nicer constructors for ASTs
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302de6266e
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@ -152,20 +152,48 @@ mutual
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%name Scoped body
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%name ScopedBody body
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||| scope which ignores all its binders
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public export %inline
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SN : {s : Nat} -> f n -> Scoped s f n
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SN = S (replicate s "_") . N
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||| scope which uses its binders
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public export %inline
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SY : Vect s BaseName -> f (s + n) -> Scoped s f n
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SY ns = S ns . Y
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||| more convenient Pi
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public export %inline
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Pi_ : (qty : q) -> (x : BaseName) ->
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(arg : Term q d n) -> (res : Term q d (S n)) -> Term q d n
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Pi_ {qty, x, arg, res} = Pi {qty, arg, res = S [x] $ Y res}
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||| non dependent function type
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public export %inline
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Arr : (qty : q) -> (arg, res : Term q d n) -> Term q d n
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Arr {qty, arg, res} = Pi {qty, arg, res = S ["_"] $ N res}
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Arr {qty, arg, res} = Pi {qty, arg, res = SN res}
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||| non dependent equality type
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||| more convenient Sig
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public export %inline
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Eq0 : (ty, l, r : Term q d n) -> Term q d n
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Eq0 {ty, l, r} = Eq {ty = S ["_"] $ N ty, l, r}
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Sig_ : (x : BaseName) -> (fst : Term q d n) ->
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(snd : Term q d (S n)) -> Term q d n
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Sig_ {x, fst, snd} = Sig {fst, snd = S [x] $ Y snd}
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||| non dependent pair type
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public export %inline
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And : (fst, snd : Term q d n) -> Term q d n
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And {fst, snd} = Sig {fst, snd = S ["_"] $ N snd}
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And {fst, snd} = Sig {fst, snd = SN snd}
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||| more convenient Eq
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public export %inline
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Eq_ : (i : BaseName) -> (ty : Term q (S d) n) ->
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(l, r : Term q d n) -> Term q d n
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Eq_ {i, ty, l, r} = Eq {ty = S [i] $ Y ty, l, r}
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||| non dependent equality type
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public export %inline
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Eq0 : (ty, l, r : Term q d n) -> Term q d n
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Eq0 {ty, l, r} = Eq {ty = SN ty, l, r}
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||| same as `F` but as a term
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public export %inline
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@ -12,10 +12,10 @@ defGlobals : Definitions Three
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defGlobals = fromList
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[("A", mkAbstract Zero $ TYPE 0),
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("B", mkAbstract Zero $ TYPE 0),
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("a", mkAbstract Any $ FT "A"),
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("a'", mkAbstract Any $ FT "A"),
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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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("a", mkAbstract Any $ FT "A"),
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("a'", mkAbstract Any $ FT "A"),
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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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@ -117,6 +117,7 @@ tests = "equality & subtyping" :- [
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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 (MkTyContext ZeroIsOne [<]) (TYPE 0) tm1 tm2,
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todo "dependent function types",
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note "[todo] should π ≤ ρ ⊢ (ρ·A) → B <: (π·A) → B?"
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],
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@ -143,8 +144,8 @@ tests = "equality & subtyping" :- [
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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 $ S ["x"] $ Y $ FT "a")
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(Lam $ S ["x"] $ N $ 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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@ -159,7 +160,8 @@ tests = "equality & subtyping" :- [
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{globals = fromList [("A", mkDef zero (TYPE 2) (TYPE 1))]} $
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equalT empty (TYPE 2)
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(Eq0 (TYPE 1) (TYPE 0) (TYPE 0))
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(Eq0 (FT "A") (TYPE 0) (TYPE 0))
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(Eq0 (FT "A") (TYPE 0) (TYPE 0)),
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todo "dependent equality types"
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],
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"equalities and uip" :-
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@ -36,8 +36,8 @@ inj act = do
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reflTy : IsQty q => Term q d n
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reflTy =
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Pi zero (TYPE 0) $ S ["A"] $ Y $
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Pi one (BVT 0) $ S ["x"] $ Y $
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Pi_ zero "A" (TYPE 0) $
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Pi_ one "x" (BVT 0) $
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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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@ -46,30 +46,28 @@ 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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(Pi_ Zero "A" (TYPE 1) $
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Pi_ Zero "B" (Arr Any (BVT 0) (TYPE 1)) $
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Arr Any (Sig_ "x" (BVT 1) $ E $ BV 1 :@ BVT 0) (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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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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(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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(Pi_ Zero "A" (TYPE 1) $
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Pi_ Zero "B" (Arr Any (BVT 0) (TYPE 1)) $
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Pi_ Any "p" (Sig_ "x" (BVT 1) $ E $ BV 1 :@ BVT 0) $
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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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(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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@ -85,8 +83,8 @@ defGlobals = fromList
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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 "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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("p", mkAbstract Any $ Pi_ One "x" (FT "A") $ E $ F "P" :@ BVT 0),
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("q", mkAbstract Any $ Pi_ One "x" (FT "A") $ E $ F "P" :@ BVT 0),
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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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@ -180,7 +178,7 @@ tests = "typechecker" :- [
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check_ (ctx [<]) szero (Arr One (FT "C") (FT "D")) (TYPE 0),
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testTC "0 · (1·x : A) → P x ⇐ ★₀" $
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check_ (ctx [<]) szero
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(Pi One (FT "A") $ S ["x"] $ Y $ E $ F "P" :@ BVT 0)
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(Pi_ One "x" (FT "A") $ E $ F "P" :@ BVT 0)
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(TYPE 0),
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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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@ -196,14 +194,14 @@ tests = "typechecker" :- [
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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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(Sig_ "x" (FT "A") $ 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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(Sig_ "x" (FT "A") $ 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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check_ (ctx [<]) szero (Sig_ "A" (TYPE 0) $ 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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check_ (ctx [<]) szero (Sig_ "A" (TYPE 0) $ 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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@ -214,15 +212,13 @@ tests = "typechecker" :- [
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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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check_ (ctx [<]) szero (Sig_ "x" (FT "A") $ 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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check_ (ctx [<]) szero (Sig_ "x" (FT "A") $ 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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check_ (ctx [<]) szero (Sig_ "A" (TYPE 0) $ 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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check_ (ctx [<]) szero (Sig_ "A" (TYPE 0) $ 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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@ -251,7 +247,7 @@ tests = "typechecker" :- [
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testTCFail "1 · A ⇏ ★₀" $
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infer_ (ctx [<]) sone (F "A"),
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note "refl : (0·A : ★₀) → (1·x : A) → (x ≡ x : A) ≔ (λ A x ⇒ λᴰ _ ⇒ x)",
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testTC "1 · refl ⇒ ⋯" $ inferAs (ctx [<]) sone (F "refl") reflTy,
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testTC "1 · refl ⇒ ⋯" $ inferAs (ctx [<]) sone (F "refl") reflTy,
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testTC "1 · [refl] ⇐ ⋯" $ check_ (ctx [<]) sone (FT "refl") reflTy
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],
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@ -296,51 +292,43 @@ tests = "typechecker" :- [
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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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(Sig_ "x" (FT "A") $ 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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(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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(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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(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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(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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(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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(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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(CasePair Zero (BV 0) (SN $ FT "B")
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(SY ["l", "r"] $ 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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(CasePair Any (BV 0) (SN $ FT "A")
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(SY ["l", "r"] $ 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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(CasePair One (BV 0) (SN $ FT "A")
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(SY ["l", "r"] $ 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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(CasePair One (BV 0) (SN $ FT "A")
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(SY ["l", "r"] $ 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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@ -356,7 +344,7 @@ tests = "typechecker" :- [
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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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(Pi_ Any "A" (Sig_ "A" (TYPE 0) $ BVT 0) $
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(E $ F "fst" :@@ [TYPE 0, ["x"] :\\ BVT 0, BVT 0]))
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],
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@ -373,20 +361,19 @@ tests = "typechecker" :- [
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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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check_ (ctx [<]) sone (DLam $ SN $ FT "a")
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(Eq0 (FT "A") (FT "a") (FT "a")),
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testTC "0 · (λ p q ⇒ λᴰ i ⇒ p) ⇐ (ω·p q : a ≡ a') → p ≡ q" $
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check_ (ctx [<]) szero
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(Lam $ S ["p"] $ Y $ Lam $ S ["q"] $ N $ DLam $ S ["i"] $ N $ BVT 0)
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(Pi Any (Eq0 (FT "A") (FT "a") (FT "a")) $ S ["p"] $ Y $
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Pi Any (Eq0 (FT "A") (FT "a") (FT "a")) $ S ["q"] $ Y $
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(["p","q"] :\\ ["i"] :\\% BVT 1)
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(Pi_ Any "p" (Eq0 (FT "A") (FT "a") (FT "a")) $
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Pi_ Any "q" (Eq0 (FT "A") (FT "a") (FT "a")) $
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Eq0 (Eq0 (FT "A") (FT "a") (FT "a")) (BVT 1) (BVT 0)),
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testTC "0 · (λ p q ⇒ λᴰ i ⇒ q) ⇐ (ω·p q : a ≡ a') → p ≡ q" $
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check_ (ctx [<]) szero
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||||
(Lam $ S ["p"] $ N $ Lam $ S ["q"] $ Y $
|
||||
DLam $ S ["i"] $ N $ BVT 0)
|
||||
(Pi Any (Eq0 (FT "A") (FT "a") (FT "a")) $ S ["p"] $ Y $
|
||||
Pi Any (Eq0 (FT "A") (FT "a") (FT "a")) $ S ["q"] $ Y $
|
||||
(["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))
|
||||
],
|
||||
|
||||
|
|
@ -398,11 +385,11 @@ tests = "typechecker" :- [
|
|||
testTC "cong" $
|
||||
check_ (ctx [<]) sone
|
||||
(["x", "y", "xy"] :\\ ["i"] :\\% E (F "p" :@ E (BV 0 :% BV 0)))
|
||||
(Pi Zero (FT "A") $ S ["x"] $ Y $
|
||||
Pi Zero (FT "A") $ S ["y"] $ Y $
|
||||
Pi One (Eq0 (FT "A") (BVT 1) (BVT 0)) $ S ["xy"] $ Y $
|
||||
Eq (S ["i"] $ Y $ E $ F "P" :@ E (BV 0 :% BV 0))
|
||||
(E $ F "p" :@ BVT 2) (E $ F "p" :@ BVT 1)),
|
||||
(Pi_ Zero "x" (FT "A") $
|
||||
Pi_ Zero "y" (FT "A") $
|
||||
Pi_ One "xy" (Eq0 (FT "A") (BVT 1) (BVT 0)) $
|
||||
Eq_ "i" (E $ F "P" :@ E (BV 0 :% BV 0))
|
||||
(E $ F "p" :@ BVT 2) (E $ F "p" :@ BVT 1)),
|
||||
note "0·A : Type, 0·P : ω·A → Type,",
|
||||
note "ω·p q : (1·x : A) → P x",
|
||||
note "⊢",
|
||||
|
|
@ -411,12 +398,10 @@ tests = "typechecker" :- [
|
|||
testTC "funext" $
|
||||
check_ (ctx [<]) sone
|
||||
(["eq"] :\\ ["i"] :\\% ["x"] :\\ E (BV 1 :@ BVT 0 :% BV 0))
|
||||
(Pi One
|
||||
(Pi One (FT "A") $ S ["x"] $ Y $
|
||||
Eq0 (E $ F "P" :@ BVT 0)
|
||||
(E $ F "p" :@ BVT 0) (E $ F "q" :@ BVT 0)) $
|
||||
S ["eq"] $ Y $
|
||||
Eq0 (Pi Any (FT "A") $ S ["x"] $ Y $ E $ F "P" :@ BVT 0)
|
||||
(FT "p") (FT "q"))
|
||||
(Pi_ One "eq"
|
||||
(Pi_ One "x" (FT "A")
|
||||
(Eq0 (E $ F "P" :@ BVT 0)
|
||||
(E $ F "p" :@ BVT 0) (E $ F "q" :@ BVT 0)))
|
||||
(Eq0 (Pi_ Any "x" (FT "A") $ E $ F "P" :@ BVT 0) (FT "p") (FT "q")))
|
||||
]
|
||||
]
|
||||
|
|
|
|||
Loading…
Reference in New Issue