more typed equality, uip, etc
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138
tests/Tests/Typechecker.idr
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138
tests/Tests/Typechecker.idr
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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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0 M : Type -> Type
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M = ReaderT (Definitions Three) $ Either (Error Three)
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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 zero "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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("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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("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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ctxWith : DContext d -> Context (\i => (Term Three d i, Three)) n ->
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TyContext Three d n
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ctxWith dctx tqctx =
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let (tctx, qctx) = unzip tqctx in MkTyContext {dctx, tctx, qctx}
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ctx : Context (\i => (Term Three 0 i, Three)) n -> TyContext Three 0 n
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ctx = ctxWith DNil
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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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ty' <- infer ctx sg e
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catchError
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(equalType (makeDimEq ctx.dctx) ctx.tctx ty ty'.type)
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(\_ : Error Three => throwError $ ClashT Equal (TYPE UAny) ty ty'.type)
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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 $ infer ctx sg e
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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 $ 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",
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testTC "0 · (1·A) → B ⇐ ★₀" $
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check_ (ctx [<]) szero (Arr One (FT "A") (FT "B")) (TYPE 0),
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testTC "0 · (1·A) → B ⇐ ★₁👈" $
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check_ (ctx [<]) szero (Arr One (FT "A") (FT "B")) (TYPE 1),
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testTC "0 · (1·C) → D ⇐ ★₁" $
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check_ (ctx [<]) szero (Arr One (FT "C") (FT "D")) (TYPE 1),
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testTCFail "0 · (1·C) → D ⇍ ★₀" $
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check_ (ctx [<]) szero (Arr One (FT "C") (FT "D")) (TYPE 0)
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],
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"free vars" :- [
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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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testTC "0 · A ⇐ ★₁👈" $
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check_ (ctx [<]) szero (FT "A") (TYPE 1),
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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) → (0·x : A) → (x ≡ x : A) ≔ (λ A x ⇒ λᴰ _ ⇒ x)",
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testTC "1 · refl ⇒ {type of refl}" $
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inferAs (ctx [<]) sone (F "refl") reflTy,
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testTC "1 · refl ⇐ {type of refl}" $
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check_ (ctx [<]) sone (FT "refl") reflTy
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],
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"lambda" :- [
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testTC #"1 · (λ A x ⇒ refl A x) ⇐ {type of refl, see "free vars"}"# $
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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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],
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"misc" :- [
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testTC "funext"
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{globals = fromList
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[("A", mkAbstract Zero $ TYPE 0),
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("B", mkAbstract Zero $ Arr Any (FT "A") (TYPE 0)),
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("f", mkAbstract Any $
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Pi Any "x" (FT "A") $ TUsed $ E $ F "B" :@ BVT 0),
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("g", mkAbstract Any $
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Pi Any "x" (FT "A") $ TUsed $ E $ F "B" :@ BVT 0)]} $
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-- 0·A : Type, 0·B : ω·A → Type,
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-- ω·f, g : (ω·x : A) → B x
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-- ⊢
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-- 0·funext : (ω·eq : (0·x : A) → f x ≡ g x) → f ≡ g
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-- = λ eq ⇒ λᴰ i ⇒ λ x ⇒ eq x i
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check_ (ctx [<]) szero
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(["eq"] :\\ ["i"] :\\% ["x"] :\\ E (BV 1 :@ BVT 0 :% BV 0))
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(Pi Any "eq"
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(Pi Zero "x" (FT "A") $ TUsed $
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Eq0 (E $ F "B" :@ BVT 0)
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(E $ F "f" :@ BVT 0) (E $ F "g" :@ BVT 0)) $ TUsed $
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Eq0 (Pi Any "x" (FT "A") $ TUsed $ E $ F "B" :@ BVT 0)
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(FT "f") (FT "g"))
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]
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]
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