quox/tests/Tests/Equal.idr

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module Tests.Equal
import Quox.Equal
import Quox.Pretty
import TAP
export
ToInfo Equal.Error where
toInfo (ClashT mode s t) =
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[("clash", "term"),
("mode", show mode),
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("left", prettyStr True s),
("right", prettyStr True t)]
toInfo (ClashU mode k l) =
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[("clash", "universe"),
("mode", show mode),
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("left", prettyStr True k),
("right", prettyStr True l)]
toInfo (ClashQ pi rh) =
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[("clash", "quantity"),
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("left", prettyStr True pi),
("right", prettyStr True rh)]
M = Either Equal.Error
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testEq : String -> Lazy (M ()) -> Test
testEq = test
testNeq : String -> Lazy (M ()) -> Test
testNeq label = testThrows label $ const True
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subT : {default 0 d, n : Nat} -> Term d n -> Term d n -> M ()
subT = Quox.Equal.subT
%hide Quox.Equal.subT
equalT : {default 0 d, n : Nat} -> Term d n -> Term d n -> M ()
equalT = Quox.Equal.equalT
%hide Quox.Equal.equalT
subE : {default 0 d, n : Nat} -> Elim d n -> Elim d n -> M ()
subE = Quox.Equal.subE
%hide Quox.Equal.subE
equalE : {default 0 d, n : Nat} -> Elim d n -> Elim d n -> M ()
equalE = Quox.Equal.equalE
%hide Quox.Equal.equalE
export
tests : Test
tests = "equality & subtyping" :- [
"universes" :- [
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testEq "★₀ ≡ ★₀" $
equalT (TYPE 0) (TYPE 0),
testNeq "★₀ ≢ ★₁" $
equalT (TYPE 0) (TYPE 1),
testNeq "★₁ ≢ ★₀" $
equalT (TYPE 1) (TYPE 0),
testEq "★₀ <: ★₀" $
subT (TYPE 0) (TYPE 0),
testEq "★₀ <: ★₁" $
subT (TYPE 0) (TYPE 1),
testNeq "★₁ ≮: ★₀" $
subT (TYPE 1) (TYPE 0)
],
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"pi" :- [
-- ⊸ for →₁, ⇾ for →₀
testEq "A ⊸ B ≡ A ⊸ B" $
let tm = Arr One (FT "A") (FT "B") in
equalT tm tm,
testNeq "A ⇾ B ≢ A ⇾ B" $
let tm1 = Arr Zero (FT "A") (FT "B")
tm2 = Arr One (FT "A") (FT "B") in
equalT tm1 tm2,
testEq "A ⊸ B <: A ⊸ B" $
let tm = Arr One (FT "A") (FT "B") in
subT tm tm,
testNeq "A ⇾ B ≮: A ⊸ B" $
let tm1 = Arr Zero (FT "A") (FT "B")
tm2 = Arr One (FT "A") (FT "B") in
subT tm1 tm2,
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testEq "★₀ ⇾ ★₀ ≡ ★₀ ⇾ ★₀" $
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let tm = Arr Zero (TYPE 0) (TYPE 0) in
equalT tm tm,
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testEq "★₀ ⇾ ★₀ <: ★₀ ⇾ ★₀" $
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let tm = Arr Zero (TYPE 0) (TYPE 0) in
subT tm tm,
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testNeq "★₁ ⊸ ★₀ ≢ ★₀ ⇾ ★₀" $
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let tm1 = Arr Zero (TYPE 1) (TYPE 0)
tm2 = Arr Zero (TYPE 0) (TYPE 0) in
equalT tm1 tm2,
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testEq "★₁ ⊸ ★₀ <: ★₀ ⊸ ★₀" $
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let tm1 = Arr One (TYPE 1) (TYPE 0)
tm2 = Arr One (TYPE 0) (TYPE 0) in
subT tm1 tm2,
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testNeq "★₀ ⊸ ★₀ ≢ ★₀ ⇾ ★₁" $
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let tm1 = Arr Zero (TYPE 0) (TYPE 0)
tm2 = Arr Zero (TYPE 0) (TYPE 1) in
equalT tm1 tm2,
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testEq "★₀ ⊸ ★₀ <: ★₀ ⊸ ★₁" $
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let tm1 = Arr One (TYPE 0) (TYPE 0)
tm2 = Arr One (TYPE 0) (TYPE 1) in
subT tm1 tm2,
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testEq "★₀ ⊸ ★₀ <: ★₀ ⊸ ★₁" $
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let tm1 = Arr One (TYPE 0) (TYPE 0)
tm2 = Arr One (TYPE 0) (TYPE 1) in
subT tm1 tm2
],
"lambda" :- [
testEq "λ x ⇒ [x] ≡ λ x ⇒ [x]" $
equalT (Lam "x" (TUsed (BVT 0))) (Lam "x" (TUsed (BVT 0))),
testEq "λ x ⇒ [x] <: λ x ⇒ [x]" $
equalT (Lam "x" (TUsed (BVT 0))) (Lam "x" (TUsed (BVT 0))),
testEq "λ x ⇒ [x] ≡ λ y ⇒ [y]" $
equalT (Lam "x" (TUsed (BVT 0))) (Lam "y" (TUsed (BVT 0))),
testEq "λ x ⇒ [x] <: λ y ⇒ [y]" $
equalT (Lam "x" (TUsed (BVT 0))) (Lam "y" (TUsed (BVT 0))),
testNeq "λ x y ⇒ [x] ≢ λ x y ⇒ [y]" $
equalT (Lam "x" (TUsed (Lam "y" (TUsed (BVT 1)))))
(Lam "x" (TUsed (Lam "y" (TUsed (BVT 0)))))
],
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todo "term closure",
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todo "term d-closure",
"free var" :- [
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testEq "A ≡ A" $
equalE (F "A") (F "A"),
testNeq "A ≢ B" $
equalE (F "A") (F "B"),
testEq "A <: A" $
subE (F "A") (F "A"),
testNeq "A ≮: B" $
subE (F "A") (F "B")
],
"bound var" :- [
testEq "#0 ≡ #0" $
equalE (BV 0) (BV 0) {n = 1},
testNeq "#0 ≢ #1" $
equalE (BV 0) (BV 1) {n = 2}
],
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"application" :- [
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testEq "f [a] ≡ f [a]" $
equalE (F "f" :@ FT "a") (F "f" :@ FT "a"),
testEq "f [a] <: f [a]" $
subE (F "f" :@ FT "a") (F "f" :@ FT "a"),
testEq "(λ x ⇒ [x] ∷ A ⊸ A) a ≡ ([a ∷ A] ∷ A) (β)" $
equalE
((Lam "x" (TUsed (BVT 0)) :# (Arr One (FT "A") (FT "A")))
:@ FT "a")
(E (FT "a" :# FT "A") :# FT "A"),
testEq "(λ x ⇒ [x] ∷ A ⊸ A) a ≡ a (βυ)" $
equalE
((Lam "x" (TUsed (BVT 0)) :# (Arr One (FT "A") (FT "A")))
:@ FT "a")
(F "a"),
testEq "(λ x ⇒ [x] ∷ A ⊸ A) a <: a" $
subE
((Lam "x" (TUsed (BVT 0)) :# (Arr One (FT "A") (FT "A")))
:@ FT "a")
(F "a")
],
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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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"clashes" :- [
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testNeq "★₀ ≢ ★₀ ⇾ ★₀" $
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equalT (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0)),
todo "others"
]
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]