use NContext/SnocVect for scope name lists etc
This commit is contained in:
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12 changed files with 165 additions and 134 deletions
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@ -16,7 +16,7 @@ defGlobals = fromList
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("a'", mkPostulate Any $ FT "A"),
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("b", mkPostulate Any $ FT "B"),
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("f", mkPostulate 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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("id", mkDef Any (Arr One (FT "A") (FT "A")) ([< "x"] :\\ BVT 0)),
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("eq-AB", mkPostulate Zero $ Eq0 (TYPE 0) (FT "A") (FT "B"))]
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parameters (label : String) (act : Lazy (M ()))
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@ -126,31 +126,31 @@ tests = "equality & subtyping" :- [
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"lambda" :- [
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testEq "λ x ⇒ [x] = λ x ⇒ [x]" $
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equalT empty (Arr One (FT "A") (FT "A"))
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(["x"] :\\ BVT 0)
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(["x"] :\\ BVT 0),
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([< "x"] :\\ BVT 0)
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([< "x"] :\\ BVT 0),
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testEq "λ x ⇒ [x] <: λ x ⇒ [x]" $
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subT empty (Arr One (FT "A") (FT "A"))
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(["x"] :\\ BVT 0)
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(["x"] :\\ BVT 0),
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([< "x"] :\\ BVT 0)
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([< "x"] :\\ BVT 0),
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testEq "λ x ⇒ [x] = λ y ⇒ [y]" $
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equalT empty (Arr One (FT "A") (FT "A"))
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(["x"] :\\ BVT 0)
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(["y"] :\\ BVT 0),
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([< "x"] :\\ BVT 0)
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([< "y"] :\\ BVT 0),
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testEq "λ x ⇒ [x] <: λ y ⇒ [y]" $
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equalT empty (Arr One (FT "A") (FT "A"))
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(["x"] :\\ BVT 0)
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(["y"] :\\ BVT 0),
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([< "x"] :\\ BVT 0)
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([< "y"] :\\ BVT 0),
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testNeq "λ x y ⇒ [x] ≠ λ x y ⇒ [y]" $
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equalT empty (Arr One (FT "A") $ Arr One (FT "A") (FT "A"))
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(["x", "y"] :\\ BVT 1)
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(["x", "y"] :\\ BVT 0),
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([< "x", "y"] :\\ BVT 1)
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([< "x", "y"] :\\ BVT 0),
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testEq "λ x ⇒ [a] = λ x ⇒ [a] (Y vs N)" $
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equalT empty (Arr Zero (FT "B") (FT "A"))
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(Lam $ SY ["x"] $ FT "a")
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(Lam $ SN $ FT "a"),
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(Lam $ SY [< "x"] $ FT "a")
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(Lam $ SN $ FT "a"),
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testEq "λ x ⇒ [f [x]] = [f] (η)" $
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equalT empty (Arr One (FT "A") (FT "A"))
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(["x"] :\\ E (F "f" :@ BVT 0))
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([< "x"] :\\ E (F "f" :@ BVT 0))
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(FT "f")
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],
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@ -168,7 +168,7 @@ tests = "equality & subtyping" :- [
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"equalities and uip" :-
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let refl : Term q d n -> Term q d n -> Elim q d n
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refl a x = (DLam $ S ["_"] $ N x) :# (Eq0 a x x)
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refl a x = (DLam $ S [< "_"] $ N x) :# (Eq0 a x x)
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in
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[
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note #""refl [A] x" is an abbreviation for "(δ i ⇒ x) ∷ (x ≡ x : A)""#,
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@ -217,7 +217,7 @@ tests = "equality & subtyping" :- [
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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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Sig (FT "E") $ S [< "_"] $ N $ FT "E" in
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equalE (extendTyN [< (Any, "x", ty), (Any, "y", ty)] empty)
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(BV 0) (BV 1),
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@ -250,12 +250,12 @@ tests = "equality & subtyping" :- [
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(FT "b"),
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testEq "(λy ⇒ [#1]){a} = λy ⇒ [a] : B ⇾ A (N)" $
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equalT empty (Arr Zero (FT "B") (FT "A"))
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(CloT (Lam $ S ["y"] $ N $ BVT 0) (F "a" ::: id))
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(Lam $ S ["y"] $ N $ FT "a"),
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(CloT (Lam $ S [< "y"] $ N $ BVT 0) (F "a" ::: id))
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(Lam $ S [< "y"] $ N $ FT "a"),
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testEq "(λy ⇒ [#1]){a} = λy ⇒ [a] : B ⇾ A (Y)" $
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equalT empty (Arr Zero (FT "B") (FT "A"))
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(CloT (["y"] :\\ BVT 1) (F "a" ::: id))
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(["y"] :\\ FT "a")
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(CloT ([< "y"] :\\ BVT 1) (F "a" ::: id))
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([< "y"] :\\ FT "a")
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],
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"term d-closure" :- [
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@ -267,8 +267,8 @@ tests = "equality & subtyping" :- [
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equalTD 1
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(extendDim "𝑗" empty)
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(Eq0 (FT "A") (FT "a") (FT "a"))
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(DCloT (["i"] :\\% FT "a") (K Zero ::: id))
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(["i"] :\\% FT "a"),
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(DCloT ([< "i"] :\\% FT "a") (K Zero ::: id))
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([< "i"] :\\% FT "a"),
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note "it is hard to think of well-typed terms with big dctxs"
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],
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@ -334,20 +334,20 @@ tests = "equality & subtyping" :- [
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subE empty (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 empty
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(((["x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
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((([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ 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 empty
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(((["x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
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((([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
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(F "a"),
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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 empty
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(((["g"] :\\ E (BV 0 :@ FT "a")) :# Arr One a2a a) :@ FT "f")
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(((["y"] :\\ E (F "f" :@ BVT 0)) :# a2a) :@ FT "a"),
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((([< "g"] :\\ E (BV 0 :@ FT "a")) :# Arr One a2a a) :@ FT "f")
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((([< "y"] :\\ 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 empty
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(((["x"] :\\ BVT 0) :# (Arr One (FT "A") (FT "A"))) :@ FT "a")
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((([< "x"] :\\ BVT 0) :# (Arr One (FT "A") (FT "A"))) :@ FT "a")
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(F "a"),
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note "id : A ⊸ A ≔ λ x ⇒ [x]",
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testEq "id [a] = a" $ equalE empty (F "id" :@ FT "a") (F "a"),
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@ -407,13 +407,13 @@ tests = "equality & subtyping" :- [
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"annotation" :- [
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testEq "(λ x ⇒ f [x]) ∷ A ⊸ A = [f] ∷ A ⊸ A" $
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equalE empty
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((["x"] :\\ E (F "f" :@ BVT 0)) :# Arr One (FT "A") (FT "A"))
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(([< "x"] :\\ E (F "f" :@ BVT 0)) :# Arr One (FT "A") (FT "A"))
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(FT "f" :# Arr One (FT "A") (FT "A")),
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testEq "[f] ∷ A ⊸ A = f" $
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equalE empty (FT "f" :# Arr One (FT "A") (FT "A")) (F "f"),
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testEq "(λ x ⇒ f [x]) ∷ A ⊸ A = f" $
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equalE empty
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((["x"] :\\ E (F "f" :@ BVT 0)) :# Arr One (FT "A") (FT "A"))
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(([< "x"] :\\ E (F "f" :@ BVT 0)) :# Arr One (FT "A") (FT "A"))
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(F "f")
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],
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@ -83,12 +83,14 @@ tests = "PTerm → Term" :- [
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parsesAs term fromPTerm' "x" $ BVT 2,
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parseFails term fromPTerm' "𝑖",
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parsesAs term fromPTerm' "f" $ FT "f",
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parsesAs term fromPTerm' "λ w ⇒ w" $ ["w"] :\\ BVT 0,
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parsesAs term fromPTerm' "λ w ⇒ x" $ ["w"] :\\ BVT 3,
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parsesAs term fromPTerm' "λ x ⇒ x" $ ["x"] :\\ BVT 0,
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parsesAs term fromPTerm' "λ w ⇒ w" $ [< "w"] :\\ BVT 0,
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parsesAs term fromPTerm' "λ w ⇒ x" $ [< "w"] :\\ BVT 3,
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parsesAs term fromPTerm' "λ x ⇒ x" $ [< "x"] :\\ BVT 0,
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parsesAs term fromPTerm' "λ a b ⇒ f a b" $
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["a", "b"] :\\ E (F "f" :@@ [BVT 1, BVT 0]),
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[< "a", "b"] :\\ E (F "f" :@@ [BVT 1, BVT 0]),
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parsesAs term fromPTerm' "f @𝑖" $
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E $ F "f" :% BV 1
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]
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],
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todo "everything else"
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]
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@ -29,9 +29,9 @@ tests = "whnf" :- [
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testNoStep "[A] ⊸ [B]" $
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Arr One (FT "A") (FT "B"),
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testNoStep "(x: [A]) ⊸ [B [x]]" $
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Pi One (FT "A") (S ["x"] $ Y $ E $ F "B" :@ BVT 0),
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Pi One (FT "A") (S [< "x"] $ Y $ E $ F "B" :@ BVT 0),
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testNoStep "λx. [x]" $
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Lam $ S ["x"] $ Y $ BVT 0,
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Lam $ S [< "x"] $ Y $ BVT 0,
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testNoStep "[f [a]]" $
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E $ F "f" :@ FT "a"
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],
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@ -51,7 +51,7 @@ tests = "whnf" :- [
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(E (TYPE 1 :# TYPE 3))
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(TYPE 1),
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testWhnf "(λx. [x] ∷ [A] ⊸ [A]) [a]"
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(((["x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
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((([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
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(F "a")
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],
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@ -87,28 +87,28 @@ tests = "whnf" :- [
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"term closure" :- [
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testWhnf "(λy. x){a/x}"
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(CloT (Lam $ S ["y"] $ N $ BVT 0) (F "a" ::: id))
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(Lam $ S ["y"] $ N $ FT "a"),
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(CloT (Lam $ S [< "y"] $ N $ BVT 0) (F "a" ::: id))
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(Lam $ S [< "y"] $ N $ FT "a"),
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testWhnf "(λy. y){a/x}"
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(CloT (["y"] :\\ BVT 0) (F "a" ::: id))
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(["y"] :\\ BVT 0)
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(CloT ([< "y"] :\\ BVT 0) (F "a" ::: id))
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([< "y"] :\\ BVT 0)
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],
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"looking inside […]" :- [
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testWhnf "[(λx. x ∷ A ⊸ A) [a]]"
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(E $ ((["x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
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(E $ (([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
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(FT "a")
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],
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"nested redex" :- [
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note "whnf only looks at top level redexes",
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testNoStep "λy. [(λx. [x] ∷ [A] ⊸ [A]) [y]]" $
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["y"] :\\ E (((["x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ BVT 0),
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[< "y"] :\\ E ((([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ BVT 0),
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testNoStep "f [(λx. [x] ∷ [A] ⊸ [A]) [a]]" $
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F "a" :@
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E (((["x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a"),
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E ((([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a"),
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testNoStep "λx. [y [x]]{x/x,a/y}" {n = 1} $
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["x"] :\\ CloT (E $ BV 1 :@ BVT 0) (BV 0 ::: F "a" ::: id),
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[< "x"] :\\ CloT (E $ BV 1 :@ BVT 0) (BV 0 ::: F "a" ::: id),
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testNoStep "f ([y [x]]{x/x,a/y})" {n = 1} $
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F "f" :@ CloT (E $ BV 1 :@ BVT 0) (BV 0 ::: F "a" ::: id)
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]
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@ -41,7 +41,7 @@ reflTy =
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Eq0 (BVT 1) (BVT 0) (BVT 0)
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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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reflDef = [< "A","x"] :\\ [< "i"] :\\% BVT 0
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fstTy : Term Three d n
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@ -52,8 +52,8 @@ fstTy =
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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) (SN $ BVT 2) (SY ["x","y"] $ BVT 1)))
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([< "A","B","p"] :\\
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E (CasePair Any (BV 0) (SN $ BVT 2) (SY [< "x","y"] $ BVT 1)))
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sndTy : Term Three d n
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sndTy =
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@ -64,10 +64,10 @@ sndTy =
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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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([< "A","B","p"] :\\
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E (CasePair Any (BV 0)
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(SY ["p"] $ E $ BV 2 :@ E (F "fst" :@@ [BVT 3, BVT 2, BVT 0]))
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(SY ["x","y"] $ BVT 0)))
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(SY [< "p"] $ E $ BV 2 :@ E (F "fst" :@@ [BVT 3, BVT 2, BVT 0]))
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(SY [< "x","y"] $ BVT 0)))
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defGlobals : Definitions Three
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@ -270,18 +270,18 @@ tests = "typechecker" :- [
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"lambda" :- [
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note "linear & unrestricted identity",
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testTC "1 · (λ x ⇒ x) ⇐ A ⊸ A" $
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check_ empty sone (["x"] :\\ BVT 0) (Arr One (FT "A") (FT "A")),
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check_ empty sone ([< "x"] :\\ BVT 0) (Arr One (FT "A") (FT "A")),
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testTC "1 · (λ x ⇒ x) ⇐ A → A" $
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check_ empty sone (["x"] :\\ BVT 0) (Arr Any (FT "A") (FT "A")),
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check_ empty sone ([< "x"] :\\ BVT 0) (Arr Any (FT "A") (FT "A")),
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note "(fail) zero binding used relevantly",
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testTCFail "1 · (λ x ⇒ x) ⇍ A ⇾ A" $
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check_ empty sone (["x"] :\\ BVT 0) (Arr Zero (FT "A") (FT "A")),
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check_ empty sone ([< "x"] :\\ BVT 0) (Arr Zero (FT "A") (FT "A")),
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note "(but ok in overall erased context)",
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testTC "0 · (λ x ⇒ x) ⇐ A ⇾ A" $
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check_ empty szero (["x"] :\\ BVT 0) (Arr Zero (FT "A") (FT "A")),
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check_ empty szero ([< "x"] :\\ BVT 0) (Arr Zero (FT "A") (FT "A")),
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testTC "1 · (λ A x ⇒ refl A x) ⇐ ⋯ # (type of refl)" $
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check_ empty sone
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(["A", "x"] :\\ E (F "refl" :@@ [BVT 1, BVT 0]))
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([< "A", "x"] :\\ E (F "refl" :@@ [BVT 1, BVT 0]))
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reflTy,
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testTC "1 · (λ A x ⇒ δ i ⇒ x) ⇐ ⋯ # (def. and type of refl)" $
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check_ empty sone reflDef reflTy
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@ -295,7 +295,7 @@ tests = "typechecker" :- [
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(Pair (BVT 0) (BVT 0)) (FT "A" `And` FT "A") [< Any],
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testTC "1 · (a, δ i ⇒ a) ⇐ (x : A) × (x ≡ a)" $
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check_ empty sone
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(Pair (FT "a") (["i"] :\\% FT "a"))
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(Pair (FT "a") ([< "i"] :\\% FT "a"))
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(Sig_ "x" (FT "A") $ Eq0 (FT "A") (BVT 0) (FT "a"))
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],
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@ -303,36 +303,36 @@ tests = "typechecker" :- [
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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 [< ("x", FT "A" `And` FT "A")]) sone
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(CasePair One (BV 0) (SN $ FT "B")
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(SY ["l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
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(SY [< "l", "r"] $ 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 [< ("x", FT "A" `And` FT "A")]) sone
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(CasePair Any (BV 0) (SN $ FT "B")
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(SY ["l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
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(SY [< "l", "r"] $ 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 [< ("x", FT "A" `And` FT "A")]) szero
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(CasePair Any (BV 0) (SN $ FT "B")
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(SY ["l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
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(SY [< "l", "r"] $ 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 [< ("x", FT "A" `And` FT "A")]) sone
|
||||
(CasePair Zero (BV 0) (SN $ FT "B")
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||||
(SY ["l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0])),
|
||||
(SY [< "l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0])),
|
||||
testTC "x : A × B ⊢ 1 · (caseω x return A of (l,r) ⇒ l) ⇒ A ⊳ ω·x" $
|
||||
inferAsQ (ctx [< ("x", FT "A" `And` FT "B")]) sone
|
||||
(CasePair Any (BV 0) (SN $ FT "A")
|
||||
(SY ["l", "r"] $ BVT 1))
|
||||
(SY [< "l", "r"] $ BVT 1))
|
||||
(FT "A") [< Any],
|
||||
testTC "x : A × B ⊢ 0 · (case1 x return A of (l,r) ⇒ l) ⇒ A ⊳ 0·x" $
|
||||
inferAsQ (ctx [< ("x", FT "A" `And` FT "B")]) szero
|
||||
(CasePair One (BV 0) (SN $ FT "A")
|
||||
(SY ["l", "r"] $ BVT 1))
|
||||
(SY [< "l", "r"] $ BVT 1))
|
||||
(FT "A") [< Zero],
|
||||
testTCFail "x : A × B ⊢ 1 · (case1 x return A of (l,r) ⇒ l) ⇏" $
|
||||
infer_ (ctx [< ("x", FT "A" `And` FT "B")]) sone
|
||||
(CasePair One (BV 0) (SN $ FT "A")
|
||||
(SY ["l", "r"] $ BVT 1)),
|
||||
(SY [< "l", "r"] $ BVT 1)),
|
||||
note "fst : (0·A : ★₁) → (0·B : A ↠ ★₁) → ((x : A) × B x) ↠ A",
|
||||
note " ≔ (λ A B p ⇒ caseω p return A of (x, y) ⇒ x)",
|
||||
testTC "0 · ‹type of fst› ⇐ ★₂" $
|
||||
|
|
@ -347,9 +347,9 @@ tests = "typechecker" :- [
|
|||
check_ empty sone sndDef sndTy,
|
||||
testTC "0 · snd ★₀ (λ x ⇒ x) ⇒ (ω·p : (A : ★₀) × A) → fst ★₀ (λ x ⇒ x) p" $
|
||||
inferAs empty szero
|
||||
(F "snd" :@@ [TYPE 0, ["x"] :\\ BVT 0])
|
||||
(F "snd" :@@ [TYPE 0, [< "x"] :\\ BVT 0])
|
||||
(Pi_ Any "A" (Sig_ "A" (TYPE 0) $ BVT 0) $
|
||||
(E $ F "fst" :@@ [TYPE 0, ["x"] :\\ BVT 0, BVT 0]))
|
||||
(E $ F "fst" :@@ [TYPE 0, [< "x"] :\\ BVT 0, BVT 0]))
|
||||
],
|
||||
|
||||
"enums" :- [
|
||||
|
|
@ -369,13 +369,13 @@ tests = "typechecker" :- [
|
|||
(Eq0 (FT "A") (FT "a") (FT "a")),
|
||||
testTC "0 · (λ p q ⇒ δ i ⇒ p) ⇐ (ω·p q : a ≡ a') → p ≡ q" $
|
||||
check_ empty szero
|
||||
(["p","q"] :\\ ["i"] :\\% BVT 1)
|
||||
([< "p","q"] :\\ [< "i"] :\\% BVT 1)
|
||||
(Pi_ Any "p" (Eq0 (FT "A") (FT "a") (FT "a")) $
|
||||
Pi_ Any "q" (Eq0 (FT "A") (FT "a") (FT "a")) $
|
||||
Eq0 (Eq0 (FT "A") (FT "a") (FT "a")) (BVT 1) (BVT 0)),
|
||||
testTC "0 · (λ p q ⇒ δ i ⇒ q) ⇐ (ω·p q : a ≡ a') → p ≡ q" $
|
||||
check_ empty szero
|
||||
(["p","q"] :\\ ["i"] :\\% BVT 0)
|
||||
([< "p","q"] :\\ [< "i"] :\\% BVT 0)
|
||||
(Pi_ Any "p" (Eq0 (FT "A") (FT "a") (FT "a")) $
|
||||
Pi_ Any "q" (Eq0 (FT "A") (FT "a") (FT "a")) $
|
||||
Eq0 (Eq0 (FT "A") (FT "a") (FT "a")) (BVT 1) (BVT 0))
|
||||
|
|
@ -388,7 +388,7 @@ tests = "typechecker" :- [
|
|||
note " ⇐ (0·x y : A) → (1·xy : x ≡ y) → Eq [i ⇒ P (xy i)] (p x) (p y)",
|
||||
testTC "cong" $
|
||||
check_ empty sone
|
||||
(["x", "y", "xy"] :\\ ["i"] :\\% E (F "p" :@ E (BV 0 :% BV 0)))
|
||||
([< "x", "y", "xy"] :\\ [< "i"] :\\% E (F "p" :@ E (BV 0 :% BV 0)))
|
||||
(Pi_ Zero "x" (FT "A") $
|
||||
Pi_ Zero "y" (FT "A") $
|
||||
Pi_ One "xy" (Eq0 (FT "A") (BVT 1) (BVT 0)) $
|
||||
|
|
@ -401,7 +401,7 @@ tests = "typechecker" :- [
|
|||
note " ⇐ (1·eq : (1·x : A) → p x ≡ q x) → p ≡ q",
|
||||
testTC "funext" $
|
||||
check_ empty sone
|
||||
(["eq"] :\\ ["i"] :\\% ["x"] :\\ E (BV 1 :@ BVT 0 :% BV 0))
|
||||
([< "eq"] :\\ [< "i"] :\\% [< "x"] :\\ E (BV 1 :@ BVT 0 :% BV 0))
|
||||
(Pi_ One "eq"
|
||||
(Pi_ One "x" (FT "A")
|
||||
(Eq0 (E $ F "P" :@ BVT 0)
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue