some equality tests
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@ -7,17 +7,17 @@ import TAP
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export
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ToInfo Equal.Error where
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toInfo (ClashT mode s t) =
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[("clash", "term"),
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("mode", show mode),
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[("clash", "term"),
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("mode", show mode),
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("left", prettyStr True s),
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("right", prettyStr True t)]
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toInfo (ClashU mode k l) =
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[("clash", "universe"),
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("mode", show mode),
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[("clash", "universe"),
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("mode", show mode),
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("left", prettyStr True k),
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("right", prettyStr True l)]
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toInfo (ClashQ pi rh) =
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[("clash", "quantity"),
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[("clash", "quantity"),
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("left", prettyStr True pi),
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("right", prettyStr True rh)]
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@ -52,50 +52,126 @@ export
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tests : Test
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tests = "equality & subtyping" :- [
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"universes" :- [
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testEq "Type 0 == Type 0" $
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equalT (TYPE (U 0)) (TYPE (U 0)),
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testNeq "Type 0 =/= Type 1" $
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equalT (TYPE (U 0)) (TYPE (U 1)),
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testNeq "Type 1 =/= Type 0" $
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equalT (TYPE (U 1)) (TYPE (U 0)),
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testEq "Type 0 <: Type 0" $
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subT (TYPE (U 0)) (TYPE (U 0)),
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testEq "Type 0 <: Type 1" $
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subT (TYPE (U 0)) (TYPE (U 1)),
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testNeq "Type 1 </: Type 0" $
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subT (TYPE (U 1)) (TYPE (U 0))
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testEq "𝒰₀ ≡ 𝒰₀" $
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equalT (TYPE 0) (TYPE 0),
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testNeq "𝒰₀ ≢ 𝒰₁" $
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equalT (TYPE 0) (TYPE 1),
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testNeq "𝒰₁ ≢ 𝒰₀" $
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equalT (TYPE 1) (TYPE 0),
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testEq "𝒰₀ <: 𝒰₀" $
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subT (TYPE 0) (TYPE 0),
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testEq "𝒰₀ <: 𝒰₁" $
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subT (TYPE 0) (TYPE 1),
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testNeq "𝒰₁ ≮: 𝒰₀" $
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subT (TYPE 1) (TYPE 0)
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],
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todo "pi",
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todo "lambda",
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"pi" :- [
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-- ⊸ for →₁, ⇾ for →₀
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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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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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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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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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testEq "𝒰₀ ⇾ 𝒰₀ ≡ 𝒰₀ ⇾ 𝒰₀" $
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let tm = Arr Zero (TYPE 0) (TYPE 0) in
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equalT tm tm,
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testEq "𝒰₀ ⇾ 𝒰₀ <: 𝒰₀ ⇾ 𝒰₀" $
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let tm = Arr Zero (TYPE 0) (TYPE 0) in
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subT tm tm,
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testNeq "𝒰₁ ⊸ 𝒰₀ ≢ 𝒰₀ ⇾ 𝒰₀" $
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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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testEq "𝒰₁ ⊸ 𝒰₀ <: 𝒰₀ ⊸ 𝒰₀" $
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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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testNeq "𝒰₀ ⊸ 𝒰₀ ≢ 𝒰₀ ⇾ 𝒰₁" $
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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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testEq "𝒰₀ ⊸ 𝒰₀ <: 𝒰₀ ⊸ 𝒰₁" $
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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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testEq "𝒰₀ ⊸ 𝒰₀ <: 𝒰₀ ⊸ 𝒰₁" $
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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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],
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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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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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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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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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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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],
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todo "term closure",
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todo "term d-closure",
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"free var" :- [
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testEq "A == A" $
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testEq "A ≡ A" $
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equalE (F "A") (F "A"),
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testNeq "A =/= B" $
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testNeq "A ≢ 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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testNeq "A </: B" $
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testNeq "A ≮: B" $
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subE (F "A") (F "B")
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],
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todo "bound var",
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"application" :-
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let a = F "a"; a' = E a
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A = FT "A"
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λxx = Lam "x" (TUsed (BVT 0))
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A_A = Arr one A A
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λxx' = λxx :# A_A
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in [
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testEq "(λx. x : A -> A) a == ((a : A) : A) (β)" $
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equalE (λxx' :@ a') (E (a' :# A) :# A),
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testEq "(λx. x : _) a == a (βυ)" $
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equalE (λxx' :@ a') a
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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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testEq "f [a] <: f [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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((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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((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 x ⇒ [x] ∷ A ⊸ A) a <: a" $
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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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],
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todo "annotation",
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todo "elim closure",
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todo "elim d-closure",
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todo "clashes"
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"clashes" :- [
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testNeq "𝒰₀ ≢ 𝒰₀ ⇾ 𝒰₀" $
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equalT (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0)),
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todo "others"
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]
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]
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