some more typechecker tests
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1 changed files with 176 additions and 10 deletions
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@ -43,6 +43,35 @@ reflTy =
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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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fstTy : Term Three d n
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fstTy =
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(Pi Zero (TYPE 1) $ S ["A"] $ Y $
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Pi Zero (Arr Any (BVT 0) (TYPE 1)) $ S ["B"] $ Y $
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Arr Any (Sig (BVT 1) $ S ["x"] $ Y $ E $ BV 1 :@ BVT 0)
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(BVT 1))
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fstDef : Term Three d n
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fstDef =
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(["A","B","p"] :\\
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E (CasePair Any (BV 0) (S ["_"] $ N $ BVT 2)
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(S ["x","y"] $ Y $ BVT 1)))
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sndTy : Term Three d n
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sndTy =
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(Pi Zero (TYPE 1) $ S ["A"] $ Y $
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Pi Zero (Arr Any (BVT 0) (TYPE 1)) $ S ["B"] $ Y $
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Pi Any (Sig (BVT 1) $ S ["x"] $ Y $ E $ BV 1 :@ BVT 0) $ S ["p"] $ Y $
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E (BV 1 :@ E (F "fst" :@@ [BVT 2, BVT 1, BVT 0])))
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sndDef : Term Three d n
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sndDef =
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(["A","B","p"] :\\
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E (CasePair Any (BV 0)
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(S ["p"] $ Y $ E $ BV 2 :@ E (F "fst" :@@ [BVT 3, BVT 2, BVT 0]))
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(S ["x","y"] $ Y $ 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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@ -55,10 +84,12 @@ 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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("g", mkAbstract Any $ Arr One (FT "A") (FT "B")),
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("f2", mkAbstract Any $ Arr One (FT "A") $ Arr One (FT "A") (FT "A")),
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("f2", mkAbstract Any $ Arr One (FT "A") $ Arr One (FT "A") (FT "B")),
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("p", mkAbstract Any $ Pi One (FT "A") $ S ["x"] $ Y $ E $ F "P" :@ BVT 0),
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("q", mkAbstract Any $ Pi One (FT "A") $ S ["x"] $ Y $ E $ F "P" :@ BVT 0),
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("refl", mkDef Any reflTy reflDef)]
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("refl", mkDef Any reflTy reflDef),
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("fst", mkDef Any fstTy fstDef),
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("snd", mkDef Any sndTy sndDef)]
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parameters (label : String) (act : Lazy (M ()))
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{default defGlobals globals : Definitions Three}
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@ -69,8 +100,9 @@ parameters (label : String) (act : Lazy (M ()))
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testTCFail = testThrows label (const True) $ runReaderT globals act
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ctx : TContext Three 0 n -> TyContext Three 0 n
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ctx, ctx01 : TContext Three 0 n -> TyContext Three 0 n
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ctx = MkTyContext new
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ctx01 = MkTyContext ZeroIsOne
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inferredTypeEq : TyContext Three d n -> (exp, got : Term Three d n) -> M ()
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inferredTypeEq ctx exp got =
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@ -111,6 +143,16 @@ 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 $ inj $ check ctx sg s ty
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-- ω is not a subject qty
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failing "Can't find an implementation"
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sany : SQty Three
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sany = Element Any %search
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enum : List TagVal -> Term q d n
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enum = Enum . SortedSet.fromList
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export
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tests : Test
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tests = "typechecker" :- [
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@ -122,8 +164,7 @@ tests = "typechecker" :- [
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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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testTC "0=1 ⊢ 0 · ★₁ ⇐ ★₀" $
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check_ (MkTyContext (ZeroIsOne {d = 0}) [<]) szero (TYPE 1) (TYPE 0)
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testTC "0=1 ⊢ 0 · ★₁ ⇐ ★₀" $ check_ (ctx01 [<]) szero (TYPE 1) (TYPE 0)
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],
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"function types" :- [
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@ -144,18 +185,59 @@ tests = "typechecker" :- [
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testTCFail "0 · A ⊸ P ⇍ ★₀" $
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check_ (ctx [<]) szero (Arr One (FT "A") $ FT "P") (TYPE 0),
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testTC "0=1 ⊢ 0 · A ⊸ P ⇐ ★₀" $
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check_ (MkTyContext (ZeroIsOne {d = 0}) [<]) szero
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(Arr One (FT "A") $ FT "P") (TYPE 0)
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check_ (ctx01 [<]) szero (Arr One (FT "A") $ FT "P") (TYPE 0)
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],
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"pair types" :- [
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note #""A × B" for "(_ : A) × B""#,
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testTC "0 · A × A ⇐ ★₀" $
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check_ (ctx [<]) szero (FT "A" `And` FT "A") (TYPE 0),
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testTCFail "0 · A × P ⇍ ★₀" $
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check_ (ctx [<]) szero (FT "A" `And` FT "P") (TYPE 0),
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testTC "0 · (x : A) × P x ⇐ ★₀" $
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check_ (ctx [<]) szero
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(Sig (FT "A") $ S ["x"] $ Y $ E $ F "P" :@ BVT 0) (TYPE 0),
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testTC "0 · (x : A) × P x ⇐ ★₁" $
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check_ (ctx [<]) szero
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(Sig (FT "A") $ S ["x"] $ Y $ E $ F "P" :@ BVT 0) (TYPE 1),
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testTC "0 · (A : ★₀) × A ⇐ ★₁" $
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check_ (ctx [<]) szero (Sig (TYPE 0) $ S ["A"] $ Y $ BVT 0) (TYPE 1),
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testTCFail "0 · (A : ★₀) × A ⇍ ★₀" $
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check_ (ctx [<]) szero (Sig (TYPE 0) $ S ["A"] $ Y $ BVT 0) (TYPE 0),
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testTCFail "1 · A × A ⇍ ★₀" $
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check_ (ctx [<]) sone (FT "A" `And` FT "A") (TYPE 0)
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],
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"enum types" :- [
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testTC "0 · {} ⇐ ★₀" $ check_ (ctx [<]) szero (enum []) (TYPE 0),
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testTC "0 · {} ⇐ ★₃" $ check_ (ctx [<]) szero (enum []) (TYPE 3),
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testTC "0 · {a,b,c} ⇐ ★₀" $
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check_ (ctx [<]) szero (enum ["a", "b", "c"]) (TYPE 0),
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testTC "0 · {a,b,c} ⇐ ★₃" $
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check_ (ctx [<]) szero
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(Sig (FT "A") $ S ["x"] $ Y $ E $ F "P" :@ BVT 0) (TYPE 0),
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testTC "0 · (x : A) × P x ⇐ ★₁" $
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check_ (ctx [<]) szero
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(Sig (FT "A") $ S ["x"] $ Y $ E $ F "P" :@ BVT 0) (TYPE 1),
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testTC "0 · (A : ★₀) × A ⇐ ★₁" $
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check_ (ctx [<]) szero (Sig (TYPE 0) $ S ["A"] $ Y $ BVT 0) (TYPE 1),
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testTCFail "0 · (A : ★₀) × A ⇍ ★₀" $
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check_ (ctx [<]) szero (Sig (TYPE 0) $ S ["A"] $ Y $ BVT 0) (TYPE 0),
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testTCFail "1 · A × A ⇍ ★₀" $
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check_ (ctx [<]) sone (FT "A" `And` FT "A") (TYPE 0)
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],
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"enum types" :- [
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testTC "0 · {} ⇐ ★₀" $ check_ (ctx [<]) szero (enum []) (TYPE 0),
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testTC "0 · {} ⇐ ★₃" $ check_ (ctx [<]) szero (enum []) (TYPE 3),
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testTC "0 · {a,b,c} ⇐ ★₀" $
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check_ (ctx [<]) szero (enum ["a", "b", "c"]) (TYPE 0),
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testTC "0 · {a,b,c} ⇐ ★₃" $
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check_ (ctx [<]) szero (enum ["a", "b", "c"]) (TYPE 3),
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testTCFail "1 · {} ⇍ ★₀" $ check_ (ctx [<]) sone (enum []) (TYPE 0),
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testTC "0=1 ⊢ 1 · {} ⇐ ★₀" $ check_ (ctx01 [<]) sone (enum []) (TYPE 0)
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],
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"free vars" :- [
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note "A : ★₀",
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testTC "0 · A ⇒ ★₀" $
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@ -179,10 +261,10 @@ tests = "typechecker" :- [
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(BV 0) (FT "A") [< one],
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testTC "x : A ⊢ 1 · [x] ⇐ A ⊳ 1·x" $
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checkQ {n = 1} (ctx [< FT "A"]) sone (BVT 0) (FT "A") [< one],
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note "f2 : A ⊸ A ⊸ A",
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testTC "x : A ⊢ 1 · f2 [x] [x] ⇒ A ⊳ ω·x" $
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note "f2 : A ⊸ A ⊸ B",
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testTC "x : A ⊢ 1 · f2 [x] [x] ⇒ B ⊳ ω·x" $
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inferAsQ {n = 1} (ctx [< FT "A"]) sone
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(F "f2" :@@ [BVT 0, BVT 0]) (FT "A") [< Any]
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(F "f2" :@@ [BVT 0, BVT 0]) (FT "B") [< Any]
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],
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"lambda" :- [
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@ -205,6 +287,90 @@ tests = "typechecker" :- [
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check_ (ctx [<]) sone reflDef reflTy
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],
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"pairs" :- [
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testTC "1 · (a, a) ⇐ A × A" $
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check_ (ctx [<]) sone (Pair (FT "a") (FT "a")) (FT "A" `And` FT "A"),
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testTC "x : A ⊢ 1 · (x, x) ⇐ A × A ⊳ ω·x" $
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checkQ (ctx [< FT "A"]) sone
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(Pair (BVT 0) (BVT 0)) (FT "A" `And` FT "A") [< Any],
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testTC "1 · (a, λᴰ i ⇒ a) ⇐ (x : A) × (x ≡ a)" $
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check_ (ctx [<]) sone
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(Pair (FT "a") (["i"] :\\% FT "a"))
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(Sig (FT "A") $ S ["x"] $ Y $
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Eq0 (FT "A") (BVT 0) (FT "a"))
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],
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"unpairing" :- [
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testTC "x : A × A ⊢ 1 · (case1 x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ 1·x" $
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inferAsQ (ctx [< FT "A" `And` FT "A"]) sone
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(CasePair One (BV 0)
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(S ["_"] $ N $ FT "B")
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(S ["l", "r"] $ Y $ E $ F "f2" :@@ [BVT 1, BVT 0]))
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(FT "B") [< One],
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testTC "x : A × A ⊢ 1 · (caseω x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ ω·x" $
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inferAsQ (ctx [< FT "A" `And` FT "A"]) sone
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(CasePair Any (BV 0)
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(S ["_"] $ N $ FT "B")
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(S ["l", "r"] $ Y $ E $ F "f2" :@@ [BVT 1, BVT 0]))
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(FT "B") [< Any],
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testTC "x : A × A ⊢ 0 · (caseω x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ 0·x" $
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inferAsQ (ctx [< FT "A" `And` FT "A"]) szero
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(CasePair Any (BV 0)
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(S ["_"] $ N $ FT "B")
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(S ["l", "r"] $ Y $ E $ F "f2" :@@ [BVT 1, BVT 0]))
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(FT "B") [< Zero],
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testTCFail "x : A × A ⊢ 1 · (case0 x return B of (l,r) ⇒ f2 l r) ⇏" $
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infer_ (ctx [< FT "A" `And` FT "A"]) sone
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(CasePair Zero (BV 0)
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(S ["_"] $ N $ FT "B")
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(S ["l", "r"] $ Y $ E $ F "f2" :@@ [BVT 1, BVT 0])),
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testTC "x : A × B ⊢ 1 · (caseω x return A of (l,r) ⇒ l) ⇒ A ⊳ ω·x" $
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inferAsQ (ctx [< FT "A" `And` FT "B"]) sone
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(CasePair Any (BV 0)
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(S ["_"] $ N $ FT "A")
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(S ["l", "r"] $ Y $ BVT 1))
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(FT "A") [< Any],
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testTC "x : A × B ⊢ 0 · (case1 x return A of (l,r) ⇒ l) ⇒ A ⊳ 0·x" $
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inferAsQ (ctx [< FT "A" `And` FT "B"]) szero
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(CasePair One (BV 0)
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(S ["_"] $ N $ FT "A")
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(S ["l", "r"] $ Y $ BVT 1))
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(FT "A") [< Zero],
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testTCFail "x : A × B ⊢ 1 · (case1 x return A of (l,r) ⇒ l) ⇏" $
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infer_ (ctx [< FT "A" `And` FT "B"]) sone
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(CasePair One (BV 0)
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(S ["_"] $ N $ FT "A")
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(S ["l", "r"] $ Y $ BVT 1)),
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note "fst : (0·A : ★₁) → (0·B : A ↠ ★₁) → ((x : A) × B x) ↠ A",
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note " ≔ (λ A B p ⇒ caseω p return A of (x, y) ⇒ x)",
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testTC "0 · ‹type of fst› ⇐ ★₂" $
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check_ (ctx [<]) szero fstTy (TYPE 2),
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testTC "1 · ‹def of fst› ⇐ ‹type of fst›" $
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check_ (ctx [<]) sone fstDef fstTy,
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note "snd : (0·A : ★₁) → (0·B : A ↠ ★₁) → (ω·p : (x : A) × B x) → B (fst A B p)",
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note " ≔ (λ A B p ⇒ caseω p return p ⇒ B (fst A B p) of (x, y) ⇒ y)",
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testTC "0 · ‹type of snd› ⇐ ★₂" $
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check_ (ctx [<]) szero sndTy (TYPE 2),
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testTC "1 · ‹def of snd› ⇐ ‹type of snd›" $
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check_ (ctx [<]) sone sndDef sndTy,
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testTC "0 · snd ★₀ (λ x ⇒ x) ⇒ (ω·p : (A : ★₀) × A) → fst ★₀ (λ x ⇒ x) p" $
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inferAs (ctx [<]) szero
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(F "snd" :@@ [TYPE 0, ["x"] :\\ BVT 0])
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(Pi Any (Sig (TYPE 0) $ S ["A"] $ Y $ BVT 0) $ S ["p"] $ Y $
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(E $ F "fst" :@@ [TYPE 0, ["x"] :\\ BVT 0, BVT 0]))
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],
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"enums" :- [
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testTC "1 · `a ⇐ {a}" $
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check_ (ctx [<]) sone (Tag "a") (enum ["a"]),
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testTC "1 · `a ⇐ {a, b, c}" $
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check_ (ctx [<]) sone (Tag "a") (enum ["a", "b", "c"]),
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testTCFail "1 · `a ⇍ {b, c}" $
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check_ (ctx [<]) sone (Tag "a") (enum ["b", "c"]),
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testTC "0=1 ⊢ 1 · `a ⇐ {b, c}" $
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check_ (ctx01 [<]) sone (Tag "a") (enum ["b", "c"])
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],
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"equalities" :- [
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testTC "1 · (λᴰ i ⇒ a) ⇐ a ≡ a" $
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check_ (ctx [<]) sone (DLam $ S ["i"] $ N $ FT "a")
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