add some dim app tests
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@ -17,7 +17,7 @@ defGlobals = fromList
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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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("id", mkDef Any (Arr One (FT "A") (FT "A")) (["x"] :\\ BVT 0)),
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("eq-ab", mkAbstract Zero $ Eq0 (TYPE 0) (FT "A") (FT "B"))]
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("eq-AB", mkAbstract Zero $ Eq0 (TYPE 0) (FT "A") (FT "B"))]
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parameters (label : String) (act : Lazy (M ()))
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{default defGlobals globals : Definitions Three}
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@ -185,8 +185,8 @@ tests = "equality & subtyping" :- [
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equalE (MkTyContext new [< ty, ty]) (BV 0) (BV 1),
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testEq "∥ x : [(a ≡ a' : A) ∷ Type 0], y : [ditto] ⊢ x = y" $
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let ty : forall n. Term Three 0 n
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:= E (Eq0 (FT "A") (FT "a") (FT "a'") :# TYPE 0) in
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let ty : forall n. Term Three 0 n :=
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E (Eq0 (FT "A") (FT "a") (FT "a'") :# TYPE 0) in
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equalE (MkTyContext new [< ty, ty]) (BV 0) (BV 1),
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testEq "E ≔ a ≡ a' : A, EE ≔ E ∥ x : EE, y : EE ⊢ x = y"
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@ -209,8 +209,8 @@ tests = "equality & subtyping" :- [
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testEq "E ≔ a ≡ a' : A ∥ x : (E×E), y : (E×E) ⊢ x = y"
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{globals = defGlobals `mergeLeft` fromList
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[("E", mkDef zero (TYPE 0) (Eq0 (FT "A") (FT "a") (FT "a'")))]} $
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let ty : forall n. Term Three 0 n
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:= Sig (FT "E") $ S ["_"] $ N $ FT "E" in
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let ty : forall n. Term Three 0 n :=
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Sig (FT "E") $ S ["_"] $ N $ FT "E" in
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equalE (MkTyContext new [< ty, ty]) (BV 0) (BV 1),
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testEq "E ≔ a ≡ a' : A, F ≔ E × E ∥ x : F, y : F ⊢ x = y"
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@ -337,7 +337,44 @@ tests = "equality & subtyping" :- [
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testEq "id [a] <: a" $ subE empty (F "id" :@ FT "a") (F "a")
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],
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todo "dim application",
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"dim application" :- [
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testEq "eq-AB @0 = eq-AB @0" $
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equalE empty (F "eq-AB" :% K Zero) (F "eq-AB" :% K Zero),
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testNeq "eq-AB @0 ≠ eq-AB @1" $
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equalE empty (F "eq-AB" :% K Zero) (F "eq-AB" :% K One),
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testEq "𝑖 | ⊢ eq-AB @𝑖 = eq-AB @𝑖" $
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equalED 1 empty (F "eq-AB" :% BV 0) (F "eq-AB" :% BV 0),
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testNeq "𝑖 | ⊢ eq-AB @𝑖 ≠ eq-AB @0" $
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equalED 1 empty (F "eq-AB" :% BV 0) (F "eq-AB" :% K Zero),
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testEq "𝑖, 𝑖=0 | ⊢ eq-AB @𝑖 = eq-AB @0" $
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let ctx = MkTyContext (set (BV 0) (K Zero) new) [<] in
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equalED 1 ctx (F "eq-AB" :% BV 0) (F "eq-AB" :% K Zero),
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testNeq "𝑖, 𝑖=1 | ⊢ eq-AB @𝑖 ≠ eq-AB @0" $
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let ctx = MkTyContext (set (BV 0) (K One) new) [<] in
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equalED 1 ctx (F "eq-AB" :% BV 0) (F "eq-AB" :% K Zero),
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testNeq "𝑖, 𝑗 | ⊢ eq-AB @𝑖 ≠ eq-AB @𝑗" $
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equalED 2 empty (F "eq-AB" :% BV 1) (F "eq-AB" :% BV 0),
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testEq "𝑖, 𝑗, 𝑖=𝑗 | ⊢ eq-AB @𝑖 = eq-AB @𝑗" $
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let ctx = MkTyContext (set (BV 0) (BV 1) new) [<] in
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equalED 2 ctx (F "eq-AB" :% BV 1) (F "eq-AB" :% BV 0),
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testNeq "𝑖, 𝑗, 𝑖=0, 𝑗=0 | ⊢ eq-AB @𝑖 ≠ eq-AB @𝑗" $
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let ctx : TyContext Three 2 0 :=
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MkTyContext (C [< Just $ K Zero, Just $ K Zero]) [<] in
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equalED 2 empty (F "eq-AB" :% BV 1) (F "eq-AB" :% BV 0),
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testEq "0=1 | ⊢ eq-AB @𝑖 = eq-AB @𝑗" $
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equalED 2 (MkTyContext ZeroIsOne [<])
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(F "eq-AB" :% BV 1) (F "eq-AB" :% BV 0),
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testEq "eq-AB @0 = A" $ equalE empty (F "eq-AB" :% K Zero) (F "A"),
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testEq "eq-AB @1 = B" $ equalE empty (F "eq-AB" :% K One) (F "B"),
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testEq "((δ i ⇒ a) ∷ a ≡ a) @0 = a" $
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equalE empty
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(((DLam $ SN $ FT "a") :# Eq0 (FT "A") (FT "a") (FT "a")) :% K Zero)
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(F "a"),
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testEq "((δ i ⇒ a) ∷ a ≡ a) @0 = ((δ i ⇒ a) ∷ a ≡ a) @1" $
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equalE empty
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(((DLam $ SN $ FT "a") :# Eq0 (FT "A") (FT "a") (FT "a")) :% K Zero)
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(((DLam $ SN $ FT "a") :# Eq0 (FT "A") (FT "a") (FT "a")) :% K One)
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],
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"annotation" :- [
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testEq "(λ x ⇒ f [x]) ∷ A ⊸ A = [f] ∷ A ⊸ A" $
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@ -361,25 +398,25 @@ tests = "equality & subtyping" :- [
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],
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"elim d-closure" :- [
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note "0·eq-ab : (A ≡ B : ★₀)",
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testEq "(eq-ab #0)‹𝟎› = eq-ab 𝟎" $
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note "0·eq-AB : (A ≡ B : ★₀)",
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testEq "(eq-AB #0)‹𝟎› = eq-AB 𝟎" $
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equalED 1 empty
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(DCloE (F "eq-ab" :% BV 0) (K Zero ::: id))
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(F "eq-ab" :% K Zero),
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testEq "(eq-ab #0)‹𝟎› = A" $
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equalED 1 empty (DCloE (F "eq-ab" :% BV 0) (K Zero ::: id)) (F "A"),
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testEq "(eq-ab #0)‹𝟏› = B" $
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equalED 1 empty (DCloE (F "eq-ab" :% BV 0) (K One ::: id)) (F "B"),
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testNeq "(eq-ab #0)‹𝟏› ≠ A" $
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equalED 1 empty (DCloE (F "eq-ab" :% BV 0) (K One ::: id)) (F "A"),
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testEq "(eq-ab #0)‹#0,𝟎› = (eq-ab #0)" $
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(DCloE (F "eq-AB" :% BV 0) (K Zero ::: id))
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(F "eq-AB" :% K Zero),
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testEq "(eq-AB #0)‹𝟎› = A" $
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equalED 1 empty (DCloE (F "eq-AB" :% BV 0) (K Zero ::: id)) (F "A"),
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testEq "(eq-AB #0)‹𝟏› = B" $
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equalED 1 empty (DCloE (F "eq-AB" :% BV 0) (K One ::: id)) (F "B"),
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testNeq "(eq-AB #0)‹𝟏› ≠ A" $
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equalED 1 empty (DCloE (F "eq-AB" :% BV 0) (K One ::: id)) (F "A"),
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testEq "(eq-AB #0)‹#0,𝟎› = (eq-AB #0)" $
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equalED 2 empty
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(DCloE (F "eq-ab" :% BV 0) (BV 0 ::: K Zero ::: id))
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(F "eq-ab" :% BV 0),
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testNeq "(eq-ab #0)‹𝟎› ≠ (eq-ab 𝟎)" $
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(DCloE (F "eq-AB" :% BV 0) (BV 0 ::: K Zero ::: id))
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(F "eq-AB" :% BV 0),
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testNeq "(eq-AB #0)‹𝟎› ≠ (eq-AB 𝟎)" $
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equalED 2 empty
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(DCloE (F "eq-ab" :% BV 0) (BV 0 ::: K Zero ::: id))
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(F "eq-ab" :% K Zero),
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(DCloE (F "eq-AB" :% BV 0) (BV 0 ::: K Zero ::: id))
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(F "eq-AB" :% K Zero),
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testEq "#0‹𝟎› = #0 # term and dim vars distinct" $
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equalED 1 (MkTyContext new [< FT "A"])
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(DCloE (BV 0) (K Zero ::: id)) (BV 0),
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