248 lines
9.2 KiB
Idris
248 lines
9.2 KiB
Idris
module Tests.Typechecker
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import Quox.Syntax
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import Quox.Syntax.Qty.Three
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import Quox.Typechecker as Lib
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import public TypingImpls
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import TAP
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data Error'
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= TCError (Typing.Error Three)
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| WrongInfer (Term Three d n) (Term Three d n)
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| WrongQOut (QOutput Three n) (QOutput Three n)
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export
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ToInfo Error' where
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toInfo (TCError e) = toInfo e
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toInfo (WrongInfer good bad) =
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[("type", "WrongInfer"),
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("wanted", prettyStr True good),
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("got", prettyStr True bad)]
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toInfo (WrongQOut good bad) =
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[("type", "WrongQOut"),
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("wanted", prettyStr True good),
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("wanted", prettyStr True bad)]
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0 M : Type -> Type
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M = ReaderT (Definitions Three) $ Either Error'
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inj : (forall m. CanTC Three m => m a) -> M a
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inj act = do
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env <- ask
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let res = runReaderT env act {m = Either (Typing.Error Three)}
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either (throwError . TCError) pure res
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reflTy : IsQty q => Term q d n
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reflTy =
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Pi zero "A" (TYPE 0) $ TUsed $
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Pi one "x" (BVT 0) $ TUsed $
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Eq0 (BVT 1) (BVT 0) (BVT 0)
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reflDef : IsQty q => Term q d n
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reflDef = ["A","x"] :\\ ["i"] :\\% BVT 0
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defGlobals : Definitions Three
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defGlobals = fromList
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[("A", mkAbstract Zero $ TYPE 0),
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("B", mkAbstract Zero $ TYPE 0),
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("C", mkAbstract Zero $ TYPE 1),
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("D", mkAbstract Zero $ TYPE 1),
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("P", mkAbstract Zero $ Arr Any (FT "A") (TYPE 0)),
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("a", mkAbstract Any $ FT "A"),
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("a'", mkAbstract Any $ FT "A"),
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("b", mkAbstract Any $ FT "B"),
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("f", mkAbstract Any $ Arr One (FT "A") (FT "A")),
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("g", mkAbstract Any $ Arr One (FT "A") (FT "B")),
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("f2", mkAbstract Any $ Arr One (FT "A") $ Arr One (FT "A") (FT "A")),
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("p", mkAbstract Any $ Pi One "x" (FT "A") $ TUsed $ E $ F "P" :@ BVT 0),
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("q", mkAbstract Any $ Pi One "x" (FT "A") $ TUsed $ E $ F "P" :@ BVT 0),
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("refl", mkDef Any reflTy reflDef)]
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parameters (label : String) (act : Lazy (M ()))
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{default defGlobals globals : Definitions Three}
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testTC : Test
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testTC = test label $ runReaderT globals act
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testTCFail : Test
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testTCFail = testThrows label (const True) $ runReaderT globals act
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ctx : TContext Three 0 n -> TyContext Three 0 n
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ctx = MkTyContext DNil
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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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catchError
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(inj $ equalType (makeDimEq ctx.dctx) ctx.tctx exp got)
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(\_ : Error' => throwError $ WrongInfer exp got)
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qoutEq : (exp, got : QOutput Three n) -> M ()
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qoutEq qout res = unless (qout == res) $ throwError $ WrongQOut qout res
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inferAs : TyContext Three d n -> (sg : SQty Three) ->
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Elim Three d n -> Term Three d n -> M ()
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inferAs ctx sg e ty = do
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res <- inj $ infer ctx sg e
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inferredTypeEq ctx ty res.type
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inferAsQ : TyContext Three d n -> (sg : SQty Three) ->
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Elim Three d n -> Term Three d n -> QOutput Three n -> M ()
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inferAsQ ctx sg e ty qout = do
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res <- inj $ infer ctx sg e
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inferredTypeEq ctx ty res.type
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qoutEq qout res.qout
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infer_ : TyContext Three d n -> (sg : SQty Three) -> Elim Three d n -> M ()
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infer_ ctx sg e = ignore $ inj $ infer ctx sg e
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checkQ : TyContext Three d n -> SQty Three ->
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Term Three d n -> Term Three d n -> QOutput Three n -> M ()
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checkQ ctx sg s ty qout = do
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res <- inj $ check ctx sg s ty
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qoutEq qout res
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check_ : TyContext Three d n -> SQty Three ->
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Term Three d n -> Term Three d n -> M ()
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check_ ctx sg s ty = ignore $ inj $ check ctx sg s ty
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export
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tests : Test
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tests = "typechecker" :- [
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"universes" :- [
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testTC "0 · ★₀ ⇐ ★₁" $ check_ (ctx [<]) szero (TYPE 0) (TYPE 1),
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testTC "0 · ★₀ ⇐ ★₂" $ check_ (ctx [<]) szero (TYPE 0) (TYPE 2),
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testTC "0 · ★₀ ⇐ ★_" $ check_ (ctx [<]) szero (TYPE 0) (TYPE UAny),
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testTCFail "0 · ★₁ ⇍ ★₀" $ check_ (ctx [<]) szero (TYPE 1) (TYPE 0),
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testTCFail "0 · ★₀ ⇍ ★₀" $ check_ (ctx [<]) szero (TYPE 0) (TYPE 0),
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testTCFail "0 · ★_ ⇍ ★_" $ check_ (ctx [<]) szero (TYPE UAny) (TYPE UAny),
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testTCFail "1 · ★₀ ⇍ ★₁" $ check_ (ctx [<]) 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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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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testTC "0 · C ⊸ D ⇐ ★₁" $
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check_ (ctx [<]) 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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testTC "0 · (1·x : A) → P x ⇐ ★₀" $
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check_ (ctx [<]) szero
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(Pi One "x" (FT "A") $ TUsed $ 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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],
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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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testTCFail "1 · A × A ⇍ ★₀" $
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check_ (ctx [<]) sone (FT "A" `And` FT "A") (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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testTC "0 · [A] ⇐ ★₀" $
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check_ (ctx [<]) 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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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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note "refl : (0·A : ★₀) → (1·x : A) → (x ≡ x : A) ≔ (λ A x ⇒ λᴰ _ ⇒ 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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],
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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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(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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note "f2 : A ⊸ A ⊸ A",
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testTC "x : A ⊢ 1 · f2 [x] [x] ⇒ A ⊳ ω·x" $
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inferAsQ {n = 1} (ctx [< FT "A"]) sone
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(F "f2" :@@ [BVT 0, BVT 0]) (FT "A") [< 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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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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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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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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testTC "1 · (λ A x ⇒ refl A x) ⇐ ⋯ # (type of refl)" $
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check_ (ctx [<]) 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 ⇒ λᴰ i ⇒ x) ⇐ ⋯ # (def. and type of refl)" $
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check_ (ctx [<]) sone reflDef reflTy
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],
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"equalities" :- [
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testTC "1 · (λᴰ i ⇒ a) ⇐ a ≡ a" $
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check_ (ctx [<]) sone (DLam "i" $ DUnused $ FT "a")
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(Eq0 (FT "A") (FT "a") (FT "a")),
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testTC "0 · (λ p q ⇒ λᴰ i ⇒ p) ⇐ (ω·p q : a ≡ a') → p ≡ q" $
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check_ (ctx [<]) szero
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(Lam "p" $ TUsed $ Lam "q" $ TUnused $
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DLam "i" $ DUnused $ BVT 0)
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(Pi Any "p" (Eq0 (FT "A") (FT "a") (FT "a")) $ TUsed $
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Pi Any "q" (Eq0 (FT "A") (FT "a") (FT "a")) $ TUsed $
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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 ⇒ λᴰ i ⇒ q) ⇐ (ω·p q : a ≡ a') → p ≡ q" $
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check_ (ctx [<]) szero
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(Lam "p" $ TUnused $ Lam "q" $ TUsed $
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DLam "i" $ DUnused $ BVT 0)
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(Pi Any "p" (Eq0 (FT "A") (FT "a") (FT "a")) $ TUsed $
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Pi Any "q" (Eq0 (FT "A") (FT "a") (FT "a")) $ TUsed $
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Eq0 (Eq0 (FT "A") (FT "a") (FT "a")) (BVT 1) (BVT 0))
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],
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"misc" :- [
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note "0·A : Type, 0·P : A → Type, ω·p : (1·x : A) → P x",
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note "⊢",
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note "1 · λ x y xy ⇒ λᴰ i ⇒ p (xy i)",
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note " ⇐ (0·x y : A) → (1·xy : x ≡ y) → Eq [i ⇒ P (xy i)] (p x) (p y)",
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testTC "cong" $
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check_ (ctx [<]) sone
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(["x", "y", "xy"] :\\ ["i"] :\\% E (F "p" :@ E (BV 0 :% BV 0)))
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(Pi Zero "x" (FT "A") $ TUsed $
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Pi Zero "y" (FT "A") $ TUsed $
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Pi One "xy" (Eq0 (FT "A") (BVT 1) (BVT 0)) $ TUsed $
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Eq "i" (DUsed $ E $ F "P" :@ E (BV 0 :% BV 0))
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(E $ F "p" :@ BVT 2) (E $ F "p" :@ BVT 1)),
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note "0·A : Type, 0·P : ω·A → Type,",
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note "ω·p q : (1·x : A) → P x",
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note "⊢",
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note "1 · λ eq ⇒ λᴰ i ⇒ λ x ⇒ eq x i",
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note " ⇐ (1·eq : (1·x : A) → p x ≡ q x) → p ≡ q",
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testTC "funext" $
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check_ (ctx [<]) sone
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(["eq"] :\\ ["i"] :\\% ["x"] :\\ E (BV 1 :@ BVT 0 :% BV 0))
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(Pi One "eq"
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(Pi One "x" (FT "A") $ TUsed $
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Eq0 (E $ F "P" :@ BVT 0)
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(E $ F "p" :@ BVT 0) (E $ F "q" :@ BVT 0)) $ TUsed $
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Eq0 (Pi Any "x" (FT "A") $ TUsed $ E $ F "P" :@ BVT 0)
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(FT "p") (FT "q"))
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]
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]
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