pass a `TyContext` into `equal` etc, rather than its components
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@ -285,8 +285,7 @@ parameters (defs : Definitions' q _) {auto _ : (CanEqual q m, Eq q)}
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compare0' _ e@(_ :# _) f _ _ = clashE e f
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parameters {auto _ : (HasDefs' q _ m, HasErr q m, Eq q)}
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(eq : DimEq d) (ctx : TContext q d n)
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parameters {auto _ : (HasDefs' q _ m, HasErr q m, Eq q)} (ctx : TyContext q d n)
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parameters (mode : EqMode)
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namespace Term
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export covering
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@ -294,16 +293,17 @@ parameters {auto _ : (HasDefs' q _ m, HasErr q m, Eq q)}
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compare ty s t = do
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defs <- ask
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runReaderT {m} (MakeEnv {mode}) $
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for_ (splits eq) $ \th =>
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compare0 defs (map (/// th) ctx) (ty /// th) (s /// th) (t /// th)
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for_ (splits ctx.dctx) $ \th =>
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compare0 defs (map (/// th) ctx.tctx)
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(ty /// th) (s /// th) (t /// th)
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export covering
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compareType : (s, t : Term q d n) -> m ()
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compareType s t = do
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defs <- ask
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runReaderT {m} (MakeEnv {mode}) $
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for_ (splits eq) $ \th =>
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compareType defs (map (/// th) ctx) (s /// th) (t /// th)
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for_ (splits ctx.dctx) $ \th =>
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compareType defs (map (/// th) ctx.tctx) (s /// th) (t /// th)
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namespace Elim
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||| you don't have to pass the type in but the arguments must still be
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@ -313,8 +313,8 @@ parameters {auto _ : (HasDefs' q _ m, HasErr q m, Eq q)}
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compare e f = do
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defs <- ask
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runReaderT {m} (MakeEnv {mode}) $
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for_ (splits eq) $ \th =>
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compare0 defs (map (/// th) ctx) (e /// th) (f /// th)
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for_ (splits ctx.dctx) $ \th =>
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compare0 defs (map (/// th) ctx.tctx) (e /// th) (f /// th)
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namespace Term
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export covering %inline
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@ -168,9 +168,9 @@ parameters {auto _ : IsQty q} {auto _ : CanTC q m}
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-- if Ψ, i | Γ ⊢ σ · t ⇐ A ⊳ Σ
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qout <- check (extendDim ctx) sg body.term ty.term
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-- if Ψ | Γ ⊢ t‹0› = l : A‹0›
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equal ctx.dctx ctx.tctx ty.zero body.zero l
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equal ctx ty.zero body.zero l
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-- if Ψ | Γ ⊢ t‹1› = r : A‹1›
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equal ctx.dctx ctx.tctx ty.one body.one r
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equal ctx ty.one body.one r
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-- then Ψ | Γ ⊢ σ · (λᴰi ⇒ t) ⇐ Eq [i ⇒ A] l r ⊳ Σ
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pure qout
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@ -178,7 +178,7 @@ parameters {auto _ : IsQty q} {auto _ : CanTC q m}
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-- if Ψ | Γ ⊢ σ · e ⇒ A' ⊳ Σ
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infres <- infer ctx sg e
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-- if Ψ | Γ ⊢ A' <: A
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subtype ctx.dctx ctx.tctx infres.type ty
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subtype ctx infres.type ty
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-- then Ψ | Γ ⊢ σ · e ⇐ A ⊳ Σ
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pure infres.qout
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@ -44,6 +44,10 @@ namespace TContext
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pushD tel = map (/// shift 1) tel
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namespace TyContext
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public export %inline
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empty : {d : Nat} -> TyContext q d 0
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empty = MkTyContext {dctx = new, tctx = [<]}
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export %inline
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extendTyN : Telescope (Term q d) from to ->
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TyContext q d from -> TyContext q d to
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@ -28,20 +28,24 @@ parameters (label : String) (act : Lazy (M ()))
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testNeq = testThrows label (const True) $ runReaderT globals act
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parameters {default 0 d, n : Nat}
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{default new eqs : DimEq d}
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(ctx : TContext Three d n)
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subT : Term Three d n -> Term Three d n -> Term Three d n -> M ()
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subT ty s t = Term.sub eqs ctx ty s t
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parameters (0 d : Nat) (ctx : TyContext Three d n)
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subTD, equalTD : Term Three d n -> Term Three d n -> Term Three d n -> M ()
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subTD ty s t = Term.sub ctx ty s t
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equalTD ty s t = Term.equal ctx ty s t
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equalT : Term Three d n -> Term Three d n -> Term Three d n -> M ()
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equalT ty s t = Term.equal eqs ctx ty s t
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subED, equalED : Elim Three d n -> Elim Three d n -> M ()
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subED e f = Elim.sub ctx e f
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equalED e f = Elim.equal ctx e f
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subE : Elim Three d n -> Elim Three d n -> M ()
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subE e f = Elim.sub eqs ctx e f
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parameters (ctx : TyContext Three 0 n)
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subT, equalT : Term Three 0 n -> Term Three 0 n -> Term Three 0 n -> M ()
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subT = subTD 0 ctx
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equalT = equalTD 0 ctx
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subE, equalE : Elim Three 0 n -> Elim Three 0 n -> M ()
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subE = subED 0 ctx
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equalE = equalED 0 ctx
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equalE : Elim Three d n -> Elim Three d n -> M ()
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equalE e f = Elim.equal eqs ctx e f
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export
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@ -52,17 +56,17 @@ tests = "equality & subtyping" :- [
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"universes" :- [
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testEq "★₀ = ★₀" $
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equalT [<] (TYPE 1) (TYPE 0) (TYPE 0),
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equalT empty (TYPE 1) (TYPE 0) (TYPE 0),
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testNeq "★₀ ≠ ★₁" $
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equalT [<] (TYPE 2) (TYPE 0) (TYPE 1),
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equalT empty (TYPE 2) (TYPE 0) (TYPE 1),
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testNeq "★₁ ≠ ★₀" $
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equalT [<] (TYPE 2) (TYPE 1) (TYPE 0),
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equalT empty (TYPE 2) (TYPE 1) (TYPE 0),
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testEq "★₀ <: ★₀" $
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subT [<] (TYPE 1) (TYPE 0) (TYPE 0),
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subT empty (TYPE 1) (TYPE 0) (TYPE 0),
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testEq "★₀ <: ★₁" $
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subT [<] (TYPE 2) (TYPE 0) (TYPE 1),
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subT empty (TYPE 2) (TYPE 0) (TYPE 1),
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testNeq "★₁ ≮: ★₀" $
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subT [<] (TYPE 2) (TYPE 1) (TYPE 0)
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subT empty (TYPE 2) (TYPE 1) (TYPE 0)
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],
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"pi" :- [
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@ -70,79 +74,79 @@ tests = "equality & subtyping" :- [
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note #""𝐴 ⇾ 𝐵" for (0·𝐴) → 𝐵"#,
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testEq "★₀ ⇾ ★₀ = ★₀ ⇾ ★₀" $
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let tm = Arr Zero (TYPE 0) (TYPE 0) in
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equalT [<] (TYPE 1) tm tm,
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equalT empty (TYPE 1) tm tm,
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testEq "★₀ ⇾ ★₀ <: ★₀ ⇾ ★₀" $
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let tm = Arr Zero (TYPE 0) (TYPE 0) in
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subT [<] (TYPE 1) tm tm,
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subT empty (TYPE 1) tm tm,
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testNeq "★₁ ⊸ ★₀ ≠ ★₀ ⇾ ★₀" $
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let tm1 = Arr Zero (TYPE 1) (TYPE 0)
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tm2 = Arr Zero (TYPE 0) (TYPE 0) in
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equalT [<] (TYPE 2) tm1 tm2,
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equalT empty (TYPE 2) tm1 tm2,
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testEq "★₁ ⊸ ★₀ <: ★₀ ⊸ ★₀" $
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let tm1 = Arr One (TYPE 1) (TYPE 0)
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tm2 = Arr One (TYPE 0) (TYPE 0) in
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subT [<] (TYPE 2) tm1 tm2,
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subT empty (TYPE 2) tm1 tm2,
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testEq "★₀ ⊸ ★₀ <: ★₀ ⊸ ★₁" $
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let tm1 = Arr One (TYPE 0) (TYPE 0)
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tm2 = Arr One (TYPE 0) (TYPE 1) in
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subT [<] (TYPE 2) tm1 tm2,
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subT empty (TYPE 2) tm1 tm2,
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testEq "★₀ ⊸ ★₀ <: ★₀ ⊸ ★₁" $
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let tm1 = Arr One (TYPE 0) (TYPE 0)
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tm2 = Arr One (TYPE 0) (TYPE 1) in
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subT [<] (TYPE 2) tm1 tm2,
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subT empty (TYPE 2) tm1 tm2,
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testEq "A ⊸ B = A ⊸ B" $
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let tm = Arr One (FT "A") (FT "B") in
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equalT [<] (TYPE 0) tm tm,
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equalT empty (TYPE 0) tm tm,
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testEq "A ⊸ B <: A ⊸ B" $
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let tm = Arr One (FT "A") (FT "B") in
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subT [<] (TYPE 0) tm tm,
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subT empty (TYPE 0) tm tm,
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note "incompatible quantities",
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testNeq "★₀ ⊸ ★₀ ≠ ★₀ ⇾ ★₁" $
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let tm1 = Arr Zero (TYPE 0) (TYPE 0)
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tm2 = Arr Zero (TYPE 0) (TYPE 1) in
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equalT [<] (TYPE 2) tm1 tm2,
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equalT empty (TYPE 2) tm1 tm2,
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testNeq "A ⇾ B ≠ A ⊸ B" $
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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 [<] (TYPE 0) tm1 tm2,
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equalT empty (TYPE 0) tm1 tm2,
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testNeq "A ⇾ B ≮: A ⊸ B" $
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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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subT [<] (TYPE 0) tm1 tm2,
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subT empty (TYPE 0) tm1 tm2,
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testEq "0=1 ⊢ A ⇾ B = A ⊸ B" $
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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 [<] (TYPE 0) tm1 tm2 {eqs = ZeroIsOne},
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equalT (MkTyContext ZeroIsOne [<]) (TYPE 0) tm1 tm2,
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note "[todo] should π ≤ ρ ⊢ (ρ·A) → B <: (π·A) → B?"
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],
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"lambda" :- [
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testEq "λ x ⇒ [x] = λ x ⇒ [x]" $
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equalT [<] (Arr One (FT "A") (FT "A"))
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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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testEq "λ x ⇒ [x] <: λ x ⇒ [x]" $
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subT [<] (Arr One (FT "A") (FT "A"))
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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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testEq "λ x ⇒ [x] = λ y ⇒ [y]" $
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equalT [<] (Arr One (FT "A") (FT "A"))
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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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testEq "λ x ⇒ [x] <: λ y ⇒ [y]" $
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equalT [<] (Arr One (FT "A") (FT "A"))
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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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testNeq "λ x y ⇒ [x] ≠ λ x y ⇒ [y]" $
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equalT [<] (Arr One (FT "A") $ Arr One (FT "A") (FT "A"))
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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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testEq "λ x ⇒ [a] = λ x ⇒ [a] (TUsed vs TUnused)" $
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equalT [<] (Arr Zero (FT "B") (FT "A"))
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equalT empty (Arr Zero (FT "B") (FT "A"))
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(Lam "x" $ TUsed $ FT "a")
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(Lam "x" $ TUnused $ FT "a"),
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testEq "λ x ⇒ [f [x]] = [f] (η)" $
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equalT [<] (Arr One (FT "A") (FT "A"))
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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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(FT "f")
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],
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@ -150,10 +154,10 @@ tests = "equality & subtyping" :- [
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"eq type" :- [
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testEq "(★₀ ≡ ★₀ : ★₁) = (★₀ ≡ ★₀ : ★₁)" $
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let tm = Eq0 (TYPE 1) (TYPE 0) (TYPE 0) in
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equalT [<] (TYPE 2) tm tm,
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equalT empty (TYPE 2) tm tm,
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testEq "A ≔ ★₁ ⊢ (★₀ ≡ ★₀ : ★₁) = (★₀ ≡ ★₀ : A)"
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{globals = fromList [("A", mkDef zero (TYPE 2) (TYPE 1))]} $
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equalT [<] (TYPE 2)
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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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],
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@ -166,86 +170,86 @@ tests = "equality & subtyping" :- [
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note #""refl [A] x" is an abbreviation for "(λᴰi ⇒ x) ∷ (x ≡ x : A)""#,
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note "binds before ∥ are globals, after it are BVs",
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testEq "refl [A] a = refl [A] a" $
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equalE [<] (refl (FT "A") (FT "a")) (refl (FT "A") (FT "a")),
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equalE empty (refl (FT "A") (FT "a")) (refl (FT "A") (FT "a")),
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testEq "p : (a ≡ a' : A), q : (a ≡ a' : A) ∥ ⊢ p = q (free)"
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{globals =
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let def = mkAbstract Zero $ Eq0 (FT "A") (FT "a") (FT "a'") in
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defGlobals `mergeLeft` fromList [("p", def), ("q", def)]} $
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equalE [<] (F "p") (F "q"),
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equalE empty (F "p") (F "q"),
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testEq "∥ x : (a ≡ a' : A), y : (a ≡ a' : A) ⊢ x = y (bound)" $
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let ty : forall n. Term Three 0 n := Eq0 (FT "A") (FT "a") (FT "a'") in
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equalE [< ty, ty] (BV 0) (BV 1) {n = 2},
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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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equalE [< ty, ty] (BV 0) (BV 1) {n = 2},
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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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{globals = defGlobals `mergeLeft` fromList
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[("E", mkDef zero (TYPE 0) (Eq0 (FT "A") (FT "a") (FT "a'"))),
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("EE", mkDef zero (TYPE 0) (FT "E"))]} $
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equalE [< FT "EE", FT "EE"] (BV 0) (BV 1) {n = 2},
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equalE (MkTyContext new [< FT "EE", FT "EE"]) (BV 0) (BV 1),
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testEq "E ≔ a ≡ a' : A, EE ≔ E ∥ x : EE, y : 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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("EE", mkDef zero (TYPE 0) (FT "E"))]} $
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equalE [< FT "EE", FT "E"] (BV 0) (BV 1) {n = 2},
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equalE (MkTyContext new [< FT "EE", FT "E"]) (BV 0) (BV 1),
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testEq "E ≔ a ≡ a' : A ∥ x : E, y : 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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equalE [< FT "E", FT "E"] (BV 0) (BV 1) {n = 2},
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equalE (MkTyContext new [< FT "E", FT "E"]) (BV 0) (BV 1),
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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") $ TUnused $ FT "E" in
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equalE [< ty, ty] (BV 0) (BV 1) {n = 2},
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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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{globals = defGlobals `mergeLeft` fromList
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[("E", mkDef zero (TYPE 0) (Eq0 (FT "A") (FT "a") (FT "a'"))),
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("W", mkDef zero (TYPE 0) (FT "E" `And` FT "E"))]} $
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equalE [< FT "W", FT "W"] (BV 0) (BV 1) {n = 2}
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equalE (MkTyContext new [< FT "W", FT "W"]) (BV 0) (BV 1)
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],
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"term closure" :- [
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testEq "[#0]{} = [#0] : A" $
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equalT [< FT "A"] (FT "A") {n = 1}
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equalT (MkTyContext new [< FT "A"]) (FT "A")
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(CloT (BVT 0) id)
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(BVT 0),
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testEq "[#0]{a} = [a] : A" $
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equalT [<] (FT "A")
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equalT empty (FT "A")
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(CloT (BVT 0) (F "a" ::: id))
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(FT "a"),
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testEq "[#0]{a,b} = [a] : A" $
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equalT [<] (FT "A")
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equalT empty (FT "A")
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(CloT (BVT 0) (F "a" ::: F "b" ::: id))
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(FT "a"),
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testEq "[#1]{a,b} = [b] : A" $
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equalT [<] (FT "A")
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equalT empty (FT "A")
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(CloT (BVT 1) (F "a" ::: F "b" ::: id))
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(FT "b"),
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testEq "(λy. [#1]){a} = λy. [a] : B ⇾ A (TUnused)" $
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equalT [<] (Arr Zero (FT "B") (FT "A"))
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equalT empty (Arr Zero (FT "B") (FT "A"))
|
||||
(CloT (Lam "y" $ TUnused $ BVT 0) (F "a" ::: id))
|
||||
(Lam "y" $ TUnused $ FT "a"),
|
||||
testEq "(λy. [#1]){a} = λy. [a] : B ⇾ A (TUsed)" $
|
||||
equalT [<] (Arr Zero (FT "B") (FT "A"))
|
||||
equalT empty (Arr Zero (FT "B") (FT "A"))
|
||||
(CloT (["y"] :\\ BVT 1) (F "a" ::: id))
|
||||
(["y"] :\\ FT "a")
|
||||
],
|
||||
|
||||
"term d-closure" :- [
|
||||
testEq "★₀‹𝟎› = ★₀ : ★₁" $
|
||||
equalT {d = 1} [<] (TYPE 1) (DCloT (TYPE 0) (K Zero ::: id)) (TYPE 0),
|
||||
equalTD 1 empty (TYPE 1) (DCloT (TYPE 0) (K Zero ::: id)) (TYPE 0),
|
||||
testEq "(λᴰ i ⇒ a)‹𝟎› = (λᴰ i ⇒ a) : (a ≡ a : A)" $
|
||||
equalT {d = 1} [<]
|
||||
equalTD 1 empty
|
||||
(Eq0 (FT "A") (FT "a") (FT "a"))
|
||||
(DCloT (["i"] :\\% FT "a") (K Zero ::: id))
|
||||
(["i"] :\\% FT "a"),
|
||||
|
|
@ -261,136 +265,137 @@ tests = "equality & subtyping" :- [
|
|||
("B", mkDef Any (TYPE (U 1)) (FT "A"))]
|
||||
in [
|
||||
testEq "A = A" $
|
||||
equalE [<] (F "A") (F "A"),
|
||||
equalE empty (F "A") (F "A"),
|
||||
testNeq "A ≠ B" $
|
||||
equalE [<] (F "A") (F "B"),
|
||||
equalE empty (F "A") (F "B"),
|
||||
testEq "0=1 ⊢ A = B" $
|
||||
equalE {eqs = ZeroIsOne} [<] (F "A") (F "B"),
|
||||
equalE (MkTyContext ZeroIsOne [<]) (F "A") (F "B"),
|
||||
testEq "A : ★₁ ≔ ★₀ ⊢ A = (★₀ ∷ ★₁)" {globals = au_bu} $
|
||||
equalE [<] (F "A") (TYPE 0 :# TYPE 1),
|
||||
equalE empty (F "A") (TYPE 0 :# TYPE 1),
|
||||
testEq "A : ★₁ ≔ ★₀ ⊢ [A] = ★₀" {globals = au_bu} $
|
||||
equalT [<] (TYPE 1) (FT "A") (TYPE 0),
|
||||
equalT empty (TYPE 1) (FT "A") (TYPE 0),
|
||||
testEq "A ≔ ★₀, B ≔ ★₀ ⊢ A = B" {globals = au_bu} $
|
||||
equalE [<] (F "A") (F "B"),
|
||||
equalE empty (F "A") (F "B"),
|
||||
testEq "A ≔ ★₀, B ≔ A ⊢ A = B" {globals = au_ba} $
|
||||
equalE [<] (F "A") (F "B"),
|
||||
equalE empty (F "A") (F "B"),
|
||||
testEq "A <: A" $
|
||||
subE [<] (F "A") (F "A"),
|
||||
subE empty (F "A") (F "A"),
|
||||
testNeq "A ≮: B" $
|
||||
subE [<] (F "A") (F "B"),
|
||||
subE empty (F "A") (F "B"),
|
||||
testEq "A : ★₃ ≔ ★₀, B : ★₃ ≔ ★₂ ⊢ A <: B"
|
||||
{globals = fromList [("A", mkDef Any (TYPE 3) (TYPE 0)),
|
||||
("B", mkDef Any (TYPE 3) (TYPE 2))]} $
|
||||
subE [<] (F "A") (F "B"),
|
||||
subE empty (F "A") (F "B"),
|
||||
note "(A and B in different universes)",
|
||||
testEq "A : ★₁ ≔ ★₀, B : ★₃ ≔ ★₂ ⊢ A <: B"
|
||||
{globals = fromList [("A", mkDef Any (TYPE 1) (TYPE 0)),
|
||||
("B", mkDef Any (TYPE 3) (TYPE 2))]} $
|
||||
subE [<] (F "A") (F "B"),
|
||||
subE empty (F "A") (F "B"),
|
||||
testEq "0=1 ⊢ A <: B" $
|
||||
subE [<] (F "A") (F "B") {eqs = ZeroIsOne}
|
||||
subE (MkTyContext ZeroIsOne [<]) (F "A") (F "B")
|
||||
],
|
||||
|
||||
"bound var" :- [
|
||||
testEq "#0 = #0" $
|
||||
equalE [< TYPE 0] (BV 0) (BV 0) {n = 1},
|
||||
equalE (MkTyContext new [< TYPE 0]) (BV 0) (BV 0),
|
||||
testEq "#0 <: #0" $
|
||||
subE [< TYPE 0] (BV 0) (BV 0) {n = 1},
|
||||
subE (MkTyContext new [< TYPE 0]) (BV 0) (BV 0),
|
||||
testNeq "#0 ≠ #1" $
|
||||
equalE [< TYPE 0, TYPE 0] (BV 0) (BV 1) {n = 2},
|
||||
equalE (MkTyContext new [< TYPE 0, TYPE 0]) (BV 0) (BV 1),
|
||||
testNeq "#0 ≮: #1" $
|
||||
subE [< TYPE 0, TYPE 0] (BV 0) (BV 1) {n = 2},
|
||||
subE (MkTyContext new [< TYPE 0, TYPE 0]) (BV 0) (BV 1),
|
||||
testEq "0=1 ⊢ #0 = #1" $
|
||||
equalE [< TYPE 0, TYPE 0] (BV 0) (BV 1)
|
||||
{n = 2, eqs = ZeroIsOne}
|
||||
equalE (MkTyContext ZeroIsOne [< TYPE 0, TYPE 0]) (BV 0) (BV 1)
|
||||
],
|
||||
|
||||
"application" :- [
|
||||
testEq "f [a] = f [a]" $
|
||||
equalE [<] (F "f" :@ FT "a") (F "f" :@ FT "a"),
|
||||
equalE empty (F "f" :@ FT "a") (F "f" :@ FT "a"),
|
||||
testEq "f [a] <: f [a]" $
|
||||
subE [<] (F "f" :@ FT "a") (F "f" :@ FT "a"),
|
||||
subE empty (F "f" :@ FT "a") (F "f" :@ FT "a"),
|
||||
testEq "(λ x ⇒ [x] ∷ A ⊸ A) a = ([a ∷ A] ∷ A) (β)" $
|
||||
equalE [<]
|
||||
equalE empty
|
||||
(((["x"] :\\ 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 [<]
|
||||
equalE empty
|
||||
(((["x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
|
||||
(F "a"),
|
||||
testEq "(λ g ⇒ [g [a]] ∷ ⋯)) [f] = (λ y ⇒ [f [y]] ∷ ⋯) [a] (β↘↙)" $
|
||||
let a = FT "A"; a2a = (Arr One a a) in
|
||||
equalE [<]
|
||||
equalE empty
|
||||
(((["g"] :\\ E (BV 0 :@ FT "a")) :# Arr One a2a a) :@ FT "f")
|
||||
(((["y"] :\\ E (F "f" :@ BVT 0)) :# a2a) :@ FT "a"),
|
||||
testEq "(λ x ⇒ [x] ∷ A ⊸ A) a <: a" $
|
||||
subE [<]
|
||||
subE empty
|
||||
(((["x"] :\\ BVT 0) :# (Arr One (FT "A") (FT "A"))) :@ FT "a")
|
||||
(F "a"),
|
||||
note "id : A ⊸ A ≔ λ x ⇒ [x]",
|
||||
testEq "id [a] = a" $ equalE [<] (F "id" :@ FT "a") (F "a"),
|
||||
testEq "id [a] <: a" $ subE [<] (F "id" :@ FT "a") (F "a")
|
||||
testEq "id [a] = a" $ equalE empty (F "id" :@ FT "a") (F "a"),
|
||||
testEq "id [a] <: a" $ subE empty (F "id" :@ FT "a") (F "a")
|
||||
],
|
||||
|
||||
todo "dim application",
|
||||
|
||||
"annotation" :- [
|
||||
testEq "(λ x ⇒ f [x]) ∷ A ⊸ A = [f] ∷ A ⊸ A" $
|
||||
equalE [<]
|
||||
equalE empty
|
||||
((["x"] :\\ E (F "f" :@ BVT 0)) :# Arr One (FT "A") (FT "A"))
|
||||
(FT "f" :# Arr One (FT "A") (FT "A")),
|
||||
testEq "[f] ∷ A ⊸ A = f" $
|
||||
equalE [<] (FT "f" :# Arr One (FT "A") (FT "A")) (F "f"),
|
||||
equalE empty (FT "f" :# Arr One (FT "A") (FT "A")) (F "f"),
|
||||
testEq "(λ x ⇒ f [x]) ∷ A ⊸ A = f" $
|
||||
equalE [<]
|
||||
equalE empty
|
||||
((["x"] :\\ E (F "f" :@ BVT 0)) :# Arr One (FT "A") (FT "A"))
|
||||
(F "f")
|
||||
],
|
||||
|
||||
"elim closure" :- [
|
||||
testEq "#0{a} = a" $
|
||||
equalE [<] (CloE (BV 0) (F "a" ::: id)) (F "a"),
|
||||
equalE empty (CloE (BV 0) (F "a" ::: id)) (F "a"),
|
||||
testEq "#1{a} = #0" $
|
||||
equalE [< FT "A"] (CloE (BV 1) (F "a" ::: id)) (BV 0) {n = 1}
|
||||
equalE (MkTyContext new [< FT "A"])
|
||||
(CloE (BV 1) (F "a" ::: id)) (BV 0)
|
||||
],
|
||||
|
||||
"elim d-closure" :- [
|
||||
note "0·eq-ab : (A ≡ B : ★₀)",
|
||||
testEq "(eq-ab #0)‹𝟎› = eq-ab 𝟎" $
|
||||
equalE {d = 1} [<]
|
||||
equalED 1 empty
|
||||
(DCloE (F "eq-ab" :% BV 0) (K Zero ::: id))
|
||||
(F "eq-ab" :% K Zero),
|
||||
testEq "(eq-ab #0)‹𝟎› = A" $
|
||||
equalE {d = 1} [<] (DCloE (F "eq-ab" :% BV 0) (K Zero ::: id)) (F "A"),
|
||||
equalED 1 empty (DCloE (F "eq-ab" :% BV 0) (K Zero ::: id)) (F "A"),
|
||||
testEq "(eq-ab #0)‹𝟏› = B" $
|
||||
equalE {d = 1} [<] (DCloE (F "eq-ab" :% BV 0) (K One ::: id)) (F "B"),
|
||||
equalED 1 empty (DCloE (F "eq-ab" :% BV 0) (K One ::: id)) (F "B"),
|
||||
testNeq "(eq-ab #0)‹𝟏› ≠ A" $
|
||||
equalE {d = 1} [<] (DCloE (F "eq-ab" :% BV 0) (K One ::: id)) (F "A"),
|
||||
equalED 1 empty (DCloE (F "eq-ab" :% BV 0) (K One ::: id)) (F "A"),
|
||||
testEq "(eq-ab #0)‹#0,𝟎› = (eq-ab #0)" $
|
||||
equalE {d = 2} [<]
|
||||
equalED 2 empty
|
||||
(DCloE (F "eq-ab" :% BV 0) (BV 0 ::: K Zero ::: id))
|
||||
(F "eq-ab" :% BV 0),
|
||||
testNeq "(eq-ab #0)‹𝟎› ≠ (eq-ab 𝟎)" $
|
||||
equalE {d = 2} [<]
|
||||
equalED 2 empty
|
||||
(DCloE (F "eq-ab" :% BV 0) (BV 0 ::: K Zero ::: id))
|
||||
(F "eq-ab" :% K Zero),
|
||||
testEq "#0‹𝟎› = #0 # term and dim vars distinct" $
|
||||
equalE {d = 1, n = 1} [< FT "A"] (DCloE (BV 0) (K Zero ::: id)) (BV 0),
|
||||
equalED 1 (MkTyContext new [< FT "A"])
|
||||
(DCloE (BV 0) (K Zero ::: id)) (BV 0),
|
||||
testEq "a‹𝟎› = a" $
|
||||
equalE {d = 1} [<] (DCloE (F "a") (K Zero ::: id)) (F "a"),
|
||||
equalED 1 empty (DCloE (F "a") (K Zero ::: id)) (F "a"),
|
||||
testEq "(f [a])‹𝟎› = f‹𝟎› [a]‹𝟎›" $
|
||||
let th = (K Zero ::: id) in
|
||||
equalE {d = 1} [<]
|
||||
equalED 1 empty
|
||||
(DCloE (F "f" :@ FT "a") th)
|
||||
(DCloE (F "f") th :@ DCloT (FT "a") th)
|
||||
],
|
||||
|
||||
"clashes" :- [
|
||||
testNeq "★₀ ≠ ★₀ ⇾ ★₀" $
|
||||
equalT [<] (TYPE 1) (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0)),
|
||||
equalT empty (TYPE 1) (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0)),
|
||||
testEq "0=1 ⊢ ★₀ = ★₀ ⇾ ★₀" $
|
||||
equalT [<] (TYPE 1) (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0))
|
||||
{eqs = ZeroIsOne},
|
||||
equalT (MkTyContext ZeroIsOne [<])
|
||||
(TYPE 1) (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0)),
|
||||
todo "others"
|
||||
]
|
||||
]
|
||||
|
|
|
|||
|
|
@ -75,7 +75,7 @@ ctx = MkTyContext new
|
|||
inferredTypeEq : TyContext Three d n -> (exp, got : Term Three d n) -> M ()
|
||||
inferredTypeEq ctx exp got =
|
||||
catchError
|
||||
(inj $ equalType ctx.dctx ctx.tctx exp got)
|
||||
(inj $ equalType ctx exp got)
|
||||
(\_ : Error' => throwError $ WrongInfer exp got)
|
||||
|
||||
qoutEq : (exp, got : QOutput Three n) -> M ()
|
||||
|
|
|
|||
Loading…
Reference in New Issue