),
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testTCFail "1 · ★₀ ⇍ ★₁ # by check" $
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check_ (ctx [<]) sone (TYPE 0) (TYPE 1)
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check_ empty sone (TYPE 0) (TYPE 1)
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],
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"function types" :- [
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note "A, B : ★₀; C, D : ★₁; P : A ⇾ ★₀",
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testTC "0 · A ⊸ B ⇐ ★₀" $
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check_ (ctx [<]) szero (Arr One (FT "A") (FT "B")) (TYPE 0),
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check_ empty szero (Arr One (FT "A") (FT "B")) (TYPE 0),
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note "subtyping",
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testTC "0 · A ⊸ B ⇐ ★₁" $
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check_ (ctx [<]) szero (Arr One (FT "A") (FT "B")) (TYPE 1),
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check_ empty szero (Arr One (FT "A") (FT "B")) (TYPE 1),
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testTC "0 · C ⊸ D ⇐ ★₁" $
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check_ (ctx [<]) szero (Arr One (FT "C") (FT "D")) (TYPE 1),
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check_ empty szero (Arr One (FT "C") (FT "D")) (TYPE 1),
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testTCFail "0 · C ⊸ D ⇍ ★₀" $
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check_ (ctx [<]) szero (Arr One (FT "C") (FT "D")) (TYPE 0),
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check_ empty szero (Arr One (FT "C") (FT "D")) (TYPE 0),
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testTC "0 · (1·x : A) → P x ⇐ ★₀" $
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check_ (ctx [<]) szero
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check_ empty szero
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(Pi_ One "x" (FT "A") $ E $ F "P" :@ BVT 0)
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(TYPE 0),
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testTCFail "0 · A ⊸ P ⇍ ★₀" $
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check_ (ctx [<]) szero (Arr One (FT "A") $ FT "P") (TYPE 0),
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check_ empty szero (Arr One (FT "A") $ FT "P") (TYPE 0),
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testTC "0=1 ⊢ 0 · A ⊸ P ⇐ ★₀" $
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check_ (ctx01 [<]) szero (Arr One (FT "A") $ FT "P") (TYPE 0)
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check_ empty01 szero (Arr One (FT "A") $ FT "P") (TYPE 0)
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],
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"pair types" :- [
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note #""A × B" for "(_ : A) × B""#,
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testTC "0 · A × A ⇐ ★₀" $
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check_ (ctx [<]) szero (FT "A" `And` FT "A") (TYPE 0),
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check_ empty szero (FT "A" `And` FT "A") (TYPE 0),
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testTCFail "0 · A × P ⇍ ★₀" $
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check_ (ctx [<]) szero (FT "A" `And` FT "P") (TYPE 0),
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check_ empty szero (FT "A" `And` FT "P") (TYPE 0),
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testTC "0 · (x : A) × P x ⇐ ★₀" $
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check_ (ctx [<]) szero
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check_ empty szero
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(Sig_ "x" (FT "A") $ E $ F "P" :@ BVT 0) (TYPE 0),
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testTC "0 · (x : A) × P x ⇐ ★₁" $
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check_ (ctx [<]) szero
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check_ empty szero
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(Sig_ "x" (FT "A") $ E $ F "P" :@ BVT 0) (TYPE 1),
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testTC "0 · (A : ★₀) × A ⇐ ★₁" $
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check_ (ctx [<]) szero (Sig_ "A" (TYPE 0) $ BVT 0) (TYPE 1),
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check_ empty szero (Sig_ "A" (TYPE 0) $ BVT 0) (TYPE 1),
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testTCFail "0 · (A : ★₀) × A ⇍ ★₀" $
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check_ (ctx [<]) szero (Sig_ "A" (TYPE 0) $ BVT 0) (TYPE 0),
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check_ empty szero (Sig_ "A" (TYPE 0) $ BVT 0) (TYPE 0),
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testTCFail "1 · A × A ⇍ ★₀" $
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check_ (ctx [<]) sone (FT "A" `And` FT "A") (TYPE 0)
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check_ empty sone (FT "A" `And` FT "A") (TYPE 0)
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],
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"enum types" :- [
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testTC "0 · {} ⇐ ★₀" $ check_ (ctx [<]) szero (enum []) (TYPE 0),
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testTC "0 · {} ⇐ ★₃" $ check_ (ctx [<]) szero (enum []) (TYPE 3),
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testTC "0 · {} ⇐ ★₀" $ check_ empty szero (enum []) (TYPE 0),
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testTC "0 · {} ⇐ ★₃" $ check_ empty szero (enum []) (TYPE 3),
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testTC "0 · {a,b,c} ⇐ ★₀" $
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check_ (ctx [<]) szero (enum ["a", "b", "c"]) (TYPE 0),
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check_ empty szero (enum ["a", "b", "c"]) (TYPE 0),
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testTC "0 · {a,b,c} ⇐ ★₃" $
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check_ (ctx [<]) szero (enum ["a", "b", "c"]) (TYPE 3),
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testTCFail "1 · {} ⇍ ★₀" $ check_ (ctx [<]) sone (enum []) (TYPE 0),
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testTC "0=1 ⊢ 1 · {} ⇐ ★₀" $ check_ (ctx01 [<]) sone (enum []) (TYPE 0)
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check_ empty szero (enum ["a", "b", "c"]) (TYPE 3),
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testTCFail "1 · {} ⇍ ★₀" $ check_ empty sone (enum []) (TYPE 0),
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testTC "0=1 ⊢ 1 · {} ⇐ ★₀" $ check_ empty01 sone (enum []) (TYPE 0)
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],
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"free vars" :- [
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note "A : ★₀",
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testTC "0 · A ⇒ ★₀" $
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inferAs (ctx [<]) szero (F "A") (TYPE 0),
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inferAs empty szero (F "A") (TYPE 0),
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testTC "0 · [A] ⇐ ★₀" $
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check_ (ctx [<]) szero (FT "A") (TYPE 0),
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check_ empty szero (FT "A") (TYPE 0),
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note "subtyping",
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testTC "0 · [A] ⇐ ★₁" $
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check_ (ctx [<]) szero (FT "A") (TYPE 1),
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check_ empty szero (FT "A") (TYPE 1),
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note "(fail) runtime-relevant type",
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testTCFail "1 · A ⇏ ★₀" $
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infer_ (ctx [<]) sone (F "A"),
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infer_ empty sone (F "A"),
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note "refl : (0·A : ★₀) → (1·x : A) → (x ≡ x : A) ≔ (λ A x ⇒ δ _ ⇒ x)",
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testTC "1 · refl ⇒ ⋯" $ inferAs (ctx [<]) sone (F "refl") reflTy,
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testTC "1 · [refl] ⇐ ⋯" $ check_ (ctx [<]) sone (FT "refl") reflTy
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testTC "1 · refl ⇒ ⋯" $ inferAs empty sone (F "refl") reflTy,
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testTC "1 · [refl] ⇐ ⋯" $ check_ empty sone (FT "refl") reflTy
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],
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"bound vars" :- [
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testTC "x : A ⊢ 1 · x ⇒ A ⊳ 1·x" $
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inferAsQ {n = 1} (ctx [< FT "A"]) sone
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inferAsQ {n = 1} (ctx [< ("x", FT "A")]) sone
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(BV 0) (FT "A") [< one],
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testTC "x : A ⊢ 1 · [x] ⇐ A ⊳ 1·x" $
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checkQ {n = 1} (ctx [< FT "A"]) sone (BVT 0) (FT "A") [< one],
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checkQ {n = 1} (ctx [< ("x", FT "A")]) sone (BVT 0) (FT "A") [< one],
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note "f2 : A ⊸ A ⊸ B",
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testTC "x : A ⊢ 1 · f2 [x] [x] ⇒ B ⊳ ω·x" $
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inferAsQ {n = 1} (ctx [< FT "A"]) sone
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inferAsQ {n = 1} (ctx [< ("x", FT "A")]) sone
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(F "f2" :@@ [BVT 0, BVT 0]) (FT "B") [< Any]
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],
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"lambda" :- [
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note "linear & unrestricted identity",
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testTC "1 · (λ x ⇒ x) ⇐ A ⊸ A" $
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check_ (ctx [<]) sone (["x"] :\\ BVT 0) (Arr One (FT "A") (FT "A")),
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check_ empty sone (["x"] :\\ BVT 0) (Arr One (FT "A") (FT "A")),
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testTC "1 · (λ x ⇒ x) ⇐ A → A" $
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check_ (ctx [<]) sone (["x"] :\\ BVT 0) (Arr Any (FT "A") (FT "A")),
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check_ empty sone (["x"] :\\ BVT 0) (Arr Any (FT "A") (FT "A")),
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note "(fail) zero binding used relevantly",
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testTCFail "1 · (λ x ⇒ x) ⇍ A ⇾ A" $
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check_ (ctx [<]) sone (["x"] :\\ BVT 0) (Arr Zero (FT "A") (FT "A")),
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check_ empty sone (["x"] :\\ BVT 0) (Arr Zero (FT "A") (FT "A")),
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note "(but ok in overall erased context)",
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testTC "0 · (λ x ⇒ x) ⇐ A ⇾ A" $
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check_ (ctx [<]) szero (["x"] :\\ BVT 0) (Arr Zero (FT "A") (FT "A")),
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check_ empty szero (["x"] :\\ BVT 0) (Arr Zero (FT "A") (FT "A")),
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testTC "1 · (λ A x ⇒ refl A x) ⇐ ⋯ # (type of refl)" $
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check_ (ctx [<]) sone
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check_ empty sone
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(["A", "x"] :\\ E (F "refl" :@@ [BVT 1, BVT 0]))
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reflTy,
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testTC "1 · (λ A x ⇒ δ i ⇒ x) ⇐ ⋯ # (def. and type of refl)" $
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check_ (ctx [<]) sone reflDef reflTy
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check_ empty sone reflDef reflTy
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],
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"pairs" :- [
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testTC "1 · (a, a) ⇐ A × A" $
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check_ (ctx [<]) sone (Pair (FT "a") (FT "a")) (FT "A" `And` FT "A"),
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check_ empty sone (Pair (FT "a") (FT "a")) (FT "A" `And` FT "A"),
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testTC "x : A ⊢ 1 · (x, x) ⇐ A × A ⊳ ω·x" $
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checkQ (ctx [< FT "A"]) sone
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checkQ (ctx [< ("x", FT "A")]) sone
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(Pair (BVT 0) (BVT 0)) (FT "A" `And` FT "A") [< Any],
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testTC "1 · (a, δ i ⇒ a) ⇐ (x : A) × (x ≡ a)" $
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check_ (ctx [<]) sone
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check_ empty sone
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(Pair (FT "a") (["i"] :\\% FT "a"))
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(Sig_ "x" (FT "A") $ Eq0 (FT "A") (BVT 0) (FT "a"))
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],
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"unpairing" :- [
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testTC "x : A × A ⊢ 1 · (case1 x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ 1·x" $
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inferAsQ (ctx [< FT "A" `And` FT "A"]) sone
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inferAsQ (ctx [< ("x", FT "A" `And` FT "A")]) sone
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(CasePair One (BV 0) (SN $ FT "B")
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(SY ["l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
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(FT "B") [< One],
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testTC "x : A × A ⊢ 1 · (caseω x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ ω·x" $
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inferAsQ (ctx [< FT "A" `And` FT "A"]) sone
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inferAsQ (ctx [< ("x", FT "A" `And` FT "A")]) sone
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(CasePair Any (BV 0) (SN $ FT "B")
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(SY ["l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
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(FT "B") [< Any],
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testTC "x : A × A ⊢ 0 · (caseω x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ 0·x" $
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inferAsQ (ctx [< FT "A" `And` FT "A"]) szero
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inferAsQ (ctx [< ("x", FT "A" `And` FT "A")]) szero
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(CasePair Any (BV 0) (SN $ FT "B")
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(SY ["l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
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(FT "B") [< Zero],
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testTCFail "x : A × A ⊢ 1 · (case0 x return B of (l,r) ⇒ f2 l r) ⇏" $
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infer_ (ctx [< FT "A" `And` FT "A"]) sone
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infer_ (ctx [< ("x", FT "A" `And` FT "A")]) sone
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(CasePair Zero (BV 0) (SN $ FT "B")
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(SY ["l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0])),
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testTC "x : A × B ⊢ 1 · (caseω x return A of (l,r) ⇒ l) ⇒ A ⊳ ω·x" $
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inferAsQ (ctx [< FT "A" `And` FT "B"]) sone
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inferAsQ (ctx [< ("x", FT "A" `And` FT "B")]) sone
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(CasePair Any (BV 0) (SN $ FT "A")
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(SY ["l", "r"] $ BVT 1))
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(FT "A") [< Any],
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testTC "x : A × B ⊢ 0 · (case1 x return A of (l,r) ⇒ l) ⇒ A ⊳ 0·x" $
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inferAsQ (ctx [< FT "A" `And` FT "B"]) szero
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inferAsQ (ctx [< ("x", FT "A" `And` FT "B")]) szero
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(CasePair One (BV 0) (SN $ FT "A")
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(SY ["l", "r"] $ BVT 1))
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(FT "A") [< Zero],
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testTCFail "x : A × B ⊢ 1 · (case1 x return A of (l,r) ⇒ l) ⇏" $
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infer_ (ctx [< FT "A" `And` FT "B"]) sone
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infer_ (ctx [< ("x", FT "A" `And` FT "B")]) sone
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(CasePair One (BV 0) (SN $ FT "A")
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(SY ["l", "r"] $ BVT 1)),
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note "fst : (0·A : ★₁) → (0·B : A ↠ ★₁) → ((x : A) × B x) ↠ A",
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note " ≔ (λ A B p ⇒ caseω p return A of (x, y) ⇒ x)",
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testTC "0 · ‹type of fst› ⇐ ★₂" $
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check_ (ctx [<]) szero fstTy (TYPE 2),
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check_ empty szero fstTy (TYPE 2),
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testTC "1 · ‹def of fst› ⇐ ‹type of fst›" $
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check_ (ctx [<]) sone fstDef fstTy,
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check_ empty sone fstDef fstTy,
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note "snd : (0·A : ★₁) → (0·B : A ↠ ★₁) → (ω·p : (x : A) × B x) → B (fst A B p)",
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note " ≔ (λ A B p ⇒ caseω p return p ⇒ B (fst A B p) of (x, y) ⇒ y)",
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testTC "0 · ‹type of snd› ⇐ ★₂" $
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check_ (ctx [<]) szero sndTy (TYPE 2),
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check_ empty szero sndTy (TYPE 2),
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testTC "1 · ‹def of snd› ⇐ ‹type of snd›" $
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check_ (ctx [<]) sone sndDef sndTy,
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check_ empty sone sndDef sndTy,
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testTC "0 · snd ★₀ (λ x ⇒ x) ⇒ (ω·p : (A : ★₀) × A) → fst ★₀ (λ x ⇒ x) p" $
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inferAs (ctx [<]) szero
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inferAs empty szero
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(F "snd" :@@ [TYPE 0, ["x"] :\\ BVT 0])
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(Pi_ Any "A" (Sig_ "A" (TYPE 0) $ BVT 0) $
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(E $ F "fst" :@@ [TYPE 0, ["x"] :\\ BVT 0, BVT 0]))
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@ -344,27 +347,27 @@ tests = "typechecker" :- [
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"enums" :- [
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testTC "1 · 'a ⇐ {a}" $
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check_ (ctx [<]) sone (Tag "a") (enum ["a"]),
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check_ empty sone (Tag "a") (enum ["a"]),
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testTC "1 · 'a ⇐ {a, b, c}" $
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check_ (ctx [<]) sone (Tag "a") (enum ["a", "b", "c"]),
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check_ empty sone (Tag "a") (enum ["a", "b", "c"]),
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testTCFail "1 · 'a ⇍ {b, c}" $
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check_ (ctx [<]) sone (Tag "a") (enum ["b", "c"]),
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check_ empty sone (Tag "a") (enum ["b", "c"]),
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testTC "0=1 ⊢ 1 · 'a ⇐ {b, c}" $
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check_ (ctx01 [<]) sone (Tag "a") (enum ["b", "c"])
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check_ empty01 sone (Tag "a") (enum ["b", "c"])
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],
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"equalities" :- [
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testTC "1 · (δ i ⇒ a) ⇐ a ≡ a" $
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check_ (ctx [<]) sone (DLam $ SN $ FT "a")
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check_ empty sone (DLam $ SN $ FT "a")
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(Eq0 (FT "A") (FT "a") (FT "a")),
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testTC "0 · (λ p q ⇒ δ i ⇒ p) ⇐ (ω·p q : a ≡ a') → p ≡ q" $
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check_ (ctx [<]) szero
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check_ empty szero
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(["p","q"] :\\ ["i"] :\\% BVT 1)
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(Pi_ Any "p" (Eq0 (FT "A") (FT "a") (FT "a")) $
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Pi_ Any "q" (Eq0 (FT "A") (FT "a") (FT "a")) $
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Eq0 (Eq0 (FT "A") (FT "a") (FT "a")) (BVT 1) (BVT 0)),
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testTC "0 · (λ p q ⇒ δ i ⇒ q) ⇐ (ω·p q : a ≡ a') → p ≡ q" $
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check_ (ctx [<]) szero
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check_ empty szero
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(["p","q"] :\\ ["i"] :\\% BVT 0)
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(Pi_ Any "p" (Eq0 (FT "A") (FT "a") (FT "a")) $
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Pi_ Any "q" (Eq0 (FT "A") (FT "a") (FT "a")) $
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@ -377,7 +380,7 @@ tests = "typechecker" :- [
|
|||
note "1 · λ x y xy ⇒ δ i ⇒ p (xy i)",
|
||||
note " ⇐ (0·x y : A) → (1·xy : x ≡ y) → Eq [i ⇒ P (xy i)] (p x) (p y)",
|
||||
testTC "cong" $
|
||||
check_ (ctx [<]) sone
|
||||
check_ empty sone
|
||||
(["x", "y", "xy"] :\\ ["i"] :\\% E (F "p" :@ E (BV 0 :% BV 0)))
|
||||
(Pi_ Zero "x" (FT "A") $
|
||||
Pi_ Zero "y" (FT "A") $
|
||||
|
|
@ -390,7 +393,7 @@ tests = "typechecker" :- [
|
|||
note "1 · λ eq ⇒ δ i ⇒ λ x ⇒ eq x i",
|
||||
note " ⇐ (1·eq : (1·x : A) → p x ≡ q x) → p ≡ q",
|
||||
testTC "funext" $
|
||||
check_ (ctx [<]) sone
|
||||
check_ empty sone
|
||||
(["eq"] :\\ ["i"] :\\% ["x"] :\\ E (BV 1 :@ BVT 0 :% BV 0))
|
||||
(Pi_ One "eq"
|
||||
(Pi_ One "x" (FT "A")
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue