typed equality
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8 changed files with 410 additions and 250 deletions
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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
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equal : HasErr q m => Eq q =>
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DimEq d -> Term q d n -> Term q d n -> m ()
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equal eqs s t {m} = runReaderT {m} (MakeEnv Equal) $ compare eqs s t
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equal, sub : (ty, s, t : Term q d n) -> m ()
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equal = compare Equal
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sub = compare Sub
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export covering %inline
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sub : HasErr q m => HasDefs' q _ m => Eq q =>
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DimEq d -> Term q d n -> Term q d n -> m ()
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sub eqs s t {m} = runReaderT {m} (MakeEnv Sub) $ compare eqs s t
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equalType, subtype : (s, t : Term q d n) -> m ()
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equalType = compareType Equal
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subtype = compareType Sub
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namespace Elim
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export covering %inline
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equal : HasErr q m => Eq q =>
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DimEq d -> Elim q d n -> Elim q d n -> m ()
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equal eqs e f {m} = runReaderT {m} (MakeEnv Equal) $ compare eqs e f
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export covering %inline
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sub : HasErr q m => HasDefs' q _ m => Eq q =>
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DimEq d -> Elim q d n -> Elim q d n -> m ()
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sub eqs e f {m} = runReaderT {m} (MakeEnv Sub) $ compare eqs e f
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equal, sub : (e, f : Elim q d n) -> m ()
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equal = compare Equal
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||||
sub = compare Sub
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue