typed equality
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3b13f0a82c
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8 changed files with 410 additions and 250 deletions
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@ -35,6 +35,10 @@ mkAbstract : IsQty q => (qty : q) -> (0 _ : IsGlobal qty) =>
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mkAbstract qty type = MkDef' {qty, type = T type, term = Nothing}
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public export %inline
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(.get0) : AnyTerm q -> Term q 0 0
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t.get0 = t.get
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public export %inline
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(.type0) : Definition' q _ -> Term q 0 0
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g.type0 = g.type.get
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@ -117,10 +121,10 @@ NonRedexTerm q d n defs = Subset (Term q d n) (NotRedex defs)
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parameters {0 isGlobal : _} (defs : Definitions' q isGlobal)
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namespace Term
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export %inline
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whnf : Term q d n -> NonRedexTerm q d n defs
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whnf = whnf $ \x => lookupElim x defs
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whnfD : Term q d n -> NonRedexTerm q d n defs
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whnfD = whnf $ \x => lookupElim x defs
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namespace Elim
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export %inline
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whnf : Elim q d n -> NonRedexElim q d n defs
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whnf = whnf $ \x => lookupElim x defs
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whnfD : Elim q d n -> NonRedexElim q d n defs
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whnfD = whnf $ \x => lookupElim x defs
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@ -9,8 +9,8 @@ import Data.Maybe
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private %inline
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ClashE : EqMode -> Elim q d n -> Elim q d n -> Error q
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ClashE mode = ClashT mode `on` E
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ClashE : EqMode -> Term q d n -> Elim q d n -> Elim q d n -> Error q
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ClashE mode ty = ClashT mode ty `on` E
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public export
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@ -34,179 +34,262 @@ mode : HasEnv m => m EqMode
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mode = asks mode
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private %inline
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clashT : CanEqual q m => Term q d n -> Term q d n -> m a
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clashT s t = throwError $ ClashT !mode s t
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clashT : CanEqual q m => Term q d n -> Term q d n -> Term q d n -> m a
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clashT ty s t = throwError $ ClashT !mode ty s t
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private %inline
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clashE : CanEqual q m => Elim q d n -> Elim q d n -> m a
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clashE e f = throwError $ ClashE !mode e f
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parameters {0 isGlobal : _} (defs : Definitions' q isGlobal)
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public export %inline
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isType : (t : Term {}) -> Bool
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isType (TYPE {}) = True
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isType (Pi {}) = True
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isType (Lam {}) = False
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isType (Sig {}) = True
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isType (Pair {}) = False
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isType (Eq {}) = True
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isType (DLam {}) = False
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isType (E {}) = True
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isType (CloT {}) = False
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isType (DCloT {}) = False
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parameters {auto _ : HasErr q m}
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export %inline
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ensure : (a -> Error q) -> (p : a -> Bool) -> (t : a) -> m (So (p t))
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ensure e p t = case nchoose $ p t of
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Left y => pure y
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Right n => throwError $ e t
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export %inline
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ensureType : (t : Term q d n) -> m (So (isType t))
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ensureType = ensure NotType isType
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parameters (defs : Definitions' q _) {auto _ : (CanEqual q m, Eq q)}
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mutual
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-- [todo] remove cumulativity & subtyping, it's too much of a pain
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-- mugen might be good
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namespace Term
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export covering
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compareN' : CanEqual q m => Eq q =>
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(s, t : Term q 0 n) ->
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(0 _ : NotRedex defs s) -> (0 _ : NotRedex defs t) ->
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export covering %inline
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compare0 : TContext q 0 n -> (ty, s, t : Term q 0 n) -> m ()
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compare0 ctx ty s t = do
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let Element ty nty = whnfD defs ty
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Element s ns = whnfD defs s
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Element t nt = whnfD defs t
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tty <- ensureType ty
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compare0' ctx ty s t
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private %inline
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toLamBody : Elim q d n -> Term q d (S n)
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toLamBody e = E $ weakE e :@ BVT 0
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private covering
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compare0' : TContext q 0 n ->
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(ty, s, t : Term q 0 n) ->
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(0 nty : NotRedex defs ty) => (0 tty : So (isType ty)) =>
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(0 ns : NotRedex defs s) => (0 nt : NotRedex defs t) =>
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m ()
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compare0' ctx (TYPE _) s t = compareType ctx s t
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compareN' (TYPE k) (TYPE l) _ _ = expectModeU !mode k l
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compareN' s@(TYPE _) t _ _ = clashT s t
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compare0' ctx ty@(Pi {arg, res, _}) s t = local {mode := Equal} $
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let ctx' = ctx :< arg
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eta : Elim q 0 ? -> ScopeTerm q 0 ? -> m ()
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eta e (TUsed b) = compare0 ctx' res.term (toLamBody e) b
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eta e (TUnused _) = clashT ty s t
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in
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case (s, t) of
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(Lam _ b1, Lam _ b2) => compare0 ctx' res.term b1.term b2.term
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(E e, Lam _ b) => eta e b
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(Lam _ b, E e) => eta e b
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(E e, E f) => ignore $ compare0 ctx e f
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_ => throwError $ WrongType ty s t
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compareN' (Pi qty1 _ arg1 res1) (Pi qty2 _ arg2 res2) _ _ = do
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expectEqualQ qty1 qty2
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compare0 arg2 arg1 -- reversed for contravariant domain
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compare0 res1 res2
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compareN' s@(Pi {}) t _ _ = clashT s t
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compare0' ctx ty@(Sig {fst, snd, _}) s t = local {mode := Equal} $
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-- no η (no fst/snd for π ≱ 0), so…
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-- [todo] η for π ≥ 0 maybe
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case (s, t) of
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(Pair sFst sSnd, Pair tFst tSnd) => do
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compare0 ctx fst sFst tFst
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compare0 ctx (sub1 snd (sFst :# fst)) sSnd tSnd
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_ => throwError $ WrongType ty s t
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-- [todo] eta
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compareN' (Lam _ body1) (Lam _ body2) _ _ =
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local {mode := Equal} $ compare0 body1 body2
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compareN' s@(Lam {}) t _ _ = clashT s t
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-- ✨ uip ✨
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compare0' _ (Eq {}) _ _ = pure ()
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compareN' (Sig _ fst1 snd1) (Sig _ fst2 snd2) _ _ = do
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compare0 fst1 fst2
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compare0 snd1 snd2
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compareN' s@(Sig {}) t _ _ = clashT s t
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compare0' ctx ty@(E _) s t = do
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-- a neutral type can only be inhabited by neutral values
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-- e.g. an abstract value in an abstract type, bound variables, …
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E e <- pure s | _ => throwError $ WrongType ty s t
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E f <- pure t | _ => throwError $ WrongType ty s t
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ignore $ compare0 ctx e f
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compareN' (Pair fst1 snd1) (Pair fst2 snd2) _ _ =
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local {mode := Equal} $ do
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compare0 fst1 fst2
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compare0 snd1 snd2
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compareN' s@(Pair {}) t _ _ = clashT s t
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export covering
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compareType : TContext q 0 n -> (s, t : Term q 0 n) -> m ()
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compareType ctx s t = do
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let Element s ns = whnfD defs s
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Element t nt = whnfD defs t
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sok <- ensureType s
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tok <- ensureType t
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compareType' ctx s t
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compareN' (Eq _ ty1 l1 r1) (Eq _ ty2 l2 r2) _ _ = do
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compare0 ty1 ty2
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local {mode := Equal} $ do
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compare0 l1 l2
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compare0 r1 r2
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compareN' s@(Eq {}) t _ _ = clashT s t
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private covering
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compareType' : TContext q 0 n -> (s, t : Term q 0 n) ->
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(0 ns : NotRedex defs s) => (0 ts : So (isType s)) =>
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(0 nt : NotRedex defs t) => (0 tt : So (isType t)) =>
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m ()
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compareType' ctx s t = do
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let err : m () = clashT (TYPE UAny) s t
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case s of
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TYPE k => do
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TYPE l <- pure t | _ => err
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expectModeU !mode k l
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compareN' (DLam _ body1) (DLam _ body2) _ _ =
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local {mode := Equal} $ do
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compare0 body1 body2
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compareN' s@(DLam {}) t _ _ = clashT s t
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Pi {qty = sQty, arg = sArg, res = sRes, _} => do
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Pi {qty = tQty, arg = tArg, res = tRes, _} <- pure t | _ => err
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expectEqualQ sQty tQty
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compareType ctx tArg sArg -- contra
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-- [todo] is using sArg also ok for subtyping?
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compareType (ctx :< sArg) sRes.term tRes.term
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compareN' (E e) (E f) ne nf = compareN' e f (noOr2 ne) (noOr2 nf)
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compareN' s@(E e) t _ _ = clashT s t
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Sig {fst = sFst, snd = sSnd, _} => do
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Sig {fst = tFst, snd = tSnd, _} <- pure t | _ => err
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compareType ctx sFst tFst
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compareType (ctx :< sFst) sSnd.term tSnd.term
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Eq {ty = sTy, l = sl, r = sr, _} => do
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Eq {ty = tTy, l = tl, r = tr, _} <- pure t | _ => err
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compareType ctx sTy.zero tTy.zero
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compareType ctx sTy.one tTy.one
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local {mode := Equal} $ do
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compare0 ctx sTy.zero sl tl
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compare0 ctx sTy.one sr tr
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E e => do
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E f <- pure t | _ => err
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-- no fanciness needed here cos anything other than a neutral
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-- has been inlined by whnfD
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ignore $ compare0 ctx e f
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namespace Elim
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export covering
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compareN' : CanEqual q m => Eq q =>
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export covering %inline
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compare0 : TContext q 0 n -> (e, f : Elim q 0 n) -> m (Term q 0 n)
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compare0 ctx e f =
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let Element e ne = whnfD defs e
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Element f nf = whnfD defs f
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in
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compare0' ctx e f
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private
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isSubSing : Term {} -> Bool
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isSubSing (TYPE _) = False
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isSubSing (Pi {res, _}) = isSubSing res.term
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isSubSing (Lam {}) = False
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isSubSing (Sig {fst, snd, _}) = isSubSing fst && isSubSing snd.term
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isSubSing (Pair {}) = False
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isSubSing (Eq {}) = True
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isSubSing (DLam {}) = False
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isSubSing (E e) = False
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isSubSing (CloT tm th) = False
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isSubSing (DCloT tm th) = False
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private covering
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compare0' : TContext q 0 n ->
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(e, f : Elim q 0 n) ->
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(0 _ : NotRedex defs e) -> (0 _ : NotRedex defs f) ->
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m ()
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(0 ne : NotRedex defs e) => (0 nf : NotRedex defs f) =>
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m (Term q 0 n)
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compare0' _ e@(F x) f@(F y) = do
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d <- lookupFree' defs x
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let ty = d.type
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-- [fixme] there is a better way to do this for sure
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unless (isSubSing ty.get0 || x == y) $ clashE e f
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pure ty.get
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compare0' _ e@(F _) f = clashE e f
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compareN' e@(F x) f@(F y) _ _ =
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unless (x == y) $ clashE e f
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compareN' e@(F _) f _ _ = clashE e f
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compare0' ctx e@(B i) f@(B j) = do
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let ty = ctx !! i
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-- [fixme] there is a better way to do this for sure
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unless (isSubSing ty || i == j) $ clashE e f
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pure ty
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compare0' _ e@(B _) f = clashE e f
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compareN' e@(B i) f@(B j) _ _ =
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unless (i == j) $ clashE e f
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compareN' e@(B _) f _ _ = clashE e f
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compare0' ctx (e :@ s) (f :@ t) = local {mode := Equal} $ do
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Pi {arg, res, _} <- compare0 ctx e f
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| ty => throwError $ ExpectedPi ty
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compare0 ctx arg s t
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pure $ sub1 res (s :# arg)
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compare0' _ e@(_ :@ _) f = clashE e f
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-- [todo] tracking variance of functions? maybe???
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-- probably not
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compareN' (fun1 :@ arg1) (fun2 :@ arg2) _ _ =
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compare0' ctx (CasePair epi e _ eret _ _ ebody)
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(CasePair fpi f _ fret _ _ fbody) =
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local {mode := Equal} $ do
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compare0 fun1 fun2
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compare0 arg1 arg2
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compareN' e@(_ :@ _) f _ _ = clashE e f
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ty@(Sig {fst, snd, _}) <- compare0 ctx e f
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| ty => throwError $ ExpectedSig ty
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unless (epi == fpi) $ throwError $ ClashQ epi fpi
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compareType (ctx :< ty) eret.term fret.term
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compare0 (ctx :< fst :< snd.term) (substCasePairRet ty eret)
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ebody.term fbody.term
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pure $ sub1 eret e
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compare0' _ e@(CasePair {}) f = clashE e f
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compareN' (CasePair pi1 pair1 _ ret1 _ _ body1)
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(CasePair pi2 pair2 _ ret2 _ _ body2) _ _ =
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local {mode := Equal} $ do
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expectEqualQ pi1 pi2
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compare0 pair1 pair2
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compare0 ret1 ret2
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compare0 body1 body2
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compareN' e@(CasePair {}) f _ _ = clashE e f
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compare0' ctx (e :% p) (f :% q) = local {mode := Equal} $ do
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Eq {ty, _} <- compare0 ctx e f
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| ty => throwError $ ExpectedEq ty
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unless (p == q) $ throwError $ ClashD p q
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pure $ dsub1 ty p
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compare0' _ e@(_ :% _) f = clashE e f
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-- retain the mode unlike above because dimensions can't do
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-- anything that would mess up variance
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compareN' (fun1 :% dim1) (fun2 :% dim2) _ _ = do
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compare0 fun1 fun2
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expectEqualD dim1 dim2
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compareN' e@(_ :% _) f _ _ = clashE e f
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-- using the same mode for the type allows, e.g.
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-- A : ★₁ ≔ ★₀, B : ★₃ ≔ ★₂ ⊢ A <: B
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-- which, since A : ★₁ implies A : ★₃, should be fine
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compareN' (tm1 :# ty1) (tm2 :# ty2) _ _ = do
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compare0 tm1 tm2
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compare0 ty1 ty2
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compareN' e@(_ :# _) f _ _ = clashE e f
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compare0' ctx (s :# a) (t :# b) = do
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compareType ctx a b
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compare0 ctx a s t
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pure b
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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 (mode : EqMode)
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namespace Term
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export covering %inline
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compareN : CanEqual q m => Eq q =>
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NonRedexTerm q 0 n defs -> NonRedexTerm q 0 n defs -> m ()
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compareN s t = compareN' s.fst t.fst s.snd t.snd
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export covering
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compare : (ty, s, t : Term q d n) -> m ()
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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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export covering %inline
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compare : CanEqual q m => Eq q =>
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DimEq d -> Term q d n -> Term q d n -> m ()
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compare eqs s t =
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for_ (splits eqs) $ \th => compare0 (s /// th) (t /// th)
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export covering %inline
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compare0 : CanEqual q m => Eq q => Term q 0 n -> Term q 0 n -> m ()
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compare0 s t = compareN (whnf defs s) (whnf defs t)
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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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namespace Elim
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covering %inline
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compareN : CanEqual q m => Eq q =>
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NonRedexElim q 0 n defs -> NonRedexElim q 0 n defs -> m ()
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compareN e f = compareN' e.fst f.fst e.snd f.snd
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-- can't return the type since it might be different in each dsubst ☹
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export covering %inline
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compare : CanEqual q m => Eq q =>
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DimEq d -> Elim q d n -> Elim q d n -> m ()
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compare eqs e f =
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for_ (splits eqs) $ \th => compare0 (e /// th) (f /// th)
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export covering %inline
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compare0 : CanEqual q m => Eq q => Elim q 0 n -> Elim q 0 n -> m ()
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compare0 e f = compareN (whnf defs e) (whnf defs f)
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namespace ScopeTermN
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export covering %inline
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compare0 : {s : Nat} -> CanEqual q m => Eq q =>
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ScopeTermN s q 0 n -> ScopeTermN s q 0 n -> m ()
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compare0 (TUnused body0) (TUnused body1) = compare0 body0 body1
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compare0 body0 body1 = compare0 body0.term body1.term
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-- [todo] extend to multi-var scopes
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namespace DScopeTerm
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export covering %inline
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compare0 : CanEqual q m => Eq q =>
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DScopeTerm q 0 n -> DScopeTerm q 0 n -> m ()
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compare0 (DUnused body0) (DUnused body1) = compare0 body0 body1
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compare0 body0 body1 = do
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compare0 body0.zero body1.zero
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compare0 body0.one body1.one
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compare : (e, f : Elim q d n) -> m ()
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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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ignore $ compare0 defs (map (/// th) ctx) (e /// th) (f /// th)
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namespace Term
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export covering %inline
|
||||
equal : HasErr q m => Eq q =>
|
||||
DimEq d -> Term q d n -> Term q d n -> m ()
|
||||
equal eqs s t {m} = runReaderT {m} (MakeEnv Equal) $ compare eqs s t
|
||||
equal, sub : (ty, s, t : Term q d n) -> m ()
|
||||
equal = compare Equal
|
||||
sub = compare Sub
|
||||
|
||||
export covering %inline
|
||||
sub : HasErr q m => HasDefs' q _ m => Eq q =>
|
||||
DimEq d -> Term q d n -> Term q d n -> m ()
|
||||
sub eqs s t {m} = runReaderT {m} (MakeEnv Sub) $ compare eqs s t
|
||||
equalType, subtype : (s, t : Term q d n) -> m ()
|
||||
equalType = compareType Equal
|
||||
subtype = compareType Sub
|
||||
|
||||
namespace Elim
|
||||
export covering %inline
|
||||
equal : HasErr q m => Eq q =>
|
||||
DimEq d -> Elim q d n -> Elim q d n -> m ()
|
||||
equal eqs e f {m} = runReaderT {m} (MakeEnv Equal) $ compare eqs e f
|
||||
|
||||
export covering %inline
|
||||
sub : HasErr q m => HasDefs' q _ m => Eq q =>
|
||||
DimEq d -> Elim q d n -> Elim q d n -> m ()
|
||||
sub eqs e f {m} = runReaderT {m} (MakeEnv Sub) $ compare eqs e f
|
||||
equal, sub : (e, f : Elim q d n) -> m ()
|
||||
equal = compare Equal
|
||||
sub = compare Sub
|
||||
|
|
|
|||
|
|
@ -125,15 +125,6 @@ parameters (th : DSubst dfrom dto) (ph : TSubst q dto from to)
|
|||
pushSubstsWith' e = (pushSubstsWith th ph e).fst
|
||||
|
||||
|
||||
public export %inline
|
||||
weakT : Term q d n -> Term q d (S n)
|
||||
weakT t = t //. shift 1
|
||||
|
||||
public export %inline
|
||||
weakE : Elim q d n -> Elim q d (S n)
|
||||
weakE t = t //. shift 1
|
||||
|
||||
|
||||
public export 0
|
||||
Lookup : TermLike
|
||||
Lookup q d n = Name -> Maybe $ Elim q d n
|
||||
|
|
|
|||
|
|
@ -184,17 +184,35 @@ comp : DSubst dfrom dto -> TSubst q dfrom from mid -> TSubst q dto mid to ->
|
|||
comp th ps ph = map (/// th) ps . ph
|
||||
|
||||
|
||||
public export %inline
|
||||
dweakT : {by : Nat} -> Term q d n -> Term q (by + d) n
|
||||
dweakT t = t /// shift by
|
||||
|
||||
public export %inline
|
||||
dweakE : {by : Nat} -> Elim q d n -> Elim q (by + d) n
|
||||
dweakE t = t /// shift by
|
||||
|
||||
|
||||
public export %inline
|
||||
weakT : {default 1 by : Nat} -> Term q d n -> Term q d (by + n)
|
||||
weakT t = t //. shift by
|
||||
|
||||
public export %inline
|
||||
weakE : {default 1 by : Nat} -> Elim q d n -> Elim q d (by + n)
|
||||
weakE t = t //. shift by
|
||||
|
||||
|
||||
namespace ScopeTermN
|
||||
export %inline
|
||||
(.term) : {s : Nat} -> ScopeTermN s q d n -> Term q d (s + n)
|
||||
(TUsed body).term = body
|
||||
(TUnused body).term = body //. shift s
|
||||
(TUnused body).term = weakT body {by = s}
|
||||
|
||||
namespace DScopeTermN
|
||||
export %inline
|
||||
(.term) : {s : Nat} -> DScopeTermN s q d n -> Term q (s + d) n
|
||||
(DUsed body).term = body
|
||||
(DUnused body).term = body /// shift s
|
||||
(DUnused body).term = dweakT body {by = s}
|
||||
|
||||
|
||||
export %inline
|
||||
|
|
|
|||
|
|
@ -22,7 +22,7 @@ CanTC q = CanTC' q IsGlobal
|
|||
private covering %inline
|
||||
expectTYPE : CanTC' q _ m => Term q d n -> m Universe
|
||||
expectTYPE s =
|
||||
case whnf !ask s of
|
||||
case whnfD !ask s of
|
||||
Element (TYPE l) _ => pure l
|
||||
_ => throwError $ ExpectedTYPE s
|
||||
|
||||
|
|
@ -30,7 +30,7 @@ private covering %inline
|
|||
expectPi : CanTC' q _ m => Term q d n ->
|
||||
m (q, Term q d n, ScopeTerm q d n)
|
||||
expectPi ty =
|
||||
case whnf !ask ty of
|
||||
case whnfD !ask ty of
|
||||
Element (Pi qty _ arg res) _ => pure (qty, arg, res)
|
||||
_ => throwError $ ExpectedPi ty
|
||||
|
||||
|
|
@ -38,7 +38,7 @@ private covering %inline
|
|||
expectSig : CanTC' q _ m => Term q d n ->
|
||||
m (Term q d n, ScopeTerm q d n)
|
||||
expectSig ty =
|
||||
case whnf !ask ty of
|
||||
case whnfD !ask ty of
|
||||
Element (Sig _ arg res) _ => pure (arg, res)
|
||||
_ => throwError $ ExpectedSig ty
|
||||
|
||||
|
|
@ -46,7 +46,7 @@ private covering %inline
|
|||
expectEq : CanTC' q _ m => Term q d n ->
|
||||
m (DScopeTerm q d n, Term q d n, Term q d n)
|
||||
expectEq ty =
|
||||
case whnf !ask ty of
|
||||
case whnfD !ask ty of
|
||||
Element (Eq _ ty l r) _ => pure (ty, l, r)
|
||||
_ => throwError $ ExpectedEq ty
|
||||
|
||||
|
|
@ -80,11 +80,8 @@ lookupBound pi (VS i) ctx =
|
|||
weakI $ lookupBound pi i (tail ctx)
|
||||
|
||||
private
|
||||
lookupFree : IsQty q => CanTC q m => Name -> m (Definition q)
|
||||
lookupFree x =
|
||||
case lookup x !ask of
|
||||
Just d => pure d
|
||||
Nothing => throwError $ NotInScope x
|
||||
lookupFree : CanTC' q g m => Name -> m (Definition' q g)
|
||||
lookupFree x = lookupFree' !ask x
|
||||
|
||||
private %inline
|
||||
subjMult : IsQty q => (sg : SQty q) -> q -> SQty q
|
||||
|
|
@ -202,9 +199,9 @@ parameters {auto _ : IsQty q} {auto _ : CanTC q m}
|
|||
qout <- check (extendDim ctx) sg body.term ty.term
|
||||
let eqs = makeDimEq ctx.dctx
|
||||
-- if Ψ ⊢ t‹0› = l
|
||||
equal !ask eqs body.zero l
|
||||
equal eqs ctx.tctx ty.zero body.zero l
|
||||
-- if Ψ ⊢ t‹1› = r
|
||||
equal !ask eqs body.one r
|
||||
equal eqs ctx.tctx ty.one body.one r
|
||||
-- then Ψ | Γ ⊢ (λᴰi ⇒ t) · σ ⇐ Eq [i ⇒ A] l r ⊳ Σ
|
||||
pure qout
|
||||
|
||||
|
|
@ -212,7 +209,7 @@ parameters {auto _ : IsQty q} {auto _ : CanTC q m}
|
|||
-- if Ψ | Γ ⊢ e · σ ⇒ A' ⊳ Σ
|
||||
infres <- infer ctx sg e
|
||||
-- if Ψ ⊢ A' <: A
|
||||
sub !ask (makeDimEq ctx.dctx) infres.type ty
|
||||
subtype (makeDimEq ctx.dctx) ctx.tctx infres.type ty
|
||||
-- then Ψ | Γ ⊢ e · σ ⇐ A ⊳ Σ
|
||||
pure infres.qout
|
||||
|
||||
|
|
@ -258,8 +255,7 @@ parameters {auto _ : IsQty q} {auto _ : CanTC q m}
|
|||
-- ⊳ Σ₂, x · π₁, y · π₂
|
||||
-- if π₁, π₂ ≤ π
|
||||
let bodyctx = extendTyN [< (tfst, pi), (tsnd.term, pi)] ctx
|
||||
retarg = Pair (BVT 0) (BVT 1) :# (pairres.type // fromNat 2)
|
||||
bodyty = ret.term // (retarg ::: shift 2)
|
||||
bodyty = substCasePairRet pairres.type ret
|
||||
bodyout <- check bodyctx sg body.term bodyty >>= popQs [< pi, pi]
|
||||
-- then Ψ | Γ ⊢ σ case ⋯ ⇒ ret[pair] ⊳ πΣ₁ + Σ₂
|
||||
pure $ InfRes {
|
||||
|
|
|
|||
|
|
@ -121,12 +121,17 @@ data Error q
|
|||
| ExpectedEq (Term q d n)
|
||||
| BadUniverse Universe Universe
|
||||
|
||||
| ClashT EqMode (Term q d n) (Term q d n)
|
||||
-- first arg of ClashT is the type
|
||||
| ClashT EqMode (Term q d n) (Term q d n) (Term q d n)
|
||||
| ClashE EqMode (Elim q d n) (Elim q d n)
|
||||
| ClashU EqMode Universe Universe
|
||||
| ClashQ q q
|
||||
| ClashD (Dim d) (Dim d)
|
||||
| NotInScope Name
|
||||
|
||||
| NotType (Term q d n)
|
||||
| WrongType (Term q d n) (Term q d n) (Term q d n)
|
||||
|
||||
public export
|
||||
0 HasErr : Type -> (Type -> Type) -> Type
|
||||
HasErr q = MonadError (Error q)
|
||||
|
|
@ -157,3 +162,18 @@ parameters {auto _ : HasErr q m}
|
|||
export %inline
|
||||
expectEqualD : Dim d -> Dim d -> m ()
|
||||
expectEqualD = expect ClashD (==)
|
||||
|
||||
|
||||
export
|
||||
lookupFree' : HasErr q m => Definitions' q g -> Name -> m (Definition' q g)
|
||||
lookupFree' defs x =
|
||||
case lookup x defs of
|
||||
Just d => pure d
|
||||
Nothing => throwError $ NotInScope x
|
||||
|
||||
|
||||
export
|
||||
substCasePairRet : Term q d n -> ScopeTerm q d n -> Term q d (2 + n)
|
||||
substCasePairRet dty retty =
|
||||
let arg = Pair (BVT 0) (BVT 1) :# (dty // fromNat 2) in
|
||||
retty.term // (arg ::: shift 2)
|
||||
|
|
|
|||
|
|
@ -26,11 +26,17 @@ ToInfo (Error Three) where
|
|||
[("type", "BadUniverse"),
|
||||
("low", show k),
|
||||
("high", show l)]
|
||||
toInfo (ClashT mode s t) =
|
||||
toInfo (ClashT mode ty s t) =
|
||||
[("type", "ClashT"),
|
||||
("mode", show mode),
|
||||
("ty", prettyStr True ty),
|
||||
("left", prettyStr True s),
|
||||
("right", prettyStr True t)]
|
||||
toInfo (ClashE mode e f) =
|
||||
[("type", "ClashE"),
|
||||
("mode", show mode),
|
||||
("left", prettyStr True e),
|
||||
("right", prettyStr True f)]
|
||||
toInfo (ClashU mode k l) =
|
||||
[("type", "ClashU"),
|
||||
("mode", show mode),
|
||||
|
|
@ -44,13 +50,29 @@ ToInfo (Error Three) where
|
|||
[("type", "ClashD"),
|
||||
("left", prettyStr True p),
|
||||
("right", prettyStr True q)]
|
||||
toInfo (NotType ty) =
|
||||
[("type", "NotType"),
|
||||
("actual", prettyStr True ty)]
|
||||
toInfo (WrongType ty s t) =
|
||||
[("type", "WrongType"),
|
||||
("ty", prettyStr True ty),
|
||||
("left", prettyStr True s),
|
||||
("right", prettyStr True t)]
|
||||
|
||||
|
||||
0 M : Type -> Type
|
||||
M = ReaderT (Definitions Three) (Either (Error Three))
|
||||
|
||||
defGlobals : Definitions Three
|
||||
defGlobals = fromList
|
||||
[("A", mkAbstract Zero $ TYPE 0),
|
||||
("B", mkAbstract Zero $ TYPE 0),
|
||||
("a", mkAbstract Any $ FT "A"),
|
||||
("b", mkAbstract Any $ FT "B"),
|
||||
("f", mkAbstract Any $ Arr One (FT "A") (FT "A"))]
|
||||
|
||||
parameters (label : String) (act : Lazy (M ()))
|
||||
{default empty globals : Definitions Three}
|
||||
{default defGlobals globals : Definitions Three}
|
||||
testEq : Test
|
||||
testEq = test label $ runReaderT globals act
|
||||
|
||||
|
|
@ -60,17 +82,18 @@ parameters (label : String) (act : Lazy (M ()))
|
|||
|
||||
parameters {default 0 d, n : Nat}
|
||||
{default new eqs : DimEq d}
|
||||
subT : Term Three d n -> Term Three d n -> M ()
|
||||
subT s t = Term.sub !ask eqs s t
|
||||
(ctx : TContext Three d n)
|
||||
subT : Term Three d n -> Term Three d n -> Term Three d n -> M ()
|
||||
subT ty s t = Term.sub eqs ctx ty s t
|
||||
|
||||
equalT : Term Three d n -> Term Three d n -> M ()
|
||||
equalT s t = Term.equal !ask eqs s t
|
||||
equalT : Term Three d n -> Term Three d n -> Term Three d n -> M ()
|
||||
equalT ty s t = Term.equal eqs ctx ty s t
|
||||
|
||||
subE : Elim Three d n -> Elim Three d n -> M ()
|
||||
subE e f = Elim.sub !ask eqs e f
|
||||
subE e f = Elim.sub eqs ctx e f
|
||||
|
||||
equalE : Elim Three d n -> Elim Three d n -> M ()
|
||||
equalE e f = Elim.equal !ask eqs e f
|
||||
equalE e f = Elim.equal eqs ctx e f
|
||||
|
||||
|
||||
export
|
||||
|
|
@ -80,17 +103,17 @@ tests = "equality & subtyping" :- [
|
|||
|
||||
"universes" :- [
|
||||
testEq "★₀ ≡ ★₀" $
|
||||
equalT (TYPE 0) (TYPE 0),
|
||||
equalT [<] (TYPE 1) (TYPE 0) (TYPE 0),
|
||||
testNeq "★₀ ≢ ★₁" $
|
||||
equalT (TYPE 0) (TYPE 1),
|
||||
equalT [<] (TYPE 2) (TYPE 0) (TYPE 1),
|
||||
testNeq "★₁ ≢ ★₀" $
|
||||
equalT (TYPE 1) (TYPE 0),
|
||||
equalT [<] (TYPE 2) (TYPE 1) (TYPE 0),
|
||||
testEq "★₀ <: ★₀" $
|
||||
subT (TYPE 0) (TYPE 0),
|
||||
subT [<] (TYPE 1) (TYPE 0) (TYPE 0),
|
||||
testEq "★₀ <: ★₁" $
|
||||
subT (TYPE 0) (TYPE 1),
|
||||
subT [<] (TYPE 2) (TYPE 0) (TYPE 1),
|
||||
testNeq "★₁ ≮: ★₀" $
|
||||
subT (TYPE 1) (TYPE 0)
|
||||
subT [<] (TYPE 2) (TYPE 1) (TYPE 0)
|
||||
],
|
||||
|
||||
"pi" :- [
|
||||
|
|
@ -98,79 +121,91 @@ tests = "equality & subtyping" :- [
|
|||
note #""A ⇾ B" for (0 _ : A) → B"#,
|
||||
testEq "A ⊸ B ≡ A ⊸ B" $
|
||||
let tm = Arr One (FT "A") (FT "B") in
|
||||
equalT tm tm,
|
||||
equalT [<] (TYPE 0) tm tm,
|
||||
testNeq "A ⇾ B ≢ A ⊸ B" $
|
||||
let tm1 = Arr Zero (FT "A") (FT "B")
|
||||
tm2 = Arr One (FT "A") (FT "B") in
|
||||
equalT tm1 tm2,
|
||||
equalT [<] (TYPE 0) tm1 tm2,
|
||||
testEq "0=1 ⊢ A ⇾ B ≢ A ⊸ B" $
|
||||
let tm1 = Arr Zero (FT "A") (FT "B")
|
||||
tm2 = Arr One (FT "A") (FT "B") in
|
||||
equalT tm1 tm2 {eqs = ZeroIsOne},
|
||||
equalT [<] (TYPE 0) tm1 tm2 {eqs = ZeroIsOne},
|
||||
testEq "A ⊸ B <: A ⊸ B" $
|
||||
let tm = Arr One (FT "A") (FT "B") in
|
||||
subT tm tm,
|
||||
subT [<] (TYPE 0) tm tm,
|
||||
testNeq "A ⇾ B ≮: A ⊸ B" $
|
||||
let tm1 = Arr Zero (FT "A") (FT "B")
|
||||
tm2 = Arr One (FT "A") (FT "B") in
|
||||
subT tm1 tm2,
|
||||
subT [<] (TYPE 0) tm1 tm2,
|
||||
testEq "★₀ ⇾ ★₀ ≡ ★₀ ⇾ ★₀" $
|
||||
let tm = Arr Zero (TYPE 0) (TYPE 0) in
|
||||
equalT tm tm,
|
||||
equalT [<] (TYPE 1) tm tm,
|
||||
testEq "★₀ ⇾ ★₀ <: ★₀ ⇾ ★₀" $
|
||||
let tm = Arr Zero (TYPE 0) (TYPE 0) in
|
||||
subT tm tm,
|
||||
subT [<] (TYPE 1) tm tm,
|
||||
testNeq "★₁ ⊸ ★₀ ≢ ★₀ ⇾ ★₀" $
|
||||
let tm1 = Arr Zero (TYPE 1) (TYPE 0)
|
||||
tm2 = Arr Zero (TYPE 0) (TYPE 0) in
|
||||
equalT tm1 tm2,
|
||||
equalT [<] (TYPE 2) tm1 tm2,
|
||||
testEq "★₁ ⊸ ★₀ <: ★₀ ⊸ ★₀" $
|
||||
let tm1 = Arr One (TYPE 1) (TYPE 0)
|
||||
tm2 = Arr One (TYPE 0) (TYPE 0) in
|
||||
subT tm1 tm2,
|
||||
subT [<] (TYPE 2) tm1 tm2,
|
||||
testNeq "★₀ ⊸ ★₀ ≢ ★₀ ⇾ ★₁" $
|
||||
let tm1 = Arr Zero (TYPE 0) (TYPE 0)
|
||||
tm2 = Arr Zero (TYPE 0) (TYPE 1) in
|
||||
equalT tm1 tm2,
|
||||
equalT [<] (TYPE 2) tm1 tm2,
|
||||
testEq "★₀ ⊸ ★₀ <: ★₀ ⊸ ★₁" $
|
||||
let tm1 = Arr One (TYPE 0) (TYPE 0)
|
||||
tm2 = Arr One (TYPE 0) (TYPE 1) in
|
||||
subT tm1 tm2,
|
||||
subT [<] (TYPE 2) tm1 tm2,
|
||||
testEq "★₀ ⊸ ★₀ <: ★₀ ⊸ ★₁" $
|
||||
let tm1 = Arr One (TYPE 0) (TYPE 0)
|
||||
tm2 = Arr One (TYPE 0) (TYPE 1) in
|
||||
subT tm1 tm2
|
||||
subT [<] (TYPE 2) tm1 tm2
|
||||
],
|
||||
|
||||
"lambda" :- [
|
||||
testEq "λ x ⇒ [x] ≡ λ x ⇒ [x]" $
|
||||
equalT (Lam "x" $ TUsed $ BVT 0) (Lam "x" $ TUsed $ BVT 0),
|
||||
equalT [<] (Arr One (FT "A") (FT "A"))
|
||||
(Lam "x" $ TUsed $ BVT 0)
|
||||
(Lam "x" $ TUsed $ BVT 0),
|
||||
testEq "λ x ⇒ [x] <: λ x ⇒ [x]" $
|
||||
equalT (Lam "x" $ TUsed $ BVT 0) (Lam "x" $ TUsed $ BVT 0),
|
||||
subT [<] (Arr One (FT "A") (FT "A"))
|
||||
(Lam "x" $ TUsed $ BVT 0)
|
||||
(Lam "x" $ TUsed $ BVT 0),
|
||||
testEq "λ x ⇒ [x] ≡ λ y ⇒ [y]" $
|
||||
equalT (Lam "x" $ TUsed $ BVT 0) (Lam "y" $ TUsed $ BVT 0),
|
||||
equalT [<] (Arr One (FT "A") (FT "A"))
|
||||
(Lam "x" $ TUsed $ BVT 0)
|
||||
(Lam "y" $ TUsed $ BVT 0),
|
||||
testEq "λ x ⇒ [x] <: λ y ⇒ [y]" $
|
||||
equalT (Lam "x" $ TUsed $ BVT 0) (Lam "y" $ TUsed $ BVT 0),
|
||||
equalT [<] (Arr One (FT "A") (FT "A"))
|
||||
(Lam "x" $ TUsed $ BVT 0)
|
||||
(Lam "y" $ TUsed $ BVT 0),
|
||||
testNeq "λ x y ⇒ [x] ≢ λ x y ⇒ [y]" $
|
||||
equalT (Lam "x" $ TUsed $ Lam "y" $ TUsed $ BVT 1)
|
||||
(Lam "x" $ TUsed $ Lam "y" $ TUsed $ BVT 0),
|
||||
equalT [<] (Arr One (FT "A") $ Arr One (FT "A") (FT "A"))
|
||||
(Lam "x" $ TUsed $ Lam "y" $ TUsed $ BVT 1)
|
||||
(Lam "x" $ TUsed $ Lam "y" $ TUsed $ BVT 0),
|
||||
testEq "λ x ⇒ [a] ≡ λ x ⇒ [a] (TUsed vs TUnused)" $
|
||||
equalT (Lam "x" $ TUsed $ FT "a")
|
||||
(Lam "x" $ TUnused $ FT "a"),
|
||||
equalT [<] (Arr Zero (FT "B") (FT "A"))
|
||||
(Lam "x" $ TUsed $ FT "a")
|
||||
(Lam "x" $ TUnused $ FT "a"),
|
||||
skipWith "(no η yet)" $
|
||||
testEq "λ x ⇒ [f [x]] ≡ [f] (η)" $
|
||||
equalT (Lam "x" $ TUsed $ E $ F "f" :@ BVT 0)
|
||||
(FT "f")
|
||||
equalT [<] (Arr One (FT "A") (FT "A"))
|
||||
(Lam "x" $ TUsed $ E $ F "f" :@ BVT 0)
|
||||
(FT "f")
|
||||
],
|
||||
|
||||
"eq type" :- [
|
||||
testEq "(★₀ = ★₀ : ★₁) ≡ (★₀ = ★₀ : ★₁)" $
|
||||
let tm = Eq0 (TYPE 1) (TYPE 0) (TYPE 0) in
|
||||
equalT tm tm,
|
||||
equalT [<] (TYPE 2) tm tm,
|
||||
testEq "A ≔ ★₁ ⊢ (★₀ = ★₀ : ★₁) ≡ (★₀ = ★₀ : A)"
|
||||
{globals = fromList [("A", mkDef zero (TYPE 2) (TYPE 1))]} $
|
||||
equalT (Eq0 (TYPE 1) (TYPE 0) (TYPE 0))
|
||||
(Eq0 (FT "A") (TYPE 0) (TYPE 0))
|
||||
equalT [<] (TYPE 2)
|
||||
(Eq0 (TYPE 1) (TYPE 0) (TYPE 0))
|
||||
(Eq0 (FT "A") (TYPE 0) (TYPE 0))
|
||||
],
|
||||
|
||||
todo "dim lambda",
|
||||
|
|
@ -178,17 +213,25 @@ tests = "equality & subtyping" :- [
|
|||
"term closure" :- [
|
||||
note "𝑖, 𝑗 for bound variables pointing outside of the current expr",
|
||||
testEq "[𝑖]{} ≡ [𝑖]" $
|
||||
equalT (CloT (BVT 0) id) (BVT 0) {n = 1},
|
||||
equalT [< FT "A"] (FT "A") {n = 1}
|
||||
(CloT (BVT 0) id)
|
||||
(BVT 0),
|
||||
testEq "[𝑖]{a/𝑖} ≡ [a]" $
|
||||
equalT (CloT (BVT 0) (F "a" ::: id)) (FT "a"),
|
||||
equalT [<] (FT "A")
|
||||
(CloT (BVT 0) (F "a" ::: id))
|
||||
(FT "a"),
|
||||
testEq "[𝑖]{a/𝑖,b/𝑗} ≡ [a]" $
|
||||
equalT (CloT (BVT 0) (F "a" ::: F "b" ::: id)) (FT "a"),
|
||||
equalT [<] (FT "A")
|
||||
(CloT (BVT 0) (F "a" ::: F "b" ::: id))
|
||||
(FT "a"),
|
||||
testEq "(λy. [𝑖]){y/y, a/𝑖} ≡ λy. [a] (TUnused)" $
|
||||
equalT (CloT (Lam "y" $ TUnused $ BVT 0) (F "a" ::: id))
|
||||
(Lam "y" $ TUnused $ FT "a"),
|
||||
equalT [<] (Arr Zero (FT "B") (FT "A"))
|
||||
(CloT (Lam "y" $ TUnused $ BVT 0) (F "a" ::: id))
|
||||
(Lam "y" $ TUnused $ FT "a"),
|
||||
testEq "(λy. [𝑖]){y/y, a/𝑖} ≡ λy. [a] (TUsed)" $
|
||||
equalT (CloT (Lam "y" $ TUsed $ BVT 1) (F "a" ::: id))
|
||||
(Lam "y" $ TUsed $ FT "a")
|
||||
equalT [<] (Arr Zero (FT "B") (FT "A"))
|
||||
(CloT (Lam "y" $ TUsed $ BVT 1) (F "a" ::: id))
|
||||
(Lam "y" $ TUsed $ FT "a")
|
||||
],
|
||||
|
||||
todo "term d-closure",
|
||||
|
|
@ -202,73 +245,74 @@ tests = "equality & subtyping" :- [
|
|||
("B", mkDef Any (TYPE (U 1)) (FT "A"))]
|
||||
in [
|
||||
testEq "A ≡ A" $
|
||||
equalE (F "A") (F "A"),
|
||||
equalE [<] (F "A") (F "A"),
|
||||
testNeq "A ≢ B" $
|
||||
equalE (F "A") (F "B"),
|
||||
equalE [<] (F "A") (F "B"),
|
||||
testEq "0=1 ⊢ A ≡ B" $
|
||||
equalE {eqs = ZeroIsOne} (F "A") (F "B"),
|
||||
equalE {eqs = ZeroIsOne} [<] (F "A") (F "B"),
|
||||
testEq "A : ★₁ ≔ ★₀ ⊢ A ≡ (★₀ ∷ ★₁)" {globals = au_bu} $
|
||||
equalE (F "A") (TYPE 0 :# TYPE 1),
|
||||
equalE [<] (F "A") (TYPE 0 :# TYPE 1),
|
||||
testEq "A ≔ ★₀, B ≔ ★₀ ⊢ A ≡ B" {globals = au_bu} $
|
||||
equalE (F "A") (F "B"),
|
||||
equalE [<] (F "A") (F "B"),
|
||||
testEq "A ≔ ★₀, B ≔ A ⊢ A ≡ B" {globals = au_ba} $
|
||||
equalE (F "A") (F "B"),
|
||||
equalE [<] (F "A") (F "B"),
|
||||
testEq "A <: A" $
|
||||
subE (F "A") (F "A"),
|
||||
subE [<] (F "A") (F "A"),
|
||||
testNeq "A ≮: B" $
|
||||
subE (F "A") (F "B"),
|
||||
subE [<] (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 [<] (F "A") (F "B"),
|
||||
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 [<] (F "A") (F "B"),
|
||||
testEq "0=1 ⊢ A <: B" $
|
||||
subE (F "A") (F "B") {eqs = ZeroIsOne}
|
||||
subE [<] (F "A") (F "B") {eqs = ZeroIsOne}
|
||||
],
|
||||
|
||||
"bound var" :- [
|
||||
note "𝑖, 𝑗 for distinct bound variables",
|
||||
testEq "𝑖 ≡ 𝑖" $
|
||||
equalE (BV 0) (BV 0) {n = 1},
|
||||
equalE [< TYPE 0] (BV 0) (BV 0) {n = 1},
|
||||
testNeq "𝑖 ≢ 𝑗" $
|
||||
equalE (BV 0) (BV 1) {n = 2},
|
||||
equalE [< TYPE 0, TYPE 0] (BV 0) (BV 1) {n = 2},
|
||||
testEq "0=1 ⊢ 𝑖 ≡ 𝑗" $
|
||||
equalE {n = 2, eqs = ZeroIsOne} (BV 0) (BV 1)
|
||||
equalE [< TYPE 0, TYPE 0] (BV 0) (BV 1)
|
||||
{n = 2, eqs = ZeroIsOne}
|
||||
],
|
||||
|
||||
"application" :- [
|
||||
testEq "f [a] ≡ f [a]" $
|
||||
equalE (F "f" :@ FT "a") (F "f" :@ FT "a"),
|
||||
equalE [<] (F "f" :@ FT "a") (F "f" :@ FT "a"),
|
||||
testEq "f [a] <: f [a]" $
|
||||
subE (F "f" :@ FT "a") (F "f" :@ FT "a"),
|
||||
subE [<] (F "f" :@ FT "a") (F "f" :@ FT "a"),
|
||||
testEq "(λ x ⇒ [x] ∷ A ⊸ A) a ≡ ([a ∷ A] ∷ A) (β)" $
|
||||
equalE
|
||||
equalE [<]
|
||||
((Lam "x" (TUsed (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 [<]
|
||||
((Lam "x" (TUsed (BVT 0)) :# (Arr One (FT "A") (FT "A")))
|
||||
:@ FT "a")
|
||||
(F "a"),
|
||||
testEq "(λ g ⇒ [g [x]] ∷ ⋯)) [f] ≡ (λ y ⇒ [f [y]] ∷ ⋯) [x] (β↘↙)" $
|
||||
testEq "(λ g ⇒ [g [a]] ∷ ⋯)) [f] ≡ (λ y ⇒ [f [y]] ∷ ⋯) [a] (β↘↙)" $
|
||||
let a = FT "A"; a2a = (Arr One a a) in
|
||||
equalE
|
||||
((Lam "g" (TUsed (E (BV 0 :@ FT "x"))) :# Arr One a2a a) :@ FT "f")
|
||||
((Lam "y" (TUsed (E (F "f" :@ BVT 0))) :# a2a) :@ FT "x"),
|
||||
equalE [<]
|
||||
((Lam "g" (TUsed (E (BV 0 :@ FT "a"))) :# Arr One a2a a) :@ FT "f")
|
||||
((Lam "y" (TUsed (E (F "f" :@ BVT 0))) :# a2a) :@ FT "a"),
|
||||
testEq "(λ x ⇒ [x] ∷ A ⊸ A) a <: a" $
|
||||
subE
|
||||
subE [<]
|
||||
((Lam "x" (TUsed (BVT 0)) :# (Arr One (FT "A") (FT "A")))
|
||||
:@ FT "a")
|
||||
(F "a"),
|
||||
testEq "f : A ⊸ A ≔ λ x ⇒ [x] ⊢ f [x] ≡ x"
|
||||
{globals = fromList
|
||||
[("f", mkDef Any (Arr One (FT "A") (FT "A"))
|
||||
testEq "id : A ⊸ A ≔ λ x ⇒ [x] ⊢ id [a] ≡ a"
|
||||
{globals = defGlobals `mergeLeft` fromList
|
||||
[("id", mkDef Any (Arr One (FT "A") (FT "A"))
|
||||
(Lam "x" (TUsed (BVT 0))))]} $
|
||||
equalE (F "f" :@ FT "x") (F "x")
|
||||
equalE [<] (F "id" :@ FT "a") (F "a")
|
||||
],
|
||||
|
||||
"dim application" :-
|
||||
|
|
@ -277,13 +321,16 @@ tests = "equality & subtyping" :- [
|
|||
in
|
||||
[
|
||||
note #""refl [A] x" is an abbreviation for "(λᴰi ⇒ x) ∷ (x ≡ x : A)""#,
|
||||
testEq "refl [A] x ≡ refl [A] x" $
|
||||
equalE (refl (FT "A") (FT "x")) (refl (FT "A") (FT "x")),
|
||||
testEq "refl [A] a ≡ refl [A] a" $
|
||||
equalE [<] (refl (FT "A") (FT "a")) (refl (FT "A") (FT "a")),
|
||||
testEq "p : (a ≡ b : A), q : (a ≡ b : A) ⊢ p ≡ q"
|
||||
{globals =
|
||||
let def = mkAbstract Zero $ Eq0 (FT "A") (FT "a") (FT "b") in
|
||||
fromList [("p", def), ("q", def)]} $
|
||||
equalE (F "p") (F "q")
|
||||
fromList [("A", mkAbstract Zero $ TYPE 0),
|
||||
("a", mkAbstract Any $ FT "A"),
|
||||
("b", mkAbstract Any $ FT "A"),
|
||||
("p", def), ("q", def)]} $
|
||||
equalE [<] (F "p") (F "q")
|
||||
],
|
||||
|
||||
todo "annotation",
|
||||
|
|
@ -294,9 +341,10 @@ tests = "equality & subtyping" :- [
|
|||
|
||||
"clashes" :- [
|
||||
testNeq "★₀ ≢ ★₀ ⇾ ★₀" $
|
||||
equalT (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0)),
|
||||
equalT [<] (TYPE 1) (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0)),
|
||||
testEq "0=1 ⊢ ★₀ ≡ ★₀ ⇾ ★₀" $
|
||||
equalT (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0)) {eqs = ZeroIsOne},
|
||||
equalT [<] (TYPE 1) (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0))
|
||||
{eqs = ZeroIsOne},
|
||||
todo "others"
|
||||
]
|
||||
]
|
||||
|
|
|
|||
|
|
@ -27,16 +27,16 @@ testNoStep whnf label e = test "\{label} (no step)" $
|
|||
|
||||
parameters {default empty defs : Definitions Three} {default 0 d, n : Nat}
|
||||
testWhnfT : String -> Term Three d n -> Term Three d n -> Test
|
||||
testWhnfT = testWhnf (whnf defs)
|
||||
testWhnfT = testWhnf (whnfD defs)
|
||||
|
||||
testWhnfE : String -> Elim Three d n -> Elim Three d n -> Test
|
||||
testWhnfE = testWhnf (whnf defs)
|
||||
testWhnfE = testWhnf (whnfD defs)
|
||||
|
||||
testNoStepE : String -> Elim Three d n -> Test
|
||||
testNoStepE = testNoStep (whnf defs)
|
||||
testNoStepE = testNoStep (whnfD defs)
|
||||
|
||||
testNoStepT : String -> Term Three d n -> Test
|
||||
testNoStepT = testNoStep (whnf defs)
|
||||
testNoStepT = testNoStep (whnfD defs)
|
||||
|
||||
|
||||
tests = "whnf" :- [
|
||||
|
|
|
|||
Loading…
Reference in a new issue