typed equality
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8 changed files with 410 additions and 250 deletions
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@ -26,11 +26,17 @@ ToInfo (Error Three) where
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[("type", "BadUniverse"),
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("low", show k),
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("high", show l)]
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toInfo (ClashT mode s t) =
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toInfo (ClashT mode ty s t) =
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[("type", "ClashT"),
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("mode", show mode),
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("ty", prettyStr True ty),
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("left", prettyStr True s),
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("right", prettyStr True t)]
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toInfo (ClashE mode e f) =
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[("type", "ClashE"),
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("mode", show mode),
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("left", prettyStr True e),
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("right", prettyStr True f)]
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toInfo (ClashU mode k l) =
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[("type", "ClashU"),
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("mode", show mode),
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@ -44,13 +50,29 @@ ToInfo (Error Three) where
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[("type", "ClashD"),
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("left", prettyStr True p),
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("right", prettyStr True q)]
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toInfo (NotType ty) =
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[("type", "NotType"),
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("actual", prettyStr True ty)]
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toInfo (WrongType ty s t) =
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[("type", "WrongType"),
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("ty", prettyStr True ty),
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("left", prettyStr True s),
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("right", prettyStr True t)]
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0 M : Type -> Type
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M = ReaderT (Definitions Three) (Either (Error Three))
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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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("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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parameters (label : String) (act : Lazy (M ()))
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{default empty globals : Definitions Three}
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{default defGlobals globals : Definitions Three}
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testEq : Test
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testEq = test label $ runReaderT globals act
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@ -60,17 +82,18 @@ parameters (label : String) (act : Lazy (M ()))
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parameters {default 0 d, n : Nat}
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{default new eqs : DimEq d}
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subT : Term Three d n -> Term Three d n -> M ()
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subT s t = Term.sub !ask eqs s t
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(ctx : TContext Three d n)
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subT : Term Three d n -> Term Three d n -> Term Three d n -> M ()
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subT ty s t = Term.sub eqs ctx ty s t
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equalT : Term Three d n -> Term Three d n -> M ()
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equalT s t = Term.equal !ask eqs s t
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equalT : Term Three d n -> Term Three d n -> Term Three d n -> M ()
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equalT ty s t = Term.equal eqs ctx ty s t
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subE : Elim Three d n -> Elim Three d n -> M ()
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subE e f = Elim.sub !ask eqs e f
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subE e f = Elim.sub eqs ctx e f
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equalE : Elim Three d n -> Elim Three d n -> M ()
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equalE e f = Elim.equal !ask eqs e f
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equalE e f = Elim.equal eqs ctx e f
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export
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@ -80,17 +103,17 @@ tests = "equality & subtyping" :- [
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"universes" :- [
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testEq "★₀ ≡ ★₀" $
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equalT (TYPE 0) (TYPE 0),
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equalT [<] (TYPE 1) (TYPE 0) (TYPE 0),
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testNeq "★₀ ≢ ★₁" $
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equalT (TYPE 0) (TYPE 1),
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equalT [<] (TYPE 2) (TYPE 0) (TYPE 1),
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testNeq "★₁ ≢ ★₀" $
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equalT (TYPE 1) (TYPE 0),
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equalT [<] (TYPE 2) (TYPE 1) (TYPE 0),
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testEq "★₀ <: ★₀" $
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subT (TYPE 0) (TYPE 0),
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subT [<] (TYPE 1) (TYPE 0) (TYPE 0),
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testEq "★₀ <: ★₁" $
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subT (TYPE 0) (TYPE 1),
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subT [<] (TYPE 2) (TYPE 0) (TYPE 1),
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testNeq "★₁ ≮: ★₀" $
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subT (TYPE 1) (TYPE 0)
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subT [<] (TYPE 2) (TYPE 1) (TYPE 0)
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],
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"pi" :- [
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@ -98,79 +121,91 @@ tests = "equality & subtyping" :- [
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note #""A ⇾ B" for (0 _ : A) → B"#,
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testEq "A ⊸ B ≡ A ⊸ B" $
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let tm = Arr One (FT "A") (FT "B") in
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equalT tm tm,
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equalT [<] (TYPE 0) tm tm,
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testNeq "A ⇾ B ≢ A ⊸ B" $
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let tm1 = Arr Zero (FT "A") (FT "B")
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tm2 = Arr One (FT "A") (FT "B") in
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equalT tm1 tm2,
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equalT [<] (TYPE 0) tm1 tm2,
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testEq "0=1 ⊢ A ⇾ B ≢ A ⊸ B" $
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let tm1 = Arr Zero (FT "A") (FT "B")
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tm2 = Arr One (FT "A") (FT "B") in
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equalT tm1 tm2 {eqs = ZeroIsOne},
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equalT [<] (TYPE 0) tm1 tm2 {eqs = ZeroIsOne},
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testEq "A ⊸ B <: A ⊸ B" $
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let tm = Arr One (FT "A") (FT "B") in
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subT tm tm,
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subT [<] (TYPE 0) tm tm,
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testNeq "A ⇾ B ≮: A ⊸ B" $
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let tm1 = Arr Zero (FT "A") (FT "B")
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tm2 = Arr One (FT "A") (FT "B") in
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subT tm1 tm2,
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subT [<] (TYPE 0) tm1 tm2,
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testEq "★₀ ⇾ ★₀ ≡ ★₀ ⇾ ★₀" $
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let tm = Arr Zero (TYPE 0) (TYPE 0) in
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equalT tm tm,
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equalT [<] (TYPE 1) tm tm,
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testEq "★₀ ⇾ ★₀ <: ★₀ ⇾ ★₀" $
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let tm = Arr Zero (TYPE 0) (TYPE 0) in
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subT tm tm,
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subT [<] (TYPE 1) tm tm,
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testNeq "★₁ ⊸ ★₀ ≢ ★₀ ⇾ ★₀" $
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let tm1 = Arr Zero (TYPE 1) (TYPE 0)
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tm2 = Arr Zero (TYPE 0) (TYPE 0) in
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equalT tm1 tm2,
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equalT [<] (TYPE 2) tm1 tm2,
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testEq "★₁ ⊸ ★₀ <: ★₀ ⊸ ★₀" $
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let tm1 = Arr One (TYPE 1) (TYPE 0)
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tm2 = Arr One (TYPE 0) (TYPE 0) in
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subT tm1 tm2,
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subT [<] (TYPE 2) tm1 tm2,
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testNeq "★₀ ⊸ ★₀ ≢ ★₀ ⇾ ★₁" $
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let tm1 = Arr Zero (TYPE 0) (TYPE 0)
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tm2 = Arr Zero (TYPE 0) (TYPE 1) in
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equalT tm1 tm2,
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equalT [<] (TYPE 2) tm1 tm2,
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testEq "★₀ ⊸ ★₀ <: ★₀ ⊸ ★₁" $
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let tm1 = Arr One (TYPE 0) (TYPE 0)
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tm2 = Arr One (TYPE 0) (TYPE 1) in
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subT tm1 tm2,
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subT [<] (TYPE 2) tm1 tm2,
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testEq "★₀ ⊸ ★₀ <: ★₀ ⊸ ★₁" $
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let tm1 = Arr One (TYPE 0) (TYPE 0)
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tm2 = Arr One (TYPE 0) (TYPE 1) in
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subT tm1 tm2
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subT [<] (TYPE 2) tm1 tm2
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],
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"lambda" :- [
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testEq "λ x ⇒ [x] ≡ λ x ⇒ [x]" $
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equalT (Lam "x" $ TUsed $ BVT 0) (Lam "x" $ TUsed $ BVT 0),
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equalT [<] (Arr One (FT "A") (FT "A"))
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(Lam "x" $ TUsed $ BVT 0)
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(Lam "x" $ TUsed $ BVT 0),
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testEq "λ x ⇒ [x] <: λ x ⇒ [x]" $
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equalT (Lam "x" $ TUsed $ BVT 0) (Lam "x" $ TUsed $ BVT 0),
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subT [<] (Arr One (FT "A") (FT "A"))
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(Lam "x" $ TUsed $ BVT 0)
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(Lam "x" $ TUsed $ BVT 0),
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testEq "λ x ⇒ [x] ≡ λ y ⇒ [y]" $
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equalT (Lam "x" $ TUsed $ BVT 0) (Lam "y" $ TUsed $ BVT 0),
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equalT [<] (Arr One (FT "A") (FT "A"))
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(Lam "x" $ TUsed $ BVT 0)
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(Lam "y" $ TUsed $ BVT 0),
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testEq "λ x ⇒ [x] <: λ y ⇒ [y]" $
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equalT (Lam "x" $ TUsed $ BVT 0) (Lam "y" $ TUsed $ BVT 0),
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equalT [<] (Arr One (FT "A") (FT "A"))
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(Lam "x" $ TUsed $ BVT 0)
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(Lam "y" $ TUsed $ BVT 0),
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testNeq "λ x y ⇒ [x] ≢ λ x y ⇒ [y]" $
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equalT (Lam "x" $ TUsed $ Lam "y" $ TUsed $ BVT 1)
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(Lam "x" $ TUsed $ Lam "y" $ TUsed $ BVT 0),
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equalT [<] (Arr One (FT "A") $ Arr One (FT "A") (FT "A"))
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(Lam "x" $ TUsed $ Lam "y" $ TUsed $ BVT 1)
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(Lam "x" $ TUsed $ Lam "y" $ TUsed $ BVT 0),
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testEq "λ x ⇒ [a] ≡ λ x ⇒ [a] (TUsed vs TUnused)" $
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equalT (Lam "x" $ TUsed $ FT "a")
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(Lam "x" $ TUnused $ FT "a"),
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equalT [<] (Arr Zero (FT "B") (FT "A"))
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(Lam "x" $ TUsed $ FT "a")
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(Lam "x" $ TUnused $ FT "a"),
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skipWith "(no η yet)" $
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testEq "λ x ⇒ [f [x]] ≡ [f] (η)" $
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equalT (Lam "x" $ TUsed $ E $ F "f" :@ BVT 0)
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(FT "f")
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equalT [<] (Arr One (FT "A") (FT "A"))
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(Lam "x" $ TUsed $ E $ F "f" :@ BVT 0)
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(FT "f")
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],
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"eq type" :- [
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testEq "(★₀ = ★₀ : ★₁) ≡ (★₀ = ★₀ : ★₁)" $
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let tm = Eq0 (TYPE 1) (TYPE 0) (TYPE 0) in
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equalT tm tm,
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equalT [<] (TYPE 2) tm tm,
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testEq "A ≔ ★₁ ⊢ (★₀ = ★₀ : ★₁) ≡ (★₀ = ★₀ : A)"
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{globals = fromList [("A", mkDef zero (TYPE 2) (TYPE 1))]} $
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equalT (Eq0 (TYPE 1) (TYPE 0) (TYPE 0))
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(Eq0 (FT "A") (TYPE 0) (TYPE 0))
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equalT [<] (TYPE 2)
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(Eq0 (TYPE 1) (TYPE 0) (TYPE 0))
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(Eq0 (FT "A") (TYPE 0) (TYPE 0))
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],
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todo "dim lambda",
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@ -178,17 +213,25 @@ tests = "equality & subtyping" :- [
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"term closure" :- [
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note "𝑖, 𝑗 for bound variables pointing outside of the current expr",
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testEq "[𝑖]{} ≡ [𝑖]" $
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equalT (CloT (BVT 0) id) (BVT 0) {n = 1},
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equalT [< FT "A"] (FT "A") {n = 1}
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(CloT (BVT 0) id)
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(BVT 0),
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testEq "[𝑖]{a/𝑖} ≡ [a]" $
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equalT (CloT (BVT 0) (F "a" ::: id)) (FT "a"),
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equalT [<] (FT "A")
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(CloT (BVT 0) (F "a" ::: id))
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(FT "a"),
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testEq "[𝑖]{a/𝑖,b/𝑗} ≡ [a]" $
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equalT (CloT (BVT 0) (F "a" ::: F "b" ::: id)) (FT "a"),
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equalT [<] (FT "A")
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(CloT (BVT 0) (F "a" ::: F "b" ::: id))
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(FT "a"),
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testEq "(λy. [𝑖]){y/y, a/𝑖} ≡ λy. [a] (TUnused)" $
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equalT (CloT (Lam "y" $ TUnused $ BVT 0) (F "a" ::: id))
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(Lam "y" $ TUnused $ FT "a"),
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equalT [<] (Arr Zero (FT "B") (FT "A"))
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(CloT (Lam "y" $ TUnused $ BVT 0) (F "a" ::: id))
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(Lam "y" $ TUnused $ FT "a"),
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testEq "(λy. [𝑖]){y/y, a/𝑖} ≡ λy. [a] (TUsed)" $
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equalT (CloT (Lam "y" $ TUsed $ BVT 1) (F "a" ::: id))
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(Lam "y" $ TUsed $ FT "a")
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equalT [<] (Arr Zero (FT "B") (FT "A"))
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(CloT (Lam "y" $ TUsed $ BVT 1) (F "a" ::: id))
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(Lam "y" $ TUsed $ FT "a")
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],
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todo "term d-closure",
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@ -202,73 +245,74 @@ tests = "equality & subtyping" :- [
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("B", mkDef Any (TYPE (U 1)) (FT "A"))]
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in [
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testEq "A ≡ A" $
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equalE (F "A") (F "A"),
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equalE [<] (F "A") (F "A"),
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testNeq "A ≢ B" $
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equalE (F "A") (F "B"),
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equalE [<] (F "A") (F "B"),
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testEq "0=1 ⊢ A ≡ B" $
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equalE {eqs = ZeroIsOne} (F "A") (F "B"),
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equalE {eqs = ZeroIsOne} [<] (F "A") (F "B"),
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testEq "A : ★₁ ≔ ★₀ ⊢ A ≡ (★₀ ∷ ★₁)" {globals = au_bu} $
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equalE (F "A") (TYPE 0 :# TYPE 1),
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equalE [<] (F "A") (TYPE 0 :# TYPE 1),
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testEq "A ≔ ★₀, B ≔ ★₀ ⊢ A ≡ B" {globals = au_bu} $
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equalE (F "A") (F "B"),
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equalE [<] (F "A") (F "B"),
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testEq "A ≔ ★₀, B ≔ A ⊢ A ≡ B" {globals = au_ba} $
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equalE (F "A") (F "B"),
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equalE [<] (F "A") (F "B"),
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testEq "A <: A" $
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subE (F "A") (F "A"),
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subE [<] (F "A") (F "A"),
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testNeq "A ≮: B" $
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subE (F "A") (F "B"),
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subE [<] (F "A") (F "B"),
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testEq "A : ★₃ ≔ ★₀, B : ★₃ ≔ ★₂ ⊢ A <: B"
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{globals = fromList [("A", mkDef Any (TYPE 3) (TYPE 0)),
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("B", mkDef Any (TYPE 3) (TYPE 2))]} $
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subE (F "A") (F "B"),
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subE [<] (F "A") (F "B"),
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testEq "A : ★₁👈 ≔ ★₀, B : ★₃ ≔ ★₂ ⊢ A <: B"
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{globals = fromList [("A", mkDef Any (TYPE 1) (TYPE 0)),
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("B", mkDef Any (TYPE 3) (TYPE 2))]} $
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subE (F "A") (F "B"),
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subE [<] (F "A") (F "B"),
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testEq "0=1 ⊢ A <: B" $
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subE (F "A") (F "B") {eqs = ZeroIsOne}
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subE [<] (F "A") (F "B") {eqs = ZeroIsOne}
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],
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"bound var" :- [
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note "𝑖, 𝑗 for distinct bound variables",
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testEq "𝑖 ≡ 𝑖" $
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equalE (BV 0) (BV 0) {n = 1},
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equalE [< TYPE 0] (BV 0) (BV 0) {n = 1},
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testNeq "𝑖 ≢ 𝑗" $
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equalE (BV 0) (BV 1) {n = 2},
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equalE [< TYPE 0, TYPE 0] (BV 0) (BV 1) {n = 2},
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testEq "0=1 ⊢ 𝑖 ≡ 𝑗" $
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equalE {n = 2, eqs = ZeroIsOne} (BV 0) (BV 1)
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equalE [< TYPE 0, TYPE 0] (BV 0) (BV 1)
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{n = 2, eqs = ZeroIsOne}
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],
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"application" :- [
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testEq "f [a] ≡ f [a]" $
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equalE (F "f" :@ FT "a") (F "f" :@ FT "a"),
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equalE [<] (F "f" :@ FT "a") (F "f" :@ FT "a"),
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testEq "f [a] <: f [a]" $
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subE (F "f" :@ FT "a") (F "f" :@ FT "a"),
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subE [<] (F "f" :@ FT "a") (F "f" :@ FT "a"),
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testEq "(λ x ⇒ [x] ∷ A ⊸ A) a ≡ ([a ∷ A] ∷ A) (β)" $
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equalE
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equalE [<]
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((Lam "x" (TUsed (BVT 0)) :# (Arr One (FT "A") (FT "A")))
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:@ FT "a")
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(E (FT "a" :# FT "A") :# FT "A"),
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testEq "(λ x ⇒ [x] ∷ A ⊸ A) a ≡ a (βυ)" $
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equalE
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equalE [<]
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((Lam "x" (TUsed (BVT 0)) :# (Arr One (FT "A") (FT "A")))
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:@ FT "a")
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(F "a"),
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testEq "(λ g ⇒ [g [x]] ∷ ⋯)) [f] ≡ (λ y ⇒ [f [y]] ∷ ⋯) [x] (β↘↙)" $
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testEq "(λ g ⇒ [g [a]] ∷ ⋯)) [f] ≡ (λ y ⇒ [f [y]] ∷ ⋯) [a] (β↘↙)" $
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let a = FT "A"; a2a = (Arr One a a) in
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equalE
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((Lam "g" (TUsed (E (BV 0 :@ FT "x"))) :# Arr One a2a a) :@ FT "f")
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((Lam "y" (TUsed (E (F "f" :@ BVT 0))) :# a2a) :@ FT "x"),
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equalE [<]
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((Lam "g" (TUsed (E (BV 0 :@ FT "a"))) :# Arr One a2a a) :@ FT "f")
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((Lam "y" (TUsed (E (F "f" :@ BVT 0))) :# a2a) :@ FT "a"),
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testEq "(λ x ⇒ [x] ∷ A ⊸ A) a <: a" $
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subE
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subE [<]
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((Lam "x" (TUsed (BVT 0)) :# (Arr One (FT "A") (FT "A")))
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:@ FT "a")
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(F "a"),
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testEq "f : A ⊸ A ≔ λ x ⇒ [x] ⊢ f [x] ≡ x"
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{globals = fromList
|
||||
[("f", mkDef Any (Arr One (FT "A") (FT "A"))
|
||||
testEq "id : A ⊸ A ≔ λ x ⇒ [x] ⊢ id [a] ≡ a"
|
||||
{globals = defGlobals `mergeLeft` fromList
|
||||
[("id", mkDef Any (Arr One (FT "A") (FT "A"))
|
||||
(Lam "x" (TUsed (BVT 0))))]} $
|
||||
equalE (F "f" :@ FT "x") (F "x")
|
||||
equalE [<] (F "id" :@ FT "a") (F "a")
|
||||
],
|
||||
|
||||
"dim application" :-
|
||||
|
|
@ -277,13 +321,16 @@ tests = "equality & subtyping" :- [
|
|||
in
|
||||
[
|
||||
note #""refl [A] x" is an abbreviation for "(λᴰi ⇒ x) ∷ (x ≡ x : A)""#,
|
||||
testEq "refl [A] x ≡ refl [A] x" $
|
||||
equalE (refl (FT "A") (FT "x")) (refl (FT "A") (FT "x")),
|
||||
testEq "refl [A] a ≡ refl [A] a" $
|
||||
equalE [<] (refl (FT "A") (FT "a")) (refl (FT "A") (FT "a")),
|
||||
testEq "p : (a ≡ b : A), q : (a ≡ b : A) ⊢ p ≡ q"
|
||||
{globals =
|
||||
let def = mkAbstract Zero $ Eq0 (FT "A") (FT "a") (FT "b") in
|
||||
fromList [("p", def), ("q", def)]} $
|
||||
equalE (F "p") (F "q")
|
||||
fromList [("A", mkAbstract Zero $ TYPE 0),
|
||||
("a", mkAbstract Any $ FT "A"),
|
||||
("b", mkAbstract Any $ FT "A"),
|
||||
("p", def), ("q", def)]} $
|
||||
equalE [<] (F "p") (F "q")
|
||||
],
|
||||
|
||||
todo "annotation",
|
||||
|
|
@ -294,9 +341,10 @@ tests = "equality & subtyping" :- [
|
|||
|
||||
"clashes" :- [
|
||||
testNeq "★₀ ≢ ★₀ ⇾ ★₀" $
|
||||
equalT (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0)),
|
||||
equalT [<] (TYPE 1) (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0)),
|
||||
testEq "0=1 ⊢ ★₀ ≡ ★₀ ⇾ ★₀" $
|
||||
equalT (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0)) {eqs = ZeroIsOne},
|
||||
equalT [<] (TYPE 1) (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0))
|
||||
{eqs = ZeroIsOne},
|
||||
todo "others"
|
||||
]
|
||||
]
|
||||
|
|
|
|||
|
|
@ -27,16 +27,16 @@ testNoStep whnf label e = test "\{label} (no step)" $
|
|||
|
||||
parameters {default empty defs : Definitions Three} {default 0 d, n : Nat}
|
||||
testWhnfT : String -> Term Three d n -> Term Three d n -> Test
|
||||
testWhnfT = testWhnf (whnf defs)
|
||||
testWhnfT = testWhnf (whnfD defs)
|
||||
|
||||
testWhnfE : String -> Elim Three d n -> Elim Three d n -> Test
|
||||
testWhnfE = testWhnf (whnf defs)
|
||||
testWhnfE = testWhnf (whnfD defs)
|
||||
|
||||
testNoStepE : String -> Elim Three d n -> Test
|
||||
testNoStepE = testNoStep (whnf defs)
|
||||
testNoStepE = testNoStep (whnfD defs)
|
||||
|
||||
testNoStepT : String -> Term Three d n -> Test
|
||||
testNoStepT = testNoStep (whnf defs)
|
||||
testNoStepT = testNoStep (whnfD defs)
|
||||
|
||||
|
||||
tests = "whnf" :- [
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue