From d9a383d8bb16a7e0d7e3a3570ba1accadd0b7150 Mon Sep 17 00:00:00 2001
From: rhiannon morris <rhi@rhiannon.website>
Date: Sun, 5 May 2024 19:42:21 +0200
Subject: [PATCH 1/9] remove TVarErr and DVarErr highlights

---
 lib/Quox/Pretty.idr | 10 +++-------
 1 file changed, 3 insertions(+), 7 deletions(-)

diff --git a/lib/Quox/Pretty.idr b/lib/Quox/Pretty.idr
index 606ec78..1083951 100644
--- a/lib/Quox/Pretty.idr
+++ b/lib/Quox/Pretty.idr
@@ -37,8 +37,8 @@ data PPrec
 public export
 data HL
 = Delim
-| Free | TVar | TVarErr
-| Dim  | DVar | DVarErr
+| Free | TVar
+| Dim  | DVar
 | Qty  | Universe
 | Syntax
 | Constant
@@ -79,10 +79,8 @@ toSGR : HL -> List SGR
 toSGR Delim    = []
 toSGR Free     = [SetForeground BrightBlue]
 toSGR TVar     = [SetForeground BrightYellow]
-toSGR TVarErr  = [SetForeground BrightYellow, SetStyle SingleUnderline]
 toSGR Dim      = [SetForeground BrightGreen]
 toSGR DVar     = [SetForeground BrightGreen]
-toSGR DVarErr  = [SetForeground BrightGreen, SetStyle SingleUnderline]
 toSGR Qty      = [SetForeground BrightMagenta]
 toSGR Universe = [SetForeground BrightRed]
 toSGR Syntax   = [SetForeground BrightCyan]
@@ -97,10 +95,8 @@ toClass : HL -> String
 toClass Delim    = "dl"
 toClass Free     = "fr"
 toClass TVar     = "tv"
-toClass TVarErr  = "tv err"
 toClass Dim      = "dc"
 toClass DVar     = "dv"
-toClass DVarErr  = "dv err"
 toClass Qty      = "qt"
 toClass Universe = "un"
 toClass Syntax   = "sy"
@@ -345,7 +341,7 @@ prettyBounds (MkBounds l1 c1 l2 c2) =
 export
 prettyLoc : {opts : LayoutOpts} -> Loc -> Eff Pretty (Doc opts)
 prettyLoc (L NoLoc) =
-  hcat <$> sequence [hl TVarErr "no location", colonD]
+  hcat <$> sequence [hl TVar "no location", colonD]
 prettyLoc (L (YesLoc file b)) =
   hcat <$> sequence [hl Free $ text file, colonD, prettyBounds b]
 
-- 
2.39.5


From e880b7165ab34f173eea7bbff9f2df73cdbcd7a8 Mon Sep 17 00:00:00 2001
From: rhiannon morris <rhi@rhiannon.website>
Date: Sun, 5 May 2024 19:44:27 +0200
Subject: [PATCH 2/9] remove Loc suffix from fromVar and Context.get

---
 lib/Quox/Syntax/Dim.idr        |  4 ++--
 lib/Quox/Syntax/Subst.idr      | 12 ++++++------
 lib/Quox/Syntax/Term/Subst.idr |  8 ++++----
 lib/Quox/Untyped/Syntax.idr    |  4 ++--
 lib/Quox/Var.idr               |  4 ++--
 5 files changed, 16 insertions(+), 16 deletions(-)

diff --git a/lib/Quox/Syntax/Dim.idr b/lib/Quox/Syntax/Dim.idr
index 5f60a17..f495486 100644
--- a/lib/Quox/Syntax/Dim.idr
+++ b/lib/Quox/Syntax/Dim.idr
@@ -84,7 +84,7 @@ DSubst : Nat -> Nat -> Type
 DSubst = Subst Dim
 
 
-public export FromVar Dim where fromVarLoc = B
+public export FromVar Dim where fromVar = B
 
 
 export
@@ -95,7 +95,7 @@ CanShift Dim where
 export
 CanSubstSelf Dim where
   K e loc // _  = K e loc
-  B i loc // th = getLoc th i loc
+  B i loc // th = get th i loc
 
 
 export Uninhabited (B i loc1 = K e loc2) where uninhabited _ impossible
diff --git a/lib/Quox/Syntax/Subst.idr b/lib/Quox/Syntax/Subst.idr
index 1e14d4d..06734b2 100644
--- a/lib/Quox/Syntax/Subst.idr
+++ b/lib/Quox/Syntax/Subst.idr
@@ -49,10 +49,10 @@ interface FromVar term => CanSubstSelf term where
 
 
 public export
-getLoc : FromVar term => Subst term from to -> Var from -> Loc -> term to
-getLoc (Shift by) i      loc = fromVarLoc (shift by i) loc
-getLoc (t ::: th) VZ     _   = t
-getLoc (t ::: th) (VS i) loc = getLoc th i loc
+get : FromVar term => Subst term from to -> Var from -> Loc -> term to
+get (Shift by) i      loc = fromVar (shift by i) loc
+get (t ::: th) VZ     _   = t
+get (t ::: th) (VS i) loc = get th i loc
 
 
 public export
@@ -97,7 +97,7 @@ map f (t ::: th) = f t ::: map f th
 
 public export %inline
 push : CanSubstSelf f => Loc -> Subst f from to -> Subst f (S from) (S to)
-push loc th = fromVarLoc VZ loc ::: (th . shift 1)
+push loc th = fromVar VZ loc ::: (th . shift 1)
 
 -- [fixme] a better way to do this?
 public export
@@ -107,7 +107,7 @@ pushN 0     _   th = th
 pushN (S s) loc th =
   rewrite plusSuccRightSucc s from in
   rewrite plusSuccRightSucc s to in
-  pushN s loc $ fromVarLoc VZ loc ::: (th . shift 1)
+  pushN s loc $ fromVar VZ loc ::: (th . shift 1)
 
 public export
 drop1 : Subst f (S from) to -> Subst f from to
diff --git a/lib/Quox/Syntax/Term/Subst.idr b/lib/Quox/Syntax/Term/Subst.idr
index afc8eef..54dd990 100644
--- a/lib/Quox/Syntax/Term/Subst.idr
+++ b/lib/Quox/Syntax/Term/Subst.idr
@@ -60,8 +60,8 @@ namespace DSubst.DScopeTermN
   S ns (N body) // th = S ns $ N $ body // th
 
 
-export %inline FromVar (Elim d) where fromVarLoc = B
-export %inline FromVar (Term d) where fromVarLoc = E .: fromVarLoc
+export %inline FromVar (Elim d) where fromVar = B
+export %inline FromVar (Term d) where fromVar = E .: fromVar
 
 
 ||| does the minimal reasonable work:
@@ -73,7 +73,7 @@ export %inline FromVar (Term d) where fromVarLoc = E .: fromVarLoc
 export
 CanSubstSelf (Elim d) where
   F x u loc       // _  = F x u loc
-  B i loc         // th = getLoc th i loc
+  B i loc         // th = get th i loc
   CloE (Sub e ph) // th = assert_total CloE $ Sub e $ ph . th
   e               // th = case force th of
                                Shift SZ => e
@@ -272,7 +272,7 @@ PushSubsts Elim Subst.isCloE where
   pushSubstsWith th ph (F x u loc) =
     nclo $ F x u loc
   pushSubstsWith th ph (B i loc) =
-    let res = getLoc ph i loc in
+    let res = get ph i loc in
     case nchoose $ isCloE res of
       Left  yes => assert_total pushSubsts res
       Right no  => Element res no
diff --git a/lib/Quox/Untyped/Syntax.idr b/lib/Quox/Untyped/Syntax.idr
index 06f02f0..fb19e46 100644
--- a/lib/Quox/Untyped/Syntax.idr
+++ b/lib/Quox/Untyped/Syntax.idr
@@ -255,7 +255,7 @@ USubst : Nat -> Nat -> Type
 USubst = Subst Term
 
 
-public export FromVar Term where fromVarLoc = B
+public export FromVar Term where fromVar = B
 
 
 public export
@@ -264,7 +264,7 @@ CanSubstSelf Term where
     F x loc =>
       F x loc
     B i loc =>
-      getLoc th i loc
+      get th i loc
     Lam x body loc =>
       Lam x (assert_total $ body // push x.loc th) loc
     App fun arg loc =>
diff --git a/lib/Quox/Var.idr b/lib/Quox/Var.idr
index 732b012..9d5bf6f 100644
--- a/lib/Quox/Var.idr
+++ b/lib/Quox/Var.idr
@@ -139,10 +139,10 @@ weakIsSpec p i = toNatInj $ trans (weakCorrect p i) (sym $ weakSpecCorrect p i)
 
 
 public export
-interface FromVar f where %inline fromVarLoc : Var n -> Loc -> f n
+interface FromVar f where %inline fromVar : Var n -> Loc -> f n
 
 
-public export FromVar Var where fromVarLoc x _ = x
+public export FromVar Var where fromVar x _ = x
 
 export
 tabulateV : {0 tm : Nat -> Type} -> (forall n. Var n -> tm n) ->
-- 
2.39.5


From 722c05225dcb4b99c454b5e4abcf46ab0cc014dd Mon Sep 17 00:00:00 2001
From: rhiannon morris <rhi@rhiannon.website>
Date: Mon, 6 May 2024 19:18:27 +0200
Subject: [PATCH 3/9] replace Context.tabulate with tabulateVar

- takes a function `Var n -> a`
- results are no longer backwards lmao
---
 lib/Quox/Context.idr     | 19 ++++++++-----------
 lib/Quox/FreeVars.idr    | 11 +++++------
 lib/Quox/Var.idr         |  8 --------
 tests/Tests/FreeVars.idr | 37 ++++++++++++++++++++++++++++++++++++-
 4 files changed, 49 insertions(+), 26 deletions(-)

diff --git a/lib/Quox/Context.idr b/lib/Quox/Context.idr
index 97daabd..6717702 100644
--- a/lib/Quox/Context.idr
+++ b/lib/Quox/Context.idr
@@ -109,21 +109,18 @@ fromSnocVect [<]       = [<]
 fromSnocVect (sx :< x) = fromSnocVect sx :< x
 
 
-public export
-tabulateLT : (n : Nat) -> ((i : Nat) -> (0 p : i `LT` n) => tm i) ->
-             Context tm n
-tabulateLT 0     f = [<]
-tabulateLT (S k) f =
-  tabulateLT k (\i => f i @{lteSuccRight %search}) :< f k @{reflexive}
+export
+tabulateVar : (n : Nat) -> (Var n -> a) -> Context' a n
+tabulateVar 0     f = [<]
+tabulateVar (S k) f = tabulateVar k (f . VS) :< f VZ
 
-public export
-tabulate : ((n : Nat) -> tm n) -> (n : Nat) -> Context tm n
-tabulate f n = tabulateLT n (\i => f i)
--- [todo] fixup argument order lol
+export
+allVars : (n : Nat) -> Context' (Var n) n
+allVars n = tabulateVar n id
 
 public export
 replicate : (n : Nat) -> a -> Context' a n
-replicate n x = tabulate (const x) n
+replicate n x = tabulateVar n $ const x
 
 
 public export
diff --git a/lib/Quox/FreeVars.idr b/lib/Quox/FreeVars.idr
index de52813..13b711f 100644
--- a/lib/Quox/FreeVars.idr
+++ b/lib/Quox/FreeVars.idr
@@ -62,7 +62,7 @@ export %inline [AndM] {n : Nat} -> Monoid (FreeVars n) where neutral = all
 
 private
 self : {n : Nat} -> Context' (FreeVars n) n
-self = tabulate (\i => FV $ tabulate (== i) n) n
+self = tabulateVar n $ \i => FV $ tabulateVar n (== i)
 
 export
 shift : forall from, to. Shift from to -> FreeVars from -> FreeVars to
@@ -74,13 +74,12 @@ shift by (FV xs) = FV $ shift' by xs where
 
 export
 fromSet : {n : Nat} -> SortedSet (Var n) -> FreeVars n
-fromSet vs = FV $ tabulateLT n $ \i => contains (V i) vs
+fromSet vs = FV $ tabulateVar n $ \i => contains i vs
 
 export
 toSet : {n : Nat} -> FreeVars n -> SortedSet (Var n)
-toSet (FV vs) =
-  foldl_ (\s, i => maybe s (\i => insert i s) i) empty $
-  zipWith (\i, b => guard b $> i) (tabulateLT n V) vs
+toSet (FV vs) = SortedSet.fromList $ fold $
+                Context.zipWith (\i, b => i <$ guard b) (allVars n) vs
 
 
 public export
@@ -230,7 +229,7 @@ HasFreeVars (Elim d) where
 
 private
 expandDShift : {d1 : Nat} -> Shift d1 d2 -> Loc -> Context' (Dim d2) d1
-expandDShift by loc = tabulateLT d1 (\i => BV i loc // by)
+expandDShift by loc = tabulateVar d1 (\i => B i loc // by)
 
 private
 expandDSubst : {d1 : Nat} -> DSubst d1 d2 -> Loc -> Context' (Dim d2) d1
diff --git a/lib/Quox/Var.idr b/lib/Quox/Var.idr
index 9d5bf6f..28f3a1c 100644
--- a/lib/Quox/Var.idr
+++ b/lib/Quox/Var.idr
@@ -144,15 +144,7 @@ interface FromVar f where %inline fromVar : Var n -> Loc -> f n
 
 public export FromVar Var where fromVar x _ = x
 
-export
-tabulateV : {0 tm : Nat -> Type} -> (forall n. Var n -> tm n) ->
-            (n : Nat) -> Vect n (tm n)
-tabulateV f 0     = []
-tabulateV f (S n) = f VZ :: tabulateV (f . VS) n
 
-export
-allVars : (n : Nat) -> Vect n (Var n)
-allVars n = tabulateV id n
 
 
 public export
diff --git a/tests/Tests/FreeVars.idr b/tests/Tests/FreeVars.idr
index a51ab9d..4a1aa51 100644
--- a/tests/Tests/FreeVars.idr
+++ b/tests/Tests/FreeVars.idr
@@ -26,6 +26,15 @@ ToInfo Failure where
               ("expected", show f.expected),
               ("got",      show f.got)]
 
+private
+testFreeVars1 : {d : Nat} -> HasFreeVars f =>
+                (f d -> String) -> f d -> FreeVars' d -> Test
+testFreeVars1 lbl tm dims =
+  test (lbl tm) $ do
+    let dims = FV dims; dims' = fv tm
+    unless (dims == dims')  $ Left $ Fail Dim dims dims'
+    Right ()
+
 private
 testFreeVars : {d, n : Nat} -> (HasFreeVars (f d), HasFreeDVars f) =>
                (f d n -> String) -> f d n -> FreeVars' d -> FreeVars' n -> Test
@@ -45,6 +54,22 @@ private
 prettyWith : (a -> Eff Pretty Doc80) -> a -> String
 prettyWith f = trim . render _ . runPretty . f
 
+parameters {d : Nat} (ds : BContext d)
+  private
+  withContext1 : Doc80 -> Eff Pretty Doc80
+  withContext1 doc =
+    if null ds then pure $ hsep ["⊢", doc]
+    else pure $ sep [hsep [!(ctx1 ds), "⊢"], doc]
+  where
+    ctx1 : forall k. BContext k -> Eff Pretty Doc80
+    ctx1 [<] = pure "·"
+    ctx1 ctx = fillSeparateTight !commaD . toList' <$>
+               traverse' (pure . prettyBind') ctx
+
+  private
+  testFreeVarsD : Dim d -> FreeVars' d -> Test
+  testFreeVarsD = testFreeVars1 $ prettyWith $ withContext1 <=< prettyDim ds
+
 parameters {d, n : Nat} (ds : BContext d) (ts : BContext n)
   private
   withContext : Doc80 -> Eff Pretty Doc80
@@ -67,7 +92,13 @@ parameters {d, n : Nat} (ds : BContext d) (ts : BContext n)
 
 export
 tests : Test
-tests = "free variables" :- [
+tests = "free variables (fv/fdv)" :- [
+  testFreeVarsD [<] (^K Zero) [<],
+  testFreeVarsD [<"i", "j"] (^K Zero) [<False, False],
+  testFreeVarsD [<"i", "j"] (^BV 0) [<False, True],
+  testFreeVarsD [<"i", "j"] (^BV 1) [<True, False],
+  testFreeVarsD [<"i", "j", "k", "l"] (^BV 2) [<False, True, False, False],
+
   testFreeVarsT [<] [<] (^TYPE 0) [<] [<],
   testFreeVarsT [<"i", "j"] [<] (^TYPE 0) [<False, False] [<],
   testFreeVarsT [<] [<"x", "y"] (^TYPE 0) [<] [<False, False],
@@ -98,6 +129,10 @@ tests = "free variables" :- [
 
   testFreeVarsT [<"i","j"] [<] (^DLamY "k" (E $ ^DApp (^F "eq" 0) (^BV 0)))
                 [<False,False] [<],
+  testFreeVarsT [<"i","j"] [<] (^DLamY "k" (E $ ^DApp (^F "eq" 0) (^BV 2)))
+                [<True,False] [<],
+  testFreeVarsT [<"i","j"] [<] (^DLamY "i" (E $ ^DApp (^F "eq" 0) (^BV 0)))
+                [<False,False] [<],
   testFreeVarsT [<"i","j"] [<] (^DLamN (E $ ^DApp (^F "eq" 0) (^BV 0)))
                 [<False,True] [<],
 
-- 
2.39.5


From 2d75b92d6dc079eb0e6049a6bbdb106824da913c Mon Sep 17 00:00:00 2001
From: rhiannon morris <rhi@rhiannon.website>
Date: Thu, 23 May 2024 23:01:45 +0200
Subject: [PATCH 4/9] telescope stuff

---
 lib/Quox/Context.idr        | 57 +++++++++++++++++++++++++++++++------
 lib/Quox/NatExtra.idr       | 40 ++++++++++++++++++++++----
 lib/Quox/OPE.idr            |  2 +-
 lib/Quox/SingletonExtra.idr | 11 +++++++
 4 files changed, 94 insertions(+), 16 deletions(-)
 create mode 100644 lib/Quox/SingletonExtra.idr

diff --git a/lib/Quox/Context.idr b/lib/Quox/Context.idr
index 6717702..c93b20f 100644
--- a/lib/Quox/Context.idr
+++ b/lib/Quox/Context.idr
@@ -3,10 +3,12 @@ module Quox.Context
 import Quox.Syntax.Shift
 import Quox.Pretty
 import Quox.Name
+import Quox.NatExtra
+import Quox.PrettyValExtra
 
 import Data.DPair
 import Data.Nat
-import Data.Singleton
+import Quox.SingletonExtra
 import Data.SnocList
 import Data.SnocVect
 import Data.Vect
@@ -45,6 +47,10 @@ public export
 BContext : Nat -> Type
 BContext = Context' BindName
 
+public export
+BTelescope : Nat -> Nat -> Type
+BTelescope = Telescope' BindName
+
 
 public export
 unsnoc : Context tm (S n) -> (Context tm n, tm n)
@@ -123,6 +129,19 @@ replicate : (n : Nat) -> a -> Context' a n
 replicate n x = tabulateVar n $ const x
 
 
+public export
+replicateLTE : from `LTE'` to => a -> Telescope' a from to
+replicateLTE @{LTERefl}    x = [<]
+replicateLTE @{LTESuccR _} x = replicateLTE x :< x
+
+public export
+replicateTel : (from, to : Nat) -> a ->
+               Either (from `GT` to) (Telescope' a from to)
+replicateTel from to x = case isLTE' from to of
+  Yes lte  => Right $ replicateLTE x
+  No  nlte => Left  $ notLTEImpliesGT $ nlte . fromLTE
+
+
 public export
 (.) : Telescope tm from mid -> Telescope tm mid to -> Telescope tm from to
 tel1 . [<]         = tel1
@@ -275,12 +294,16 @@ lengthPrf [<]        = Element 0 Refl
 lengthPrf (tel :< _) =
   let len = lengthPrf tel in Element (S len.fst) (cong S len.snd)
 
-export
+public export
+lengthPrfSing : Telescope _ from to -> Singleton from -> Singleton to
+lengthPrfSing tel (Val from) =
+  let Element len prf = lengthPrf tel in
+  rewrite sym prf in
+  Val (len + from)
+
+public export
 lengthPrf0 : Context _ to -> Singleton to
-lengthPrf0 ctx =
-  let Element len prf = lengthPrf ctx in
-  rewrite sym prf `trans` plusZeroRightNeutral len in
-  [|len|]
+lengthPrf0 ctx = lengthPrfSing ctx (Val 0)
 
 public export %inline
 length : Telescope {} -> Nat
@@ -327,14 +350,30 @@ export %inline
 (forall n. Eq (tm n)) => Eq (Telescope tm from to) where
   (==) = foldLazy @{All} .: zipWithLazy (==)
 
+export %inline
+(forall n. DecEq (tm n)) => DecEq (Telescope tm from to) where
+  decEq [<] [<] = Yes Refl
+  decEq (xs :< x) (ys :< y) = do
+    let Yes Refl = decEq xs ys
+      | No n => No $ \case Refl => n Refl
+    let Yes Refl = decEq x y
+      | No n => No $ \case Refl => n Refl
+    Yes Refl
+  decEq [<]      (_ :< _) = No $ \case _ impossible
+  decEq (_ :< _) [<]      = No $ \case _ impossible
+
 export %inline
 (forall n. Ord (tm n)) => Ord (Telescope tm from to) where
   compare = foldLazy .: zipWithLazy compare
 
 export %inline
 (forall n. Show (tm n)) => Show (Telescope tm from to) where
-  showPrec d = showPrec d . toSnocList
-    where Show (Exists tm) where showPrec d t = showPrec d t.snd
+  showPrec d = showPrec d . toSnocList where
+    Show (Exists tm) where showPrec d t = showPrec d t.snd
+
+export %inline
+(forall n. PrettyVal (tm n)) => PrettyVal (Telescope tm from to) where
+  prettyVal xs = prettyVal $ toSnocList' $ map prettyVal xs
 
 
 parameters {opts : LayoutOpts} {0 tm : Nat -> Type}
@@ -361,5 +400,5 @@ parameters {opts : LayoutOpts} {0 tm : Nat -> Type}
 
 namespace BContext
   export
-  toNames : BContext n -> SnocList BaseName
+  toNames : BTelescope {} -> SnocList BaseName
   toNames = foldl (\xs, x => xs :< x.val) [<]
diff --git a/lib/Quox/NatExtra.idr b/lib/Quox/NatExtra.idr
index 714add1..79589a0 100644
--- a/lib/Quox/NatExtra.idr
+++ b/lib/Quox/NatExtra.idr
@@ -5,6 +5,7 @@ import Data.Nat.Division
 import Data.SnocList
 import Data.Vect
 import Data.String
+import Quox.Decidable
 
 %default total
 
@@ -14,26 +15,53 @@ data LTE' : Nat -> Nat -> Type where
   LTERefl  : LTE' n n
   LTESuccR : LTE' m n -> LTE' m (S n)
 %builtin Natural LTE'
+%name LTE' p, q
 
 public export %hint
 lteZero' : {n : Nat} -> LTE' 0 n
 lteZero' {n = 0}   = LTERefl
 lteZero' {n = S n} = LTESuccR lteZero'
+%transform "NatExtra.lteZero'" lteZero' {n} = believe_me n
 
 public export %hint
 lteSucc' : LTE' m n -> LTE' (S m) (S n)
 lteSucc' LTERefl      = LTERefl
 lteSucc' (LTESuccR p) = LTESuccR $ lteSucc' p
+%transform "NatExtra.lteSucc'" lteSucc' p = believe_me p
 
 public export
-fromLte : {n : Nat} -> LTE m n -> LTE' m n
-fromLte LTEZero     = lteZero'
-fromLte (LTESucc p) = lteSucc' $ fromLte p
+fromLTE : {n : Nat} -> LTE m n -> LTE' m n
+fromLTE LTEZero     = lteZero'
+fromLTE (LTESucc p) = lteSucc' $ fromLTE p
+-- %transform "NatExtra.fromLTE"
+--   fromLTE {n} p = believe_me (n `minus` believe_me p)
 
 public export
-toLte : {n : Nat} -> m `LTE'` n -> m `LTE` n
-toLte LTERefl      = reflexive
-toLte (LTESuccR p) = lteSuccRight (toLte p)
+toLTE : {m : Nat} -> m `LTE'` n -> m `LTE` n
+toLTE LTERefl      = reflexive
+toLTE (LTESuccR p) = lteSuccRight (toLTE p)
+-- %transform "NatExtra.toLTE" toLTE {m} p = believe_me m
+
+public export
+lteLTE' : {m, n : Nat} -> LTE m n <=> LTE' m n
+lteLTE' = MkEquivalence fromLTE toLTE
+
+public export
+isLTE' : (m, n : Nat) -> Dec (LTE' m n)
+isLTE' m n = map lteLTE' $ isLTE m n
+
+
+public export
+data LT' : Nat -> Nat -> Type where
+  LTZero : LT' 0 (S n)
+  LTSucc : LT' m n -> LT' (S m) (S n)
+%builtin Natural LT'
+%name LT' p, q
+
+public export
+Transitive Nat LT' where
+  transitive LTZero     (LTSucc q) = LTZero
+  transitive (LTSucc p) (LTSucc q) = LTSucc $ transitive p q
 
 
 private
diff --git a/lib/Quox/OPE.idr b/lib/Quox/OPE.idr
index 31203eb..a82d106 100644
--- a/lib/Quox/OPE.idr
+++ b/lib/Quox/OPE.idr
@@ -50,7 +50,7 @@ dropInner' (LTESuccR p) = Drop $ dropInner' $ force p
 
 public export
 dropInner : {n : Nat} -> LTE m n -> OPE m n
-dropInner = dropInner' . fromLte
+dropInner = dropInner' . fromLTE
 
 public export
 dropInnerN : (m : Nat) -> OPE n (m + n)
diff --git a/lib/Quox/SingletonExtra.idr b/lib/Quox/SingletonExtra.idr
new file mode 100644
index 0000000..fac4bcf
--- /dev/null
+++ b/lib/Quox/SingletonExtra.idr
@@ -0,0 +1,11 @@
+module Quox.SingletonExtra
+
+import public Data.Singleton
+
+public export
+map : (f : a -> b) -> Singleton x -> Singleton (f x)
+map f x = [|f x|]
+
+public export
+(<$>) : (f : a -> b) -> Singleton x -> Singleton (f x)
+(<$>) = map
-- 
2.39.5


From 42c2217907e9092960d5c67a6d89b94306d94cb2 Mon Sep 17 00:00:00 2001
From: rhiannon morris <rhi@rhiannon.website>
Date: Thu, 23 May 2024 23:27:00 +0200
Subject: [PATCH 5/9] Eq/Ord/Show for No

---
 lib/Quox/No.idr | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/lib/Quox/No.idr b/lib/Quox/No.idr
index 4134485..508e31a 100644
--- a/lib/Quox/No.idr
+++ b/lib/Quox/No.idr
@@ -13,6 +13,10 @@ data No : Pred Bool where
 
 export Uninhabited (No True) where uninhabited _ impossible
 
+export Eq   (No p) where _ == _ = True
+export Ord  (No p) where compare _ _ = EQ
+export Show (No p) where showPrec _ _ = "Ah"
+
 export %inline
 soNo : So b -> No b -> Void
 soNo Oh Ah impossible
-- 
2.39.5


From 85f20680e6382895fb90dad37e7cb3d8f94c1653 Mon Sep 17 00:00:00 2001
From: rhiannon morris <rhi@rhiannon.website>
Date: Thu, 23 May 2024 23:28:43 +0200
Subject: [PATCH 6/9] add constructors to Located/Relocatable interfaces

---
 lib/Quox/Loc.idr | 9 +++++++--
 1 file changed, 7 insertions(+), 2 deletions(-)

diff --git a/lib/Quox/Loc.idr b/lib/Quox/Loc.idr
index fae1bf8..5e25d13 100644
--- a/lib/Quox/Loc.idr
+++ b/lib/Quox/Loc.idr
@@ -125,7 +125,9 @@ extendOr l1 l2 = (l1 `extendL` l2) `or` l2
 
 
 public export
-interface Located a where (.loc) : a -> Loc
+interface Located a where
+  constructor MkLocated
+  (.loc) : a -> Loc
 
 public export
 0 Located1 : (a -> Type) -> Type
@@ -136,7 +138,10 @@ public export
 Located2 f = forall x, y. Located (f x y)
 
 public export
-interface Located a => Relocatable a where setLoc : Loc -> a -> a
+public export
+interface Located a => Relocatable a where
+  constructor MkRelocatable
+  setLoc : Loc -> a -> a
 
 public export
 0 Relocatable1 : (a -> Type) -> Type
-- 
2.39.5


From c063107ecc478dcf1183f345448beb6f921a2137 Mon Sep 17 00:00:00 2001
From: rhiannon morris <rhi@rhiannon.website>
Date: Fri, 24 May 2024 00:23:09 +0200
Subject: [PATCH 7/9] add FromVarR, etc

`FromVarR` is a version of `FromVar` which needs the scope size
to be relevant at runtime
---
 lib/Quox/Syntax/Dim.idr        | 18 +++++--
 lib/Quox/Syntax/Subst.idr      | 97 ++++++++++++++++++++++++++++-----
 lib/Quox/Syntax/Term/Subst.idr | 36 +++++++++----
 lib/Quox/Untyped/Syntax.idr    | 99 ++++++++++++++++++++--------------
 lib/Quox/Var.idr               | 18 +++++--
 5 files changed, 199 insertions(+), 69 deletions(-)

diff --git a/lib/Quox/Syntax/Dim.idr b/lib/Quox/Syntax/Dim.idr
index f495486..63b7797 100644
--- a/lib/Quox/Syntax/Dim.idr
+++ b/lib/Quox/Syntax/Dim.idr
@@ -84,7 +84,11 @@ DSubst : Nat -> Nat -> Type
 DSubst = Subst Dim
 
 
-public export FromVar Dim where fromVar = B
+public export
+FromVarR Dim where fromVarR = B
+
+public export
+FromVar Dim where fromVar = B; fromVarSame _ _ = Refl
 
 
 export
@@ -92,10 +96,16 @@ CanShift Dim where
   K e loc // _  = K e loc
   B i loc // by = B (i // by) loc
 
+private
+substDim : Dim from -> Lazy (DSubst from to) -> Dim to
+substDim (K e loc) _  = K e loc
+substDim (B i loc) th = get th i loc
+
 export
-CanSubstSelf Dim where
-  K e loc // _  = K e loc
-  B i loc // th = get th i loc
+CanSubstSelfR Dim where (//?) = substDim
+
+export
+CanSubstSelf Dim where (//) = substDim; substSame _ _ = Refl
 
 
 export Uninhabited (B i loc1 = K e loc2) where uninhabited _ impossible
diff --git a/lib/Quox/Syntax/Subst.idr b/lib/Quox/Syntax/Subst.idr
index 06734b2..a3f86d5 100644
--- a/lib/Quox/Syntax/Subst.idr
+++ b/lib/Quox/Syntax/Subst.idr
@@ -42,12 +42,28 @@ export Ord  (f to) => Ord  (Subst f from to) where compare = compare `on` repr
 export Show (f to) => Show (Subst f from to) where show = show . repr
 
 
-export infixl 8 //
-public export
-interface FromVar term => CanSubstSelf term where
-  (//) : term from -> Lazy (Subst term from to) -> term to
+export infixl 8 //?, //
 
 
+public export
+interface FromVarR term => CanSubstSelfR term where
+  (//?) : {from, to : Nat} ->
+          term from -> Lazy (Subst term from to) -> term to
+
+public export
+interface (FromVar term, CanSubstSelfR term) => CanSubstSelf term where
+  (//) : term from -> Lazy (Subst term from to) -> term to
+  0 substSame : (t : term from) -> (th : Subst term from to) ->
+                t //? th === t // th
+
+
+public export
+getR : {to : Nat} -> FromVarR term =>
+       Subst term from to -> Var from -> Loc -> term to
+getR (Shift by) i      loc = fromVarR (shift by i) loc
+getR (t ::: th) VZ     _   = t
+getR (t ::: th) (VS i) loc = getR th i loc
+
 public export
 get : FromVar term => Subst term from to -> Var from -> Loc -> term to
 get (Shift by) i      loc = fromVar (shift by i) loc
@@ -56,10 +72,16 @@ get (t ::: th) (VS i) loc = get th i loc
 
 
 public export
-CanSubstSelf Var where
-  i    // Shift by   = shift by i
-  VZ   // (t ::: th) = t
-  VS i // (t ::: th) = i // th
+substVar : Var from -> Lazy (Subst Var from to) -> Var to
+substVar i      (Shift by) = shift by i
+substVar VZ     (t ::: th) = t
+substVar (VS i) (t ::: th) = substVar i th
+
+public export
+CanSubstSelfR Var where (//?) = substVar
+
+public export
+CanSubstSelf Var where (//) = substVar; substSame _ _ = Refl
 
 
 public export %inline
@@ -71,6 +93,16 @@ shift0 : (by : Nat) -> Subst env 0 by
 shift0 by = rewrite sym $ plusZeroRightNeutral by in Shift $ fromNat by
 
 
+export infixr 9 .?
+
+public export
+(.?) : CanSubstSelfR f => {from, mid, to : Nat} ->
+       Subst f from mid -> Subst f mid to -> Subst f from to
+Shift by      .? Shift bz   = Shift $ by . bz
+Shift SZ      .? ph         = ph
+Shift (SS by) .? (t ::: th) = Shift by .? th
+(t ::: th)    .? ph         = (t //? ph) ::: (th .? ph)
+
 public export
 (.) : CanSubstSelf f => Subst f from mid -> Subst f mid to -> Subst f from to
 Shift by      . Shift bz   = Shift $ by . bz
@@ -78,6 +110,7 @@ Shift SZ      . ph         = ph
 Shift (SS by) . (t ::: th) = Shift by . th
 (t ::: th)    . ph         = (t // ph) ::: (th . ph)
 
+
 public export %inline
 id : Subst f n n
 id = shift 0
@@ -95,11 +128,20 @@ map f (Shift by) = Shift by
 map f (t ::: th) = f t ::: map f th
 
 
-public export %inline
-push : CanSubstSelf f => Loc -> Subst f from to -> Subst f (S from) (S to)
-push loc th = fromVar VZ loc ::: (th . shift 1)
+public export
+pushNR : {from, to : Nat} -> CanSubstSelfR f => (s : Nat) -> Loc ->
+         Subst f from to -> Subst f (s + from) (s + to)
+pushNR 0     _   th = th
+pushNR (S s) loc th =
+  rewrite plusSuccRightSucc s from in
+  rewrite plusSuccRightSucc s to in
+  pushNR s loc $ fromVarR VZ loc ::: (th .? shift 1)
+
+public export %inline
+pushR : {from, to : Nat} -> CanSubstSelfR f =>
+        Loc -> Subst f from to -> Subst f (S from) (S to)
+pushR = pushNR 1
 
--- [fixme] a better way to do this?
 public export
 pushN : CanSubstSelf f => (s : Nat) -> Loc ->
         Subst f from to -> Subst f (s + from) (s + to)
@@ -109,6 +151,10 @@ pushN (S s) loc th =
   rewrite plusSuccRightSucc s to in
   pushN s loc $ fromVar VZ loc ::: (th . shift 1)
 
+public export %inline
+push : CanSubstSelf f => Loc -> Subst f from to -> Subst f (S from) (S to)
+push = pushN 1
+
 public export
 drop1 : Subst f (S from) to -> Subst f from to
 drop1 (Shift by) = Shift $ ssDown by
@@ -167,3 +213,30 @@ export %hint
 ShowWithSubst : (Show (env n), forall n. Show (tm n)) =>
                 Show (WithSubst tm env n)
 ShowWithSubst = deriveShow
+
+public export
+record WithSubstR tm env n where
+  constructor SubR
+  {from : Nat}
+  term  : tm from
+  subst : Lazy (Subst env from n)
+
+export
+(Eq (env n), forall n. Eq (tm n)) => Eq (WithSubstR tm env n) where
+  SubR {from = m1} t1 s1 == SubR {from = m2} t2 s2 =
+    case decEq m1 m2 of
+      Yes Refl => t1 == t2 && s1 == s2
+      No  _    => False
+
+export
+(Ord (env n), forall n. Ord (tm n)) => Ord (WithSubstR tm env n) where
+  SubR {from = m1} t1 s1 `compare` SubR {from = m2} t2 s2 =
+    case cmp m1 m2 of
+      CmpLT _ => LT
+      CmpEQ   => compare (t1, s1) (t2, s2)
+      CmpGT _ => GT
+
+export %hint
+ShowWithSubstR : (Show (env n), forall n. Show (tm n)) =>
+                 Show (WithSubstR tm env n)
+ShowWithSubstR = deriveShow
diff --git a/lib/Quox/Syntax/Term/Subst.idr b/lib/Quox/Syntax/Term/Subst.idr
index 54dd990..bb13d38 100644
--- a/lib/Quox/Syntax/Term/Subst.idr
+++ b/lib/Quox/Syntax/Term/Subst.idr
@@ -60,9 +60,31 @@ namespace DSubst.DScopeTermN
   S ns (N body) // th = S ns $ N $ body // th
 
 
-export %inline FromVar (Elim d) where fromVar = B
-export %inline FromVar (Term d) where fromVar = E .: fromVar
+export %inline
+FromVarR (Elim d) where fromVarR = B
 
+export %inline
+FromVar (Elim d) where fromVar = B; fromVarSame _ _ = Refl
+
+export %inline
+FromVarR (Term d) where fromVarR = E .: fromVarR
+
+export %inline
+FromVar (Term d) where fromVar = E .: fromVar; fromVarSame _ _ = Refl
+
+
+export
+CanSubstSelf (Elim d)
+
+private
+tsubstElim : Elim d from -> Lazy (TSubst d from to) -> Elim d to
+tsubstElim (F x u loc)       _  = F x u loc
+tsubstElim (B i loc)         th = get th i loc
+tsubstElim (CloE (Sub e ph)) th = assert_total CloE $ Sub e $ ph . th
+tsubstElim e                 th =
+  case force th of
+       Shift SZ => e
+       th       => CloE $ Sub e th
 
 ||| does the minimal reasonable work:
 ||| - deletes the closure around a *free* name
@@ -70,14 +92,10 @@ export %inline FromVar (Term d) where fromVar = E .: fromVar
 ||| - composes (lazily) with an existing top-level closure
 ||| - immediately looks up a bound variable
 ||| - otherwise, wraps in a new closure
+CanSubstSelfR (Elim d) where (//?) = tsubstElim
+
 export
-CanSubstSelf (Elim d) where
-  F x u loc       // _  = F x u loc
-  B i loc         // th = get th i loc
-  CloE (Sub e ph) // th = assert_total CloE $ Sub e $ ph . th
-  e               // th = case force th of
-                               Shift SZ => e
-                               th       => CloE $ Sub e th
+CanSubstSelf (Elim d) where (//) = tsubstElim; substSame _ _ = Refl
 
 namespace CanTSubst
   public export
diff --git a/lib/Quox/Untyped/Syntax.idr b/lib/Quox/Untyped/Syntax.idr
index fb19e46..d501c1e 100644
--- a/lib/Quox/Untyped/Syntax.idr
+++ b/lib/Quox/Untyped/Syntax.idr
@@ -255,49 +255,66 @@ USubst : Nat -> Nat -> Type
 USubst = Subst Term
 
 
-public export FromVar Term where fromVar = B
+public export %inline
+FromVarR Term where fromVarR = B
+
+public export %inline
+FromVar Term where fromVar = B; fromVarSame _ _ = Refl
 
 
-public export
-CanSubstSelf Term where
-  s // th = case s of
-    F x loc =>
-      F x loc
-    B i loc =>
-      get th i loc
-    Lam x body loc =>
-      Lam x (assert_total $ body // push x.loc th) loc
-    App fun arg loc =>
-      App (fun // th) (arg // th) loc
-    Pair fst snd loc =>
-      Pair (fst // th) (snd // th) loc
-    Fst pair loc =>
-      Fst (pair // th) loc
-    Snd pair loc =>
-      Snd (pair // th) loc
-    Tag tag loc =>
-      Tag tag loc
-    CaseEnum tag cases loc =>
-      CaseEnum (tag // th) (map (assert_total mapSnd (// th)) cases) loc
-    Absurd loc =>
-      Absurd loc
-    Nat n loc =>
-      Nat n loc
-    Succ nat loc =>
-      Succ (nat // th) loc
-    CaseNat nat zer suc loc =>
-      CaseNat (nat // th) (zer // th) (assert_total substSuc suc th) loc
-    Str s loc =>
-      Str s loc
-    Let u x rhs body loc =>
-      Let u x (rhs // th) (assert_total $ body // push x.loc th) loc
-    Erased loc =>
-      Erased loc
-  where
-    substSuc : forall from, to.
-               CaseNatSuc from -> USubst from to -> CaseNatSuc to
-    substSuc (NSRec    x ih t) th = NSRec    x ih $ t // pushN 2 x.loc th
-    substSuc (NSNonrec x    t) th = NSNonrec x    $ t // push    x.loc th
+export
+CanSubstSelf Term
+
+substTerm : Term from -> Lazy (USubst from to) -> Term to
+substTerm s th = case s of
+  F x loc =>
+    F x loc
+  B i loc =>
+    get th i loc
+  Lam x body loc =>
+    Lam x (assert_total substTerm body $ push x.loc th) loc
+  App fun arg loc =>
+    App (substTerm fun th) (substTerm arg th) loc
+  Pair fst snd loc =>
+    Pair (substTerm fst th) (substTerm snd th) loc
+  Fst pair loc =>
+    Fst (substTerm pair th) loc
+  Snd pair loc =>
+    Snd (substTerm pair th) loc
+  Tag tag loc =>
+    Tag tag loc
+  CaseEnum tag cases loc =>
+    CaseEnum (substTerm tag th)
+             (map (mapSnd (\b => assert_total substTerm b th)) cases) loc
+  Absurd loc =>
+    Absurd loc
+  Nat n loc =>
+    Nat n loc
+  Succ nat loc =>
+    Succ (substTerm nat th) loc
+  CaseNat nat zer suc loc =>
+    CaseNat (substTerm nat th)
+            (substTerm zer th)
+            (assert_total substSuc suc th) loc
+  Str s loc =>
+    Str s loc
+  Let u x rhs body loc =>
+    Let u x (substTerm rhs th)
+            (assert_total substTerm body $ push x.loc th) loc
+  Erased loc =>
+    Erased loc
+where
+  substSuc : forall from, to.
+             CaseNatSuc from -> Lazy (USubst from to) -> CaseNatSuc to
+  substSuc (NSRec    x ih t) th = NSRec    x ih $ substTerm t $ pushN 2 x.loc th
+  substSuc (NSNonrec x    t) th = NSNonrec x    $ substTerm t $ push    x.loc th
+
+export
+CanSubstSelfR Term where (//?) = substTerm
+
+export
+CanSubstSelf Term where (//) = substTerm; substSame _ _ = Refl
+
 
 public export
 subN : SnocVect s (Term n) -> Term (s + n) -> Term n
diff --git a/lib/Quox/Var.idr b/lib/Quox/Var.idr
index 28f3a1c..af5024e 100644
--- a/lib/Quox/Var.idr
+++ b/lib/Quox/Var.idr
@@ -138,13 +138,25 @@ export
 weakIsSpec p i = toNatInj $ trans (weakCorrect p i) (sym $ weakSpecCorrect p i)
 
 
+||| inject a variable (with a source location) into some kind of term. in this
+||| case, the scope size may be needed at run time
 public export
-interface FromVar f where %inline fromVar : Var n -> Loc -> f n
+interface FromVarR f where
+  %inline fromVarR : {n : Nat} -> Var n -> Loc -> f n
+
+||| inject a variable (with a source location) into some kind of term, without
+||| needing the scope size
+public export
+interface FromVarR f => FromVar f where
+  %inline fromVar : Var n -> Loc -> f n
+  0 fromVarSame : (i : Var n) -> (l : Loc) -> fromVarR i l === fromVar i l
 
 
-public export FromVar Var where fromVar x _ = x
-
+public export
+FromVarR Var where fromVarR x _ = x
 
+public export
+FromVar Var where fromVar x _ = x; fromVarSame _ _ = Refl
 
 
 public export
-- 
2.39.5


From 1d8a6bb325cc5c119816dc3cb3c4e7db4b1d0699 Mon Sep 17 00:00:00 2001
From: rhiannon morris <rhi@rhiannon.website>
Date: Mon, 27 May 2024 20:22:32 +0200
Subject: [PATCH 8/9] add polynomials

---
 lib/Quox/Polynomial.idr | 189 ++++++++++++++++++++++++++++++++++++++++
 lib/Quox/Semiring.idr   | 122 ++++++++++++++++++++++++++
 lib/quox-lib.ipkg       |   2 +
 3 files changed, 313 insertions(+)
 create mode 100644 lib/Quox/Polynomial.idr
 create mode 100644 lib/Quox/Semiring.idr

diff --git a/lib/Quox/Polynomial.idr b/lib/Quox/Polynomial.idr
new file mode 100644
index 0000000..e6195a9
--- /dev/null
+++ b/lib/Quox/Polynomial.idr
@@ -0,0 +1,189 @@
+module Quox.Polynomial
+
+import public Quox.Syntax.Subst
+import public Quox.Context
+import public Quox.Semiring
+import Data.Maybe
+import Data.SortedMap
+import Data.Singleton
+import Quox.PrettyValExtra
+
+%default total
+
+%hide Prelude.toList
+
+public export
+Monom : Nat -> Type
+Monom = Context' Nat
+
+export %inline
+mZero : {n : Nat} -> Monom n
+mZero = replicate n 0
+
+export %inline
+mIsZero : Monom n -> Bool
+mIsZero = all (== 0)
+
+
+private
+PolyBody : Type -> Nat -> Type
+PolyBody coeff scope = SortedMap (Monom scope) coeff
+
+private %inline
+getScope : PolyBody coeff scope -> Maybe (Singleton scope)
+getScope p = lengthPrf0 . fst <$> leftMost p
+
+export
+data Polynomial : (coeff : Type) -> (scope : Nat) -> Type where
+  Const : (k : coeff) -> Polynomial coeff scope
+  Many  : (p : PolyBody coeff scope) -> Polynomial coeff scope
+%name Polynomial p, q
+-- the Const constructor exists so that `pconst` (and by extension, `one`, and
+-- the TimesMonoid instance) doesn't need to know the scope size
+
+export %inline
+toConst' : List (Monom scope, coeff) -> Maybe coeff
+toConst' [(m, k)] = k <$ guard (mIsZero m)
+toConst' _        = Nothing
+
+export %inline
+toConst : PolyBody coeff scope -> Maybe coeff
+toConst = toConst' . toList
+
+export %inline
+toTrimmedList : AddMonoid v => SortedMap k v -> List (k, v)
+toTrimmedList = List.filter (not . isZero . snd) . toList
+
+export %inline
+toList : {scope : Nat} -> AddMonoid coeff =>
+         Polynomial coeff scope -> List (Monom scope, coeff)
+toList (Const k) = [(mZero, k)]
+toList (Many  p) = toTrimmedList p
+
+private %inline
+addBody : AddMonoid coeff =>
+          PolyBody coeff scope -> PolyBody coeff scope -> PolyBody coeff scope
+addBody = mergeWith (+.)
+
+export %inline
+fromList : AddMonoid coeff =>
+           List (Monom scope, coeff) -> Polynomial coeff scope
+fromList xs = case toConst' xs of
+  Just k  => Const k
+  Nothing => Many $ foldl add1 empty xs
+where
+  add1 : PolyBody coeff scope -> (Monom scope, coeff) -> PolyBody coeff scope
+  add1 p (x, k) = p `addBody` singleton x k
+
+
+export %inline
+(AddMonoid coeff, Eq coeff) => Eq (Polynomial coeff scope) where
+  Const x == Const y = x == y
+  Const x == Many  q = maybe False (== x) $ toConst q
+  Many  p == Const y = maybe False (== y) $ toConst p
+  Many  p == Many  q = toTrimmedList p == toTrimmedList q
+
+export %inline
+(AddMonoid coeff, Ord coeff) => Ord (Polynomial coeff scope) where
+  compare (Const x) (Const y) = compare x y
+  compare (Const x) (Many  q) = maybe LT (compare x) $ toConst q
+  compare (Many  p) (Const y) = maybe GT (flip compare y) $ toConst p
+  compare (Many  p) (Many  q) = compare (toTrimmedList p) (toTrimmedList q)
+
+export %inline
+{scope : Nat} -> (AddMonoid coeff, Show coeff) =>
+Show (Polynomial coeff scope) where
+  showPrec d p = showCon d "fromList" $ showArg (toList p)
+
+export %inline
+{scope : Nat} -> (AddMonoid coeff, PrettyVal coeff) =>
+PrettyVal (Polynomial coeff scope) where
+  prettyVal p = Con "fromList" [prettyVal $ toList p]
+
+
+export %inline
+pconst : a -> Polynomial a n
+pconst = Const
+
+export %inline
+(.at) : AddMonoid a => Polynomial a n -> Monom n -> a
+(Const k).at m = if mIsZero m then k else zero
+(Many  p).at m = fromMaybe zero $ lookup m p
+
+export %inline
+(.at0) : AddMonoid a => Polynomial a n -> a
+(Const k).at0 = k
+(Many  p).at0 = fromMaybe zero $ do
+  (m, k) <- leftMost p
+  guard $ mIsZero m
+  pure k
+
+
+private %inline
+addConstMany : AddMonoid coeff =>
+               coeff -> PolyBody coeff scope -> Polynomial coeff scope
+addConstMany k p = case getScope p of
+  Nothing      => Const k
+  Just (Val _) => Many $ p `addBody` singleton mZero k
+
+export %inline
+AddMonoid a => AddMonoid (Polynomial a n) where
+  zero   = Const zero
+
+  isZero (Const k) = isZero k
+  isZero (Many  p) = maybe False isZero $ toConst p
+
+  Const j +. Const k = Const $ j +. k
+  Const j +. Many  q = addConstMany j q
+  Many  p +. Const k = addConstMany k p
+  Many  p +. Many  q = Many $ p `addBody` q
+
+export %inline
+Semiring a => TimesMonoid (Polynomial a n) where
+  one = pconst one
+
+  Const j *. Const k = Const $ j *. k
+  Const j *. Many  q = Many $ map (j *.) q
+  Many  p *. Const k = Many $ map (*. k) p
+  Many  p *. Many  q = fromList $ do
+    (xs, i) <- toList p
+    (ys, j) <- toList q
+    let k = i *. j
+    guard $ not $ isZero k
+    pure (zipWith (+) xs ys, i *. j)
+
+export %inline
+Semiring a => VecSpace a (Polynomial a n) where
+  x *: xs = Const x *. xs
+
+
+private
+shiftMonom : Shift from to -> Monom from -> Monom to
+shiftMonom SZ      m = m
+shiftMonom (SS by) m = shiftMonom by m :< 0
+
+export
+CanShift (Polynomial coeff) where
+  Const k // _  = Const k
+  Many  p // by =
+    let xs = mapFst (shiftMonom by) <$> toList p in
+    Many $ fromList xs
+
+
+export
+TimesMonoid a => FromVarR (Polynomial a) where
+  fromVarR i l {n} =
+    let m = tabulateVar n $ \j => if i == j then 1 else 0 in
+    Many $ singleton m one
+
+
+private
+substMonom : Semiring a => {from, to : Nat} ->
+             Subst (Polynomial a) from to -> Monom from -> a -> Polynomial a to
+substMonom th m k = sproduct {init = pconst k} $
+  zipWith (\i, p => getR th i noLoc ^. p) (allVars from) m
+
+export
+Semiring a => CanSubstSelfR (Polynomial a) where
+  Const k //? _  = Const k
+  Many  p //? th = ssum $ map (uncurry $ substMonom th) $ toList p
diff --git a/lib/Quox/Semiring.idr b/lib/Quox/Semiring.idr
new file mode 100644
index 0000000..cd8a457
--- /dev/null
+++ b/lib/Quox/Semiring.idr
@@ -0,0 +1,122 @@
+module Quox.Semiring
+
+import Quox.Context
+import public Quox.NatExtra
+import Data.Bool.Decidable
+import Quox.No
+
+%hide Nat.isZero
+
+export infixl 8 +.
+export infixl 9 *., *:, :*
+export infixr 10 ^.
+
+public export
+interface AddMonoid a where
+  zero   : a
+  isZero : a -> Bool
+  (+.)   : a -> a -> a
+
+public export
+interface TimesMonoid a where
+  one : a
+  (*.) : a -> a -> a
+
+public export
+0 Semiring : Type -> Type
+Semiring a = (AddMonoid a, TimesMonoid a)
+
+public export
+interface (Semiring base, AddMonoid vec) => VecSpace base vec | vec where
+  (*:) : base -> vec -> vec
+  (:*) : vec -> base -> vec
+
+  x  *: xs = xs :* x
+  xs :* x  = x  *: xs
+
+
+namespace Foldable
+  public export %inline %tcinline
+  ssum : AddMonoid a => Foldable t => {default zero init : a} -> t a -> a
+  ssum = foldl (+.) init
+
+  public export %inline %tcinline
+  sproduct : TimesMonoid a => Foldable t => {default one init : a} -> t a -> a
+  sproduct = foldl (*.) init
+
+namespace Context
+  public export %inline %tcinline
+  ssum : AddMonoid a => {default zero init : a} ->
+         Telescope' a from to -> a
+  ssum = foldl_ (+.) zero
+
+  public export %inline %tcinline
+  sproduct : TimesMonoid a => {default one init : a} ->
+             Telescope' a from to -> a
+  sproduct = foldl_ (*.) one
+
+
+public export
+(^.) : TimesMonoid a => a -> Nat -> a
+x ^. 0   = one
+x ^. S k = x *. x^.k
+
+
+export %inline
+[NumAdd] Eq a => Num a => AddMonoid a where
+  zero = 0; (+.) = (+); isZero = (== 0)
+
+export %inline
+[NumTimes] Num a => TimesMonoid a where
+  one = 1; (*.) = (*)
+
+
+export %inline %hint
+NatAM : AddMonoid Nat
+NatAM = NumAdd
+
+export %inline %hint
+NatTM : TimesMonoid Nat
+NatTM = NumTimes
+
+export %inline %hint
+IntegerAM : AddMonoid Integer
+IntegerAM = NumAdd
+
+export %inline %hint
+IntegerTM : TimesMonoid Integer
+IntegerTM = NumTimes
+
+export %inline %hint
+IntAM : AddMonoid Int
+IntAM = NumAdd
+
+export %inline %hint
+IntTM : TimesMonoid Int
+IntTM = NumTimes
+
+
+export %inline
+(from `LTE'` to, AddMonoid a) => AddMonoid (Telescope' a from to) where
+  zero   = replicateLTE zero
+  (+.)   = zipWith (+.)
+  isZero = all isZero
+
+export %inline
+(from `LTE'` to, Semiring a) => VecSpace a (Telescope' a from to) where
+  x *: xs = map (x *.) xs
+
+
+public export
+interface AddMonoid a => MonoAddMonoid a where
+  0 zeroPlus : (x, y : a) ->
+               No (isZero x) -> No (isZero y) -> No (isZero (x +. y))
+
+export
+MonoAddMonoid Nat where
+  zeroPlus (S _) (S _) Ah Ah = Ah
+
+
+public export
+0 MonoAddSemiring : Type -> Type
+MonoAddSemiring a = (MonoAddMonoid a, TimesMonoid a)
diff --git a/lib/quox-lib.ipkg b/lib/quox-lib.ipkg
index f715226..2b7a471 100644
--- a/lib/quox-lib.ipkg
+++ b/lib/quox-lib.ipkg
@@ -21,6 +21,8 @@ modules =
   Quox.No,
   Quox.Log,
   Quox.Loc,
+  Quox.Semiring,
+  Quox.Polynomial,
   Quox.Var,
   Quox.Scoped,
   Quox.OPE,
-- 
2.39.5


From 4c008577b4c48f630a7f138455a9653b24b6d715 Mon Sep 17 00:00:00 2001
From: rhiannon morris <rhi@rhiannon.website>
Date: Mon, 27 May 2024 21:28:22 +0200
Subject: [PATCH 9/9] wip make qtys into polynomials

---
 lib/Quox/Context.idr              |  65 ++++
 lib/Quox/Decidable.idr            |   6 +
 lib/Quox/Definition.idr           |  99 +++--
 lib/Quox/Displace.idr             |  16 +-
 lib/Quox/FreeVars.idr             |  38 +-
 lib/Quox/Loc.idr                  |   7 +
 lib/Quox/Pretty.idr               |  23 +-
 lib/Quox/Syntax/Builtin.idr       |   4 +-
 lib/Quox/Syntax/Qty.idr           | 214 +++++++----
 lib/Quox/Syntax/Term/Base.idr     | 269 +++++++-------
 lib/Quox/Syntax/Term/Pretty.idr   | 593 ++++++++++++++++--------------
 lib/Quox/Syntax/Term/Subst.idr    | 338 +++++++++++------
 lib/Quox/Syntax/Term/Tighten.idr  | 118 +++---
 lib/Quox/Typing.idr               |  71 ++--
 lib/Quox/Typing/Context.idr       | 339 ++++++++++-------
 lib/Quox/Typing/Error.idr         | 237 +++++-------
 lib/Quox/Whnf/Coercion.idr        | 197 +++++-----
 lib/Quox/Whnf/ComputeElimType.idr |  64 ++--
 lib/Quox/Whnf/Interface.idr       |  36 +-
 lib/Quox/Whnf/Main.idr            |  82 +++--
 lib/Quox/Whnf/TypeCase.idr        |  80 ++--
 tests/Tests/Qty.idr               |   8 +
 22 files changed, 1650 insertions(+), 1254 deletions(-)
 create mode 100644 tests/Tests/Qty.idr

diff --git a/lib/Quox/Context.idr b/lib/Quox/Context.idr
index c93b20f..3ff37c6 100644
--- a/lib/Quox/Context.idr
+++ b/lib/Quox/Context.idr
@@ -13,7 +13,9 @@ import Data.SnocList
 import Data.SnocVect
 import Data.Vect
 import Control.Monad.Identity
+import Derive.Prelude
 
+%language ElabReflection
 %default total
 
 
@@ -402,3 +404,66 @@ namespace BContext
   export
   toNames : BTelescope {} -> SnocList BaseName
   toNames = foldl (\xs, x => xs :< x.val) [<]
+
+
+public export
+record NameContexts q d n where
+  constructor MkNameContexts
+  {auto qtyLen  : Singleton q}
+  {auto dimLen  : Singleton d}
+  {auto termLen : Singleton n}
+  qnames : BContext q
+  dnames : BContext d
+  tnames : BContext n
+%runElab deriveIndexed "NameContexts" [Show]
+
+namespace NameContexts
+  export
+  MkNameContexts' : (qnames : BContext q) -> (dnames : BContext d) ->
+                    (tnames : BContext n) -> NameContexts q d n
+  MkNameContexts' {qnames, dnames, tnames} =
+    MkNameContexts {
+      qnames, dnames, tnames,
+      qtyLen  = lengthPrf0 qnames,
+      dimLen  = lengthPrf0 dnames,
+      termLen = lengthPrf0 tnames
+    }
+
+  export
+  fromQNames : BContext q -> NameContexts q 0 0
+  fromQNames qnames =
+    MkNameContexts qnames [<] [<] {qtyLen = lengthPrf0 qnames}
+
+  export %inline
+  empty : NameContexts 0 0 0
+  empty = fromQNames [<]
+
+  export
+  extendQtyN' : BTelescope q q' -> NameContexts q d n -> NameContexts q' d n
+  extendQtyN' xs = {qnames $= (. xs), qtyLen $= lengthPrfSing xs}
+
+  export
+  extendDimN' : BTelescope d d' -> NameContexts q d n -> NameContexts q d' n
+  extendDimN' xs = {dnames $= (. xs), dimLen $= lengthPrfSing xs}
+
+  export
+  extendDimN : {s : Nat} -> BContext s ->
+               NameContexts q d n -> NameContexts q (s + d) n
+  extendDimN xs = {dnames $= (++ toSnocVect' xs), dimLen $= map (s +)}
+
+  export
+  extendDim : BindName -> NameContexts q d n -> NameContexts q (S d) n
+  extendDim i = extendDimN [< i]
+
+  export
+  extendTermN' : BTelescope n n' -> NameContexts q d n -> NameContexts q d n'
+  extendTermN' xs = {tnames $= (. xs), termLen $= lengthPrfSing xs}
+
+  export
+  extendTermN : {s : Nat} -> BContext s ->
+                NameContexts q d n -> NameContexts q d (s + n)
+  extendTermN xs = {tnames $= (++ toSnocVect' xs), termLen $= map (s +)}
+
+  export
+  extendTerm : BindName -> NameContexts q d n -> NameContexts q d (S n)
+  extendTerm x = extendTermN [< x]
diff --git a/lib/Quox/Decidable.idr b/lib/Quox/Decidable.idr
index 680b341..f809f9a 100644
--- a/lib/Quox/Decidable.idr
+++ b/lib/Quox/Decidable.idr
@@ -47,6 +47,12 @@ Yes _  && No  n2 = No $ n2 . snd
 No  n1 && _      = No $ n1 . fst
 
 
+public export
+map : p <=> q -> Dec p -> Dec q
+map (MkEquivalence l r) (Yes y) = Yes $ l y
+map (MkEquivalence l r) (No  n) = No  $ n . r
+
+
 public export
 reflectToDec : p `Reflects` b -> Dec p
 reflectToDec (RTrue  y) = Yes y
diff --git a/lib/Quox/Definition.idr b/lib/Quox/Definition.idr
index 900536d..b8fee86 100644
--- a/lib/Quox/Definition.idr
+++ b/lib/Quox/Definition.idr
@@ -12,74 +12,93 @@ import Decidable.Decidable
 
 
 public export
-data DefBody =
-    Concrete (Term 0 0)
-  | Postulate
+data DefBody : (q : Nat) -> Type where
+  MonoDef   : Term 0 0 0 -> DefBody 0
+  PolyDef   : (0 nz : IsSucc q) => Term q 0 0 -> DefBody q
+  Postulate : DefBody q
 
 namespace DefBody
   public export
-  (.term0) : DefBody -> Maybe (Term 0 0)
-  (Concrete t).term0 = Just t
-  (Postulate).term0  = Nothing
+  (.term0) : DefBody q -> Maybe (Term q 0 0)
+  (MonoDef t).term0    = Just t
+  (PolyDef t).term0    = Just t
+  (Postulate).term0 = Nothing
 
 
 public export
 record Definition where
   constructor MkDef
   qty    : GQty
-  type0  : Term 0 0
-  body0  : DefBody
+  {qlen  : Nat}
+  qargs  : BContext qlen
+  type0  : Term qlen 0 0
+  body0  : DefBody qlen
   scheme : Maybe String
   isMain : Bool
   loc_   : Loc
 
 public export %inline
-mkPostulate : GQty -> (type0 : Term 0 0) -> Maybe String -> Bool -> Loc ->
-              Definition
-mkPostulate qty type0 scheme isMain loc_ =
-  MkDef {qty, type0, body0 = Postulate, scheme, isMain, loc_}
+mkPostulate : GQty -> BContext q -> Term q 0 0 ->
+              Maybe String -> Bool -> Loc -> Definition
+mkPostulate qty qargs type0 scheme isMain loc_ =
+  let Val q = lengthPrf0 qargs in
+  MkDef {qty, qargs, type0, body0 = Postulate, scheme, isMain, loc_}
 
 public export %inline
-mkDef : GQty -> (type0, term0 : Term 0 0) -> Maybe String -> Bool -> Loc ->
-        Definition
-mkDef qty type0 term0 scheme isMain loc_ =
-  MkDef {qty, type0, body0 = Concrete term0, scheme, isMain, loc_}
+mkDef : GQty -> BContext q -> (type0, term0 : Term q 0 0) -> Maybe String ->
+        Bool -> Loc -> Definition
+mkDef qty qargs type0 term0 scheme isMain loc_ =
+  case (lengthPrf0 qargs) of
+    Val 0 =>
+      MkDef {qty, qargs, type0, body0 = MonoDef term0, scheme, isMain, loc_}
+    Val (S _) =>
+      MkDef {qty, qargs, type0, body0 = PolyDef term0, scheme, isMain, loc_}
 
 export Located Definition where def.loc = def.loc_
 export Relocatable Definition where setLoc loc = {loc_ := loc}
 
 
+public export
+record Poly (0 tm : TermLike) d n where
+  constructor P
+  qlen : Nat
+  type : tm qlen d n
+
+
 parameters {d, n : Nat}
   public export %inline
-  (.type) : Definition -> Term d n
-  g.type = g.type0 // shift0 d // shift0 n
+  (.type) : Definition -> Poly Term d n
+  def.type = P def.qlen $ def.type0 // shift0 d // shift0 n
 
   public export %inline
-  (.typeAt) : Definition -> Universe -> Term d n
-  g.typeAt u = displace u g.type
+  (.typeAt) : Definition -> Universe -> Poly Term d n
+  def.typeAt u = {type $= displace u} def.type
 
   public export %inline
-  (.term) : Definition -> Maybe (Term d n)
-  g.term = g.body0.term0 <&> \t => t // shift0 d // shift0 n
+  (.term) : Definition -> Maybe (Poly Term d n)
+  def.term = def.body0.term0 <&> \t => P def.qlen $ t // shift0 d // shift0 n
 
   public export %inline
-  (.termAt) : Definition -> Universe -> Maybe (Term d n)
-  g.termAt u = displace u <$> g.term
+  (.termAt) : Definition -> Universe -> Maybe (Poly Term d n)
+  def.termAt u = {type $= displace u} <$> def.term
 
   public export %inline
-  toElim : Definition -> Universe -> Maybe $ Elim d n
-  toElim def u = pure $ Ann !(def.termAt u) (def.typeAt u) def.loc
+  toElim : Definition -> Universe -> Maybe (Poly Elim d n)
+  toElim def u = do
+    tm <- def.body0.term0; let ty = def.type0
+    pure $ P def.qlen $ Ann tm ty def.loc // shift0 d // shift0 n
 
 public export
-(.typeWith) : Definition -> Singleton d -> Singleton n -> Term d n
-g.typeWith (Val d) (Val n) = g.type
+(.typeWith) : Definition -> Singleton d -> Singleton n -> Poly Term d n
+def.typeWith (Val d) (Val n) = def.type
 
 public export
-(.typeWithAt) : Definition -> Singleton d -> Singleton n -> Universe -> Term d n
-g.typeWithAt d n u = displace u $ g.typeWith d n
+(.typeWithAt) : Definition -> Singleton d -> Singleton n ->
+                Universe -> Poly Term d n
+def.typeWithAt (Val d) (Val n) u = def.typeAt u
 
 public export
-(.termWith) : Definition -> Singleton d -> Singleton n -> Maybe (Term d n)
+(.termWith) : Definition -> Singleton d -> Singleton n -> Maybe (Poly Term d n)
 g.termWith (Val d) (Val n) = g.term
 
 
@@ -108,20 +127,28 @@ DefsState : Type -> Type
 DefsState = StateL DEFS Definitions
 
 public export %inline
-lookupElim : {d, n : Nat} -> Name -> Universe -> Definitions -> Maybe (Elim d n)
+lookupElim : {d, n : Nat} ->
+             Name -> Universe -> Definitions -> Maybe (Poly Elim d n)
 lookupElim x u defs = toElim !(lookup x defs) u
 
 public export %inline
-lookupElim0 : Name -> Universe -> Definitions -> Maybe (Elim 0 0)
+lookupElim0 : Name -> Universe -> Definitions -> Maybe (Poly Elim 0 0)
 lookupElim0 = lookupElim
 
 
+export
+prettyQBinders : {opts : LayoutOpts} -> BContext q -> Eff Pretty (Doc opts)
+prettyQBinders [<] = pure empty
+prettyQBinders qnames =
+  qbrackets . separateTight !commaD =<< traverse prettyQBind (toList' qnames)
+
 export
 prettyDef : {opts : LayoutOpts} -> Name -> Definition -> Eff Pretty (Doc opts)
 prettyDef name def = withPrec Outer $ do
-  qty   <- prettyQty def.qty.qty
+  qty   <- prettyQConst def.qty.qconst
   dot   <- dotD
   name  <- prettyFree name
+  qargs <- prettyQBinders def.qargs
   colon <- colonD
-  type  <- prettyTerm [<] [<] def.type
-  hangDSingle (hsep [hcat [qty, dot, name], colon]) type
+  type  <- prettyTerm (fromQNames def.qargs) def.type0
+  hangDSingle (hsep [hcat [qty, dot, name, qargs], colon]) type
diff --git a/lib/Quox/Displace.idr b/lib/Quox/Displace.idr
index 6f8e1ed..c48409f 100644
--- a/lib/Quox/Displace.idr
+++ b/lib/Quox/Displace.idr
@@ -7,12 +7,12 @@ import Quox.Syntax
 
 parameters (k : Universe)
   namespace Term
-    export doDisplace   : Term d n          -> Term d n
-    export doDisplaceS  : ScopeTermN s d n  -> ScopeTermN s d n
-    export doDisplaceDS : DScopeTermN s d n -> DScopeTermN s d n
+    export doDisplace   : Term q d n          -> Term q d n
+    export doDisplaceS  : ScopeTermN s q d n  -> ScopeTermN s q d n
+    export doDisplaceDS : DScopeTermN s q d n -> DScopeTermN s q d n
 
   namespace Elim
-    export doDisplace : Elim d n -> Elim d n
+    export doDisplace : Elim q d n -> Elim q d n
 
   namespace Term
     doDisplace (TYPE l loc) = TYPE (k + l) loc
@@ -41,6 +41,8 @@ parameters (k : Universe)
       CloT (Sub (doDisplace t) (assert_total $ map doDisplace th))
     doDisplace (DCloT (Sub t th)) =
       DCloT (Sub (doDisplace t) th)
+    doDisplace (QCloT (SubR t th)) =
+      QCloT (SubR (doDisplace t) th)
 
     doDisplaceS (S names (Y body)) = S names $ Y $ doDisplace body
     doDisplaceS (S names (N body)) = S names $ N $ doDisplace body
@@ -80,16 +82,18 @@ parameters (k : Universe)
       CloE (Sub (doDisplace e) (assert_total $ map doDisplace th))
     doDisplace (DCloE (Sub e th)) =
       DCloE (Sub (doDisplace e) th)
+    doDisplace (QCloE (SubR e th)) =
+      QCloE (SubR (doDisplace e) th)
 
 
 namespace Term
   export
-  displace : Universe -> Term d n -> Term d n
+  displace : Universe -> Term q d n -> Term q d n
   displace 0 t = t
   displace u t = doDisplace u t
 
 namespace Elim
   export
-  displace : Universe -> Elim d n -> Elim d n
+  displace : Universe -> Elim q d n -> Elim q d n
   displace 0 t = t
   displace u t = doDisplace u t
diff --git a/lib/Quox/FreeVars.idr b/lib/Quox/FreeVars.idr
index 13b711f..8b9f59e 100644
--- a/lib/Quox/FreeVars.idr
+++ b/lib/Quox/FreeVars.idr
@@ -88,7 +88,7 @@ interface HasFreeVars (0 tm : Nat -> Type) where
   fv : {n : Nat} -> tm n -> FreeVars n
 
 public export
-interface HasFreeDVars (0 tm : TermLike) where
+interface HasFreeDVars (0 tm : Nat -> Nat -> Type) where
   constructor HFDV
   fdv : {d, n : Nat} -> tm d n -> FreeVars d
 
@@ -101,7 +101,7 @@ fdvWith : HasFreeDVars tm => Singleton d -> Singleton n -> tm d n -> FreeVars d
 fdvWith (Val d) (Val n) = fdv
 
 export
-Fdv : (0 tm : TermLike) -> {n : Nat} ->
+Fdv : (0 tm : _) -> {n : Nat} ->
       HasFreeDVars tm => HasFreeVars (\d => tm d n)
 Fdv tm @{HFDV fdv} = HFV fdv
 
@@ -139,7 +139,7 @@ where
   fdv (S _ (N body)) = fdv body
 
 export
-fvD : {0 tm : TermLike} -> {n : Nat} -> (forall d. HasFreeVars (tm d)) =>
+fvD : {0 tm : _} -> {n : Nat} -> (forall d. HasFreeVars (tm d)) =>
       Scoped s (\d => tm d n) d -> FreeVars n
 fvD (S _ (Y body)) = fv body
 fvD (S _ (N body)) = fv body
@@ -174,11 +174,10 @@ where
     foldMap (uncurry guardM) (zipWith (,) (fv term).vars (fdvEach subst))
 
 
-export HasFreeVars (Term d)
-export HasFreeVars (Elim d)
+export HasFreeVars (Term q d)
+export HasFreeVars (Elim q d)
 
-export
-HasFreeVars (Term d) where
+HasFreeVars (Term q d) where
   fv (TYPE    {})             = none
   fv (IOState {})             = none
   fv (Pi      {arg, res, _})  = fv arg <+> fv res
@@ -200,9 +199,9 @@ HasFreeVars (Term d) where
   fv (E       e)              = fv e
   fv (CloT    s)              = fv s
   fv (DCloT   s)              = fv s.term
+  fv (QCloT   s)              = fv s.term
 
-export
-HasFreeVars (Elim d) where
+HasFreeVars (Elim q d) where
   fv (F {}) = none
   fv (B i _) = only i
   fv (App {fun, arg, _}) = fv fun <+> fv arg
@@ -224,6 +223,7 @@ HasFreeVars (Elim d) where
     fv ty <+> fv ret <+> fv def <+> foldMap (\x => fv x.snd) (toList arms)
   fv (CloE s) = fv s
   fv (DCloE s) = fv s.term
+  fv (QCloE s) = fv s.term
 
 
 
@@ -253,11 +253,10 @@ fdvSubst : {d, n : Nat} -> (Located2 tm, HasFreeDVars tm) =>
 fdvSubst (Sub t th) = let Val from = getFrom th in fdvSubst' t th
 
 
-export HasFreeDVars Term
-export HasFreeDVars Elim
+export HasFreeDVars (Term q)
+export HasFreeDVars (Elim q)
 
-export
-HasFreeDVars Term where
+HasFreeDVars (Term q) where
   fdv (TYPE    {})             = none
   fdv (IOState {})             = none
   fdv (Pi      {arg, res, _})  = fdv arg <+> fdvT res
@@ -279,9 +278,9 @@ HasFreeDVars Term where
   fdv (E       e)              = fdv e
   fdv (CloT    s)              = fdv s @{WithSubst}
   fdv (DCloT   s)              = fdvSubst s
+  fdv (QCloT   s)              = fdv s.term
 
-export
-HasFreeDVars Elim where
+HasFreeDVars (Elim q) where
   fdv (F {}) = none
   fdv (B {}) = none
   fdv (App {fun, arg, _}) = fdv fun <+> fdv arg
@@ -298,12 +297,13 @@ HasFreeDVars Elim where
     fdv fun <+> fv arg
   fdv (Ann {tm, ty, _}) =
     fdv tm <+> fdv ty
-  fdv (Coe {ty, p, q, val, _}) =
-    fdv @{DScope} ty <+> fv p <+> fv q <+> fdv val
-  fdv (Comp {ty, p, q, val, r, zero, one, _}) =
-    fdv ty <+> fv p <+> fv q <+> fdv val <+>
+  fdv (Coe {ty, p, p', val, _}) =
+    fdv @{DScope} ty <+> fv p <+> fv p' <+> fdv val
+  fdv (Comp {ty, p, p', val, r, zero, one, _}) =
+    fdv ty <+> fv p <+> fv p' <+> fdv val <+>
     fv r <+> fdv @{DScope} zero <+> fdv @{DScope} one
   fdv (TypeCase {ty, ret, arms, def, _}) =
     fdv ty <+> fdv ret <+> fdv def <+> foldMap (\x => fdvT x.snd) (toList arms)
   fdv (CloE s) = fdv s @{WithSubst}
   fdv (DCloE s) = fdvSubst s
+  fdv (QCloE s) = fdv s.term
diff --git a/lib/Quox/Loc.idr b/lib/Quox/Loc.idr
index 5e25d13..196bb6f 100644
--- a/lib/Quox/Loc.idr
+++ b/lib/Quox/Loc.idr
@@ -138,6 +138,9 @@ public export
 Located2 f = forall x, y. Located (f x y)
 
 public export
+0 Located3 : (a -> b -> c -> Type) -> Type
+Located3 f = forall x, y, z. Located (f x y z)
+
 public export
 interface Located a => Relocatable a where
   constructor MkRelocatable
@@ -151,6 +154,10 @@ public export
 0 Relocatable2 : (a -> b -> Type) -> Type
 Relocatable2 f = forall x, y. Relocatable (f x y)
 
+public export
+0 Relocatable3 : (a -> b -> c -> Type) -> Type
+Relocatable3 f = forall x, y, z. Relocatable (f x y z)
+
 
 export
 locs : Located a => Foldable t => t a -> Loc
diff --git a/lib/Quox/Pretty.idr b/lib/Quox/Pretty.idr
index 1083951..0e20161 100644
--- a/lib/Quox/Pretty.idr
+++ b/lib/Quox/Pretty.idr
@@ -39,7 +39,8 @@ data HL
 = Delim
 | Free | TVar
 | Dim  | DVar
-| Qty  | Universe
+| Qty  | QVar
+| Universe
 | Syntax
 | Constant
 %runElab derive "HL" [Eq, Ord, Show]
@@ -82,6 +83,7 @@ toSGR TVar     = [SetForeground BrightYellow]
 toSGR Dim      = [SetForeground BrightGreen]
 toSGR DVar     = [SetForeground BrightGreen]
 toSGR Qty      = [SetForeground BrightMagenta]
+toSGR QVar     = [SetForeground BrightMagenta]
 toSGR Universe = [SetForeground BrightRed]
 toSGR Syntax   = [SetForeground BrightCyan]
 toSGR Constant = [SetForeground BrightRed]
@@ -98,6 +100,7 @@ toClass TVar     = "tv"
 toClass Dim      = "dc"
 toClass DVar     = "dv"
 toClass Qty      = "qt"
+toClass QVar     = "qv"
 toClass Universe = "un"
 toClass Syntax   = "sy"
 toClass Constant = "co"
@@ -205,6 +208,10 @@ parameters {opts : LayoutOpts} {auto _ : Foldable t}
   separateTight : Doc opts -> t (Doc opts) -> Doc opts
   separateTight d = sep . exceptLast (<+> d) . toList
 
+  export
+  sepSingleTight : Doc opts -> t (Doc opts) -> Doc opts
+  sepSingleTight d = sepSingle . exceptLast (<+> d) . toList
+
   export
   hseparateTight : Doc opts -> t (Doc opts) -> Doc opts
   hseparateTight d = hsep . exceptLast (<+> d) . toList
@@ -238,6 +245,10 @@ export %inline
 withPrec : PPrec -> Eff Pretty a -> Eff Pretty a
 withPrec = localAt_ PREC
 
+export %inline
+qbrackets : {opts : LayoutOpts} -> Doc opts -> Eff Pretty (Doc opts)
+qbrackets doc = tightDelims !(ifUnicode "‹" ".{") !(ifUnicode "›" "}") doc
+
 
 export
 prettyName : Name -> Doc opts
@@ -259,12 +270,16 @@ export
 prettyDBind : {opts : LayoutOpts} -> BindName -> Eff Pretty (Doc opts)
 prettyDBind = hl DVar . prettyBind'
 
+export
+prettyQBind : {opts : LayoutOpts} -> BindName -> Eff Pretty (Doc opts)
+prettyQBind = hl QVar . prettyBind'
 
 
 export %inline
 typeD, ioStateD, arrowD, darrowD, timesD, lamD, eqndD, dlamD, annD, natD,
 stringD, eqD, colonD, commaD, semiD, atD, caseD, typecaseD, returnD, ofD, dotD,
-zeroD, succD, coeD, compD, undD, cstD, pipeD, fstD, sndD, letD, inD :
+zeroD, succD, coeD, compD, undD, cstD, pipeD, fstD, sndD, letD, inD,
+qplusD, qtimesD :
   {opts : LayoutOpts} -> Eff Pretty (Doc opts)
 typeD     = hl Syntax . text =<< ifUnicode "★" "Type"
 ioStateD  = hl Syntax $ text "IOState"
@@ -298,6 +313,8 @@ fstD      = hl Syntax   $ text "fst"
 sndD      = hl Syntax   $ text "snd"
 letD      = hl Syntax   $ text "let"
 inD       = hl Syntax   $ text "in"
+qplusD    = hl Syntax   $ text "+"
+qtimesD   = hl Syntax . text =<< ifUnicode "·" "*"
 
 
 export
@@ -311,7 +328,7 @@ prettyApp ind f args =
 export
 prettyAppD : {opts : LayoutOpts} -> Doc opts -> List (Doc opts) ->
              Eff Pretty (Doc opts)
-prettyAppD f args = pure $ prettyApp !(askAt INDENT) f args
+prettyAppD f args = parensIfM App $ prettyApp !(askAt INDENT) f args
 
 
 export
diff --git a/lib/Quox/Syntax/Builtin.idr b/lib/Quox/Syntax/Builtin.idr
index 09ac392..15ea3d9 100644
--- a/lib/Quox/Syntax/Builtin.idr
+++ b/lib/Quox/Syntax/Builtin.idr
@@ -21,7 +21,7 @@ builtinDesc Main = "a function declared as #[main]"
 public export
 builtinTypeDoc : {opts : LayoutOpts} -> Builtin -> Eff Pretty (Doc opts)
 builtinTypeDoc Main =
-  prettyTerm [<] [<] $
-    Pi One (IOState noLoc)
+  prettyTerm empty $
+    Pi {q = 0} (one noLoc) (IOState noLoc)
       (SN $ Sig (Enum (fromList [!(ifUnicode "𝑎" "a")]) noLoc)
                 (SN (IOState noLoc)) noLoc) noLoc
diff --git a/lib/Quox/Syntax/Qty.idr b/lib/Quox/Syntax/Qty.idr
index d0d3d79..50cd519 100644
--- a/lib/Quox/Syntax/Qty.idr
+++ b/lib/Quox/Syntax/Qty.idr
@@ -4,10 +4,14 @@
 ||| it's worth in a language that has other stuff going on too
 module Quox.Syntax.Qty
 
+import public Quox.Polynomial
+import Quox.Name
+import Quox.Syntax.Subst
 import Quox.Pretty
 import Quox.Decidable
 import Quox.PrettyValExtra
 import Data.DPair
+import Data.Singleton
 import Derive.Prelude
 
 %default total
@@ -20,61 +24,124 @@ import Derive.Prelude
 ||| - 1: a variable is used exactly once at run time
 ||| - ω (or #): don't care. an ω variable *can* also be used 0/1 time
 public export
-data Qty = Zero | One | Any
-%runElab derive "Qty" [Eq, Ord, Show, PrettyVal]
-%name Qty.Qty pi, rh
+data QConst = Zero | One | Any
+%runElab derive "QConst" [Eq, Ord, Show, PrettyVal]
+%name QConst q, r
 
 
 export
-prettyQty : {opts : _} -> Qty -> Eff Pretty (Doc opts)
-prettyQty Zero = hl Qty $ text "0"
-prettyQty One  = hl Qty $ text "1"
-prettyQty Any  = hl Qty =<< ifUnicode (text "ω") (text "#")
+prettyQConst : {opts : _} -> QConst -> Eff Pretty (Doc opts)
+prettyQConst Zero = hl Qty $ text "0"
+prettyQConst One  = hl Qty $ text "1"
+prettyQConst Any  = hl Qty =<< ifUnicode (text "ω") (text "#")
+
+-- ||| prints in a form that can be a suffix of "case"
+-- public export
+-- prettySuffix : {opts : _} -> Qty -> Eff Pretty (Doc opts)
+-- prettySuffix = prettyQty
+
+
+namespace QConst
+  ||| e.g. if in the expression `(s, t)`, the variable `x` is
+  ||| used π times in `s` and ρ times in `t`, then it's used
+  ||| (π + ρ) times in the whole expression
+  public export
+  plus : QConst -> QConst -> QConst
+  plus Zero rh   = rh
+  plus pi   Zero = pi
+  plus _    _    = Any
+
+  ||| e.g. if a function `f` uses its argument π times,
+  ||| and `f x` occurs in a σ context, then `x` is used `πσ` times overall
+  public export
+  times : QConst -> QConst -> QConst
+  times Zero _    = Zero
+  times _    Zero = Zero
+  times One  rh   = rh
+  times pi   One  = pi
+  times Any  Any  = Any
+
+  -- ||| "π ∨ ρ"
+  -- |||
+  -- ||| returns a quantity τ with π ≤ τ and ρ ≤ τ.
+  -- ||| if π = ρ, then it's that, otherwise it's ω.
+  -- public export
+  -- lub : QConst -> QConst -> QConst
+  -- lub p q = if p == q then p else Any
+
+export %inline
+AddMonoid QConst where zero = Zero; (+.) = plus; isZero = (== Zero)
+
+export %inline
+TimesMonoid QConst where one = One; (*.) = times
+
 
-||| prints in a form that can be a suffix of "case"
 public export
-prettySuffix : {opts : _} -> Qty -> Eff Pretty (Doc opts)
-prettySuffix = prettyQty
+record Qty n where
+  constructor Q
+  value : Polynomial QConst n
+  loc   : Loc
+%runElab deriveIndexed "Qty" [Eq, Ord]
+
+export %hint
+ShowQty : {n : Nat} -> Show (Qty n)
+ShowQty = deriveShow
+
+export %hint
+PrettyValQty : {n : Nat} -> PrettyVal (Qty n)
+PrettyValQty = derivePrettyVal
 
 
-||| e.g. if in the expression `(s, t)`, the variable `x` is
-||| used π times in `s` and ρ times in `t`, then it's used
-||| (π + ρ) times in the whole expression
-public export
-(+) : Qty -> Qty -> Qty
-Zero + rh   = rh
-pi   + Zero = pi
-_    + _    = Any
+export
+zero, one, any : {n : Nat} -> Loc -> Qty n
+zero = Q zero
+one  = Q one
+any  = Q $ pconst Any
 
-||| e.g. if a function `f` uses its argument π times,
-||| and `f x` occurs in a σ context, then `x` is used `πσ` times overall
-public export
-(*) : Qty -> Qty -> Qty
-Zero * _    = Zero
-_    * Zero = Zero
-One  * rh   = rh
-pi   * One  = pi
-Any  * Any  = Any
+export
+(+) : Qty n -> Qty n -> Qty n
+Q xs l1 + Q ys l2 = Q (xs +. ys) (l1 `or` l2)
+
+export
+(*) : Qty n -> Qty n -> Qty n
+Q xs l1 * Q ys l2 = Q (xs *. ys) (l1 `or` l2)
+
+export
+isAny : Qty n -> Bool
+isAny (Q pi _) = pi.at0 == Any
+
+export
+lub : {n : Nat} -> Qty n -> Qty n -> Qty n
+lub pi rh = if pi == rh then pi else any pi.loc
 
 ||| "π ≤ ρ"
 |||
-||| if a variable is bound with quantity ρ, then it can be used with a total
+||| if a variable is bound with quantity ρ, then it can be used with an actual
 ||| quantity π as long as π ≤ ρ. for example, an ω variable can be used any
 ||| number of times, so π ≤ ω for any π.
 public export
-compat : Qty -> Qty -> Bool
-compat pi Any = True
-compat pi rh  = pi == rh
+compat : Qty n -> Qty n -> Bool
+compat pi rh = isAny rh || pi == rh
 
 
-||| "π ∨ ρ"
-|||
-||| returns a quantity τ with π ≤ τ and ρ ≤ τ.
-||| if π = ρ, then it's that, otherwise it's ω.
-public export
-lub : Qty -> Qty -> Qty
-lub p q = if p == q then p else Any
+private
+toVarString : BContext n -> Monom n -> List BindName
+toVarString ns ds = fold $ zipWith replicate ds ns
 
+private
+prettyTerm : {opts : LayoutOpts} ->
+             BContext n -> Monom n -> QConst -> Eff Pretty (Doc opts)
+prettyTerm ns ds pi = do
+  pi <- prettyQConst pi
+  xs <- traverse prettyQBind (toVarString ns ds)
+  pure $ separateTight !qtimesD $ pi :: xs
+
+export
+prettyQty : {opts : LayoutOpts} -> BContext n -> Qty n -> Eff Pretty (Doc opts)
+prettyQty ns (Q q _) =
+  let Val _ = lengthPrf0 ns in
+  separateLoose !qplusD <$>
+  traverse (uncurry $ prettyTerm ns) (toList q)
 
 ||| to maintain subject reduction, only 0 or 1 can occur
 ||| for the subject of a typing judgment. see @qtt, §2.3 for more detail
@@ -87,9 +154,8 @@ data SQty = SZero | SOne
 |||
 ||| σ ⨴ π is 0 if either of σ or π are, otherwise it is σ.
 public export
-subjMult : SQty -> Qty -> SQty
-subjMult _  Zero = SZero
-subjMult sg _    = sg
+subjMult : SQty -> Qty n -> SQty
+subjMult sg pi = if isZero pi.value then SZero else sg
 
 
 ||| it doesn't make much sense for a top level declaration to have a
@@ -100,12 +166,6 @@ data GQty = GZero | GAny
 %runElab derive "GQty" [Eq, Ord, Show, PrettyVal]
 %name GQty rh
 
-public export
-toGlobal : Qty -> Maybe GQty
-toGlobal Zero = Just GZero
-toGlobal Any  = Just GAny
-toGlobal One  = Nothing
-
 ||| when checking a definition, a 0 definition is checked at 0,
 ||| but an ω definition is checked at 1 since ω isn't a subject quantity
 public export %inline
@@ -114,18 +174,6 @@ globalToSubj GZero = SZero
 globalToSubj GAny  = SOne
 
 
-public export
-DecEq Qty where
-  decEq Zero Zero = Yes Refl
-  decEq Zero One  = No $ \case _ impossible
-  decEq Zero Any  = No $ \case _ impossible
-  decEq One  Zero = No $ \case _ impossible
-  decEq One  One  = Yes Refl
-  decEq One  Any  = No $ \case _ impossible
-  decEq Any  Zero = No $ \case _ impossible
-  decEq Any  One  = No $ \case _ impossible
-  decEq Any  Any  = Yes Refl
-
 public export
 DecEq SQty where
   decEq SZero SZero = Yes Refl
@@ -143,12 +191,48 @@ DecEq GQty where
 
 namespace SQty
   public export %inline
-  (.qty) : SQty -> Qty
-  (SZero).qty = Zero
-  (SOne).qty  = One
+  toQty : {n : Nat} -> Loc -> SQty -> Qty n
+  toQty loc SZero = zero loc
+  toQty loc SOne  = one  loc
+
+  public export %inline
+  (.qconst) : SQty -> QConst
+  (SZero).qconst = Zero
+  (SOne).qconst  = One
 
 namespace GQty
   public export %inline
-  (.qty) : GQty -> Qty
-  (GZero).qty = Zero
-  (GAny).qty  = Any
+  toQty : {n : Nat} -> Loc -> GQty -> Qty n
+  toQty loc GZero = zero loc
+  toQty loc GAny  = any  loc
+
+  public export %inline
+  (.qconst) : GQty -> QConst
+  (GZero).qconst = Zero
+  (GAny).qconst  = Any
+
+
+export
+prettySQty : {opts : _} -> SQty -> Eff Pretty (Doc opts)
+prettySQty sg = prettyQConst sg.qconst
+
+export
+prettyGQty : {opts : _} -> GQty -> Eff Pretty (Doc opts)
+prettyGQty pi = prettyQConst pi.qconst
+
+
+public export
+QSubst : Nat -> Nat -> Type
+QSubst = Subst Qty
+
+export
+FromVarR Qty where
+  fromVarR i loc = Q (fromVarR i loc) loc
+
+export
+CanShift Qty where
+  Q p loc // by = Q (p // by) loc
+
+export
+CanSubstSelfR Qty where
+  Q q loc //? th = Q (q //? map (.value) th) loc
diff --git a/lib/Quox/Syntax/Term/Base.idr b/lib/Quox/Syntax/Term/Base.idr
index 75bae76..029f80c 100644
--- a/lib/Quox/Syntax/Term/Base.idr
+++ b/lib/Quox/Syntax/Term/Base.idr
@@ -32,11 +32,11 @@ import Derive.Prelude
 
 public export
 TermLike : Type
-TermLike = Nat -> Nat -> Type
+TermLike = (q, d, n : Nat) -> Type
 
 public export
 TSubstLike : Type
-TSubstLike = Nat -> Nat -> Nat -> Type
+TSubstLike = (q, d, n1, n2 : Nat) -> Type
 
 public export
 Universe : Type
@@ -50,156 +50,162 @@ TagVal = String
 mutual
   public export
   TSubst : TSubstLike
-  TSubst d = Subst $ \n => Elim d n
+  TSubst q d = Subst $ \n => Elim q d n
 
   ||| first argument `d` is dimension scope size;
   ||| second `n` is term scope size
   public export
-  data Term : (d, n : Nat) -> Type where
+  data Term : (q, d, n : Nat) -> Type where
     ||| type of types
-    TYPE : (l : Universe) -> (loc : Loc) -> Term d n
+    TYPE : (l : Universe) -> (loc : Loc) -> Term q d n
 
     ||| IO state token. this is a builtin because otherwise #[main] being a
     ||| builtin makes no sense
-    IOState : (loc : Loc) -> Term d n
+    IOState : (loc : Loc) -> Term q d n
 
     ||| function type
-    Pi  : (qty : Qty) -> (arg : Term d n) ->
-          (res : ScopeTerm d n) -> (loc : Loc) -> Term d n
+    Pi  : (qty : Qty q) -> (arg : Term q d n) ->
+          (res : ScopeTerm q d n) -> (loc : Loc) -> Term q d n
     ||| function term
-    Lam : (body : ScopeTerm d n) -> (loc : Loc) -> Term d n
+    Lam : (body : ScopeTerm q d n) -> (loc : Loc) -> Term q d n
 
     ||| pair type
-    Sig : (fst : Term d n) -> (snd : ScopeTerm d n) -> (loc : Loc) -> Term d n
+    Sig : (fst : Term q d n) -> (snd : ScopeTerm q d n) -> (loc : Loc) ->
+          Term q d n
     ||| pair value
-    Pair : (fst, snd : Term d n) -> (loc : Loc) -> Term d n
+    Pair : (fst, snd : Term q d n) -> (loc : Loc) -> Term q d n
 
     ||| enumeration type
-    Enum : (cases : SortedSet TagVal) -> (loc : Loc) -> Term d n
+    Enum : (cases : SortedSet TagVal) -> (loc : Loc) -> Term q d n
     ||| enumeration value
-    Tag : (tag : TagVal) -> (loc : Loc) -> Term d n
+    Tag : (tag : TagVal) -> (loc : Loc) -> Term q d n
 
     ||| equality type
-    Eq : (ty : DScopeTerm d n) -> (l, r : Term d n) -> (loc : Loc) -> Term d n
+    Eq : (ty : DScopeTerm q d n) -> (l, r : Term q d n) -> (loc : Loc) ->
+         Term q d n
     ||| equality term
-    DLam : (body : DScopeTerm d n) -> (loc : Loc) -> Term d n
+    DLam : (body : DScopeTerm q d n) -> (loc : Loc) -> Term q d n
 
     ||| natural numbers (temporary until 𝐖 gets added)
-    NAT : (loc : Loc) -> Term d n
-    Nat : (val : Nat) -> (loc : Loc) -> Term d n
-    Succ : (p : Term d n) -> (loc : Loc) -> Term d n
+    NAT : (loc : Loc) -> Term q d n
+    Nat : (val : Nat) -> (loc : Loc) -> Term q d n
+    Succ : (p : Term q d n) -> (loc : Loc) -> Term q d n
 
     ||| strings
-    STRING : (loc : Loc) -> Term d n
-    Str    : (str : String) -> (loc : Loc) -> Term d n
+    STRING : (loc : Loc) -> Term q d n
+    Str    : (str : String) -> (loc : Loc) -> Term q d n
 
     ||| "box" (package a value up with a certain quantity)
-    BOX : (qty : Qty) -> (ty : Term d n) -> (loc : Loc) -> Term d n
-    Box : (val : Term d n) -> (loc : Loc) -> Term d n
+    BOX : (qty : Qty q) -> (ty : Term q d n) -> (loc : Loc) -> Term q d n
+    Box : (val : Term q d n) -> (loc : Loc) -> Term q d n
 
-    Let : (qty : Qty) -> (rhs : Elim d n) ->
-          (body : ScopeTerm d n) -> (loc : Loc) -> Term d n
+    Let : (qty : Qty q) -> (rhs : Elim q d n) ->
+          (body : ScopeTerm q d n) -> (loc : Loc) -> Term q d n
 
     ||| elimination
-    E : (e : Elim d n) -> Term d n
+    E : (e : Elim q d n) -> Term q d n
 
     ||| term closure/suspended substitution
-    CloT  : WithSubst (Term d) (Elim d) n -> Term d n
+    CloT  : WithSubst (Term q d) (Elim q d) n -> Term q d n
     ||| dimension closure/suspended substitution
-    DCloT : WithSubst (\d => Term d n) Dim d -> Term d n
+    DCloT : WithSubst (\d => Term q d n) Dim d -> Term q d n
+    ||| quantity closure/suspended substitution
+    QCloT : WithSubstR (\q => Term q d n) Qty q -> Term q d n
   %name Term s, t, r
 
   ||| first argument `d` is dimension scope size, second `n` is term scope size
   public export
-  data Elim : (d, n : Nat) -> Type where
+  data Elim : (q, d, n : Nat) -> Type where
     ||| free variable, possibly with a displacement (see @crude, or @mugen for a
     ||| more abstract and formalised take)
     |||
     ||| e.g. if f : ★₀ → ★₁, then f¹ : ★₁ → ★₂
-    F : (x : Name) -> (u : Universe) -> (loc : Loc) -> Elim d n
+    F : (x : Name) -> (u : Universe) -> (loc : Loc) -> Elim q d n
     ||| bound variable
-    B : (i : Var n) -> (loc : Loc) -> Elim d n
+    B : (i : Var n) -> (loc : Loc) -> Elim q d n
 
     ||| term application
-    App : (fun : Elim d n) -> (arg : Term d n) -> (loc : Loc) -> Elim d n
+    App : (fun : Elim q d n) -> (arg : Term q d n) -> (loc : Loc) -> Elim q d n
 
     ||| pair destruction
     |||
     ||| `CasePair 𝜋 𝑒 ([𝑟], 𝐴) ([𝑥, 𝑦], 𝑡)` is
     ||| `𝐜𝐚𝐬𝐞 𝜋 · 𝑒 𝐫𝐞𝐭𝐮𝐫𝐧 𝑟 ⇒ 𝐴 𝐨𝐟 { (𝑥, 𝑦) ⇒ 𝑡 }`
-    CasePair : (qty : Qty) -> (pair : Elim d n) ->
-               (ret : ScopeTerm d n) ->
-               (body : ScopeTermN 2 d n) ->
+    CasePair : (qty : Qty q) -> (pair : Elim q d n) ->
+               (ret : ScopeTerm q d n) ->
+               (body : ScopeTermN 2 q d n) ->
                (loc : Loc) ->
-               Elim d n
+               Elim q d n
 
     ||| first element of a pair. only works in non-linear contexts.
-    Fst : (pair : Elim d n) -> (loc : Loc) -> Elim d n
+    Fst : (pair : Elim q d n) -> (loc : Loc) -> Elim q d n
 
     ||| second element of a pair. only works in non-linear contexts.
-    Snd : (pair : Elim d n) -> (loc : Loc) -> Elim d n
+    Snd : (pair : Elim q d n) -> (loc : Loc) -> Elim q d n
 
     ||| enum matching
-    CaseEnum : (qty : Qty) -> (tag : Elim d n) ->
-               (ret : ScopeTerm d n) ->
-               (arms : CaseEnumArms d n) ->
+    CaseEnum : (qty : Qty q) -> (tag : Elim q d n) ->
+               (ret : ScopeTerm q d n) ->
+               (arms : CaseEnumArms q d n) ->
                (loc : Loc) ->
-               Elim d n
+               Elim q d n
 
     ||| nat matching
-    CaseNat : (qty, qtyIH : Qty) -> (nat : Elim d n) ->
-              (ret : ScopeTerm d n) ->
-              (zero : Term d n) ->
-              (succ : ScopeTermN 2 d n) ->
+    CaseNat : (qty, qtyIH : Qty q) -> (nat : Elim q d n) ->
+              (ret : ScopeTerm q d n) ->
+              (zero : Term q d n) ->
+              (succ : ScopeTermN 2 q d n) ->
               (loc : Loc) ->
-              Elim d n
+              Elim q d n
 
     ||| unboxing
-    CaseBox : (qty : Qty) -> (box : Elim d n) ->
-              (ret : ScopeTerm d n) ->
-              (body : ScopeTerm d n) ->
+    CaseBox : (qty : Qty q) -> (box : Elim q d n) ->
+              (ret : ScopeTerm q d n) ->
+              (body : ScopeTerm q d n) ->
               (loc : Loc) ->
-              Elim d n
+              Elim q d n
 
     ||| dim application
-    DApp : (fun : Elim d n) -> (arg : Dim d) -> (loc : Loc) -> Elim d n
+    DApp : (fun : Elim q d n) -> (arg : Dim d) -> (loc : Loc) -> Elim q d n
 
     ||| type-annotated term
-    Ann : (tm, ty : Term d n) -> (loc : Loc) -> Elim d n
+    Ann : (tm, ty : Term q d n) -> (loc : Loc) -> Elim q d n
 
     ||| coerce a value along a type equality, or show its coherence
     ||| [@xtt; §2.1.1]
-    Coe : (ty : DScopeTerm d n) -> (p, q : Dim d) ->
-          (val : Term d n) -> (loc : Loc) -> Elim d n
+    Coe : (ty : DScopeTerm q d n) -> (p, p' : Dim d) ->
+          (val : Term q d n) -> (loc : Loc) -> Elim q d n
 
     ||| "generalised composition" [@xtt; §2.1.2]
-    Comp : (ty : Term d n) -> (p, q : Dim d) ->
-           (val : Term d n) -> (r : Dim d) ->
-           (zero, one : DScopeTerm d n) -> (loc : Loc) -> Elim d n
+    Comp : (ty : Term q d n) -> (p, p' : Dim d) ->
+           (val : Term q d n) -> (r : Dim d) ->
+           (zero, one : DScopeTerm q d n) -> (loc : Loc) -> Elim q d n
 
     ||| match on types. needed for b.s. of coercions [@xtt; §2.2]
-    TypeCase : (ty : Elim d n) -> (ret : Term d n) ->
-               (arms : TypeCaseArms d n) -> (def : Term d n) ->
+    TypeCase : (ty : Elim q d n) -> (ret : Term q d n) ->
+               (arms : TypeCaseArms q d n) -> (def : Term q d n) ->
                (loc : Loc) ->
-               Elim d n
+               Elim q d n
 
     ||| term closure/suspended substitution
-    CloE  : WithSubst (Elim d) (Elim d) n -> Elim d n
+    CloE  : WithSubst (Elim q d) (Elim q d) n -> Elim q d n
     ||| dimension closure/suspended substitution
-    DCloE : WithSubst (\d => Elim d n) Dim d -> Elim d n
+    DCloE : WithSubst (\d => Elim q d n) Dim d -> Elim q d n
+    ||| quantity closure/suspended substitution
+    QCloE : WithSubstR (\q => Elim q d n) Qty q -> Elim q d n
   %name Elim e, f
 
   public export
   CaseEnumArms : TermLike
-  CaseEnumArms d n = SortedMap TagVal (Term d n)
+  CaseEnumArms q d n = SortedMap TagVal (Term q d n)
 
   public export
   TypeCaseArms : TermLike
-  TypeCaseArms d n = SortedDMap TyConKind (\k => TypeCaseArmBody k d n)
+  TypeCaseArms q d n = SortedDMap TyConKind (\k => TypeCaseArmBody k q d n)
 
   public export
   TypeCaseArm : TermLike
-  TypeCaseArm d n = (k ** TypeCaseArmBody k d n)
+  TypeCaseArm q d n = (k ** TypeCaseArmBody k q d n)
 
   public export
   TypeCaseArmBody : TyConKind -> TermLike
@@ -208,35 +214,27 @@ mutual
 
   public export
   ScopeTermN, DScopeTermN : Nat -> TermLike
-  ScopeTermN  s d n = Scoped s (Term d) n
-  DScopeTermN s d n = Scoped s (\d => Term d n) d
+  ScopeTermN  s q d n = Scoped s (Term q d) n
+  DScopeTermN s q d n = Scoped s (\d => Term q d n) d
 
   public export
   ScopeTerm, DScopeTerm : TermLike
   ScopeTerm  = ScopeTermN 1
   DScopeTerm = DScopeTermN 1
 
-mutual
-  export %hint
-  EqTerm : Eq (Term d n)
-  EqTerm = assert_total {a = Eq (Term d n)} deriveEq
+export %hint EqTerm : Eq (Term q d n)
+export %hint EqElim : Eq (Elim q d n)
+EqTerm = assert_total {a = Eq (Term q d n)} deriveEq
+EqElim = assert_total {a = Eq (Elim q d n)} deriveEq
 
-  export %hint
-  EqElim : Eq (Elim d n)
-  EqElim = assert_total {a = Eq (Elim d n)} deriveEq
-
-mutual
-  export %hint
-  ShowTerm : Show (Term d n)
-  ShowTerm = assert_total {a = Show (Term d n)} deriveShow
-
-  export %hint
-  ShowElim : Show (Elim d n)
-  ShowElim = assert_total {a = Show (Elim d n)} deriveShow
+-- export %hint ShowTerm : {q, d, n : Nat} -> Show (Term q d n)
+-- export %hint ShowElim : {q, d, n : Nat} -> Show (Elim q d n)
+-- ShowTerm = assert_total {a = Show (Term q d n)} deriveShow
+-- ShowElim = assert_total {a = Show (Elim q d n)} deriveShow
 
 
 export
-Located (Elim d n) where
+Located (Elim q d n) where
   (F _ _ loc).loc               = loc
   (B _ loc).loc                 = loc
   (App _ _ loc).loc             = loc
@@ -253,30 +251,32 @@ Located (Elim d n) where
   (TypeCase _ _ _ _ loc).loc    = loc
   (CloE (Sub e _)).loc          = e.loc
   (DCloE (Sub e _)).loc         = e.loc
+  (QCloE (SubR e _)).loc        = e.loc
 
 export
-Located (Term d n) where
-  (TYPE _ loc).loc      = loc
-  (IOState loc).loc     = loc
-  (Pi _ _ _ loc).loc    = loc
-  (Lam _ loc).loc       = loc
-  (Sig _ _ loc).loc     = loc
-  (Pair _ _ loc).loc    = loc
-  (Enum _ loc).loc      = loc
-  (Tag _ loc).loc       = loc
-  (Eq _ _ _ loc).loc    = loc
-  (DLam _ loc).loc      = loc
-  (NAT loc).loc         = loc
-  (Nat _ loc).loc       = loc
-  (STRING loc).loc      = loc
-  (Str _ loc).loc       = loc
-  (Succ _ loc).loc      = loc
-  (BOX _ _ loc).loc     = loc
-  (Box _ loc).loc       = loc
-  (Let _ _ _ loc).loc   = loc
-  (E e).loc             = e.loc
-  (CloT (Sub t _)).loc  = t.loc
-  (DCloT (Sub t _)).loc = t.loc
+Located (Term q d n) where
+  (TYPE _ loc).loc       = loc
+  (IOState loc).loc      = loc
+  (Pi _ _ _ loc).loc     = loc
+  (Lam _ loc).loc        = loc
+  (Sig _ _ loc).loc      = loc
+  (Pair _ _ loc).loc     = loc
+  (Enum _ loc).loc       = loc
+  (Tag _ loc).loc        = loc
+  (Eq _ _ _ loc).loc     = loc
+  (DLam _ loc).loc       = loc
+  (NAT loc).loc          = loc
+  (Nat _ loc).loc        = loc
+  (STRING loc).loc       = loc
+  (Str _ loc).loc        = loc
+  (Succ _ loc).loc       = loc
+  (BOX _ _ loc).loc      = loc
+  (Box _ loc).loc        = loc
+  (Let _ _ _ loc).loc    = loc
+  (E e).loc              = e.loc
+  (CloT (Sub t _)).loc   = t.loc
+  (DCloT (Sub t _)).loc  = t.loc
+  (QCloT (SubR t _)).loc = t.loc
 
 export
 Located1 f => Located (ScopedBody s f n) where
@@ -289,7 +289,7 @@ Located1 f => Located (Scoped s f n) where
 
 
 export
-Relocatable (Elim d n) where
+Relocatable (Elim q d n) where
   setLoc loc (F x u _) = F x u loc
   setLoc loc (B i _) = B i loc
   setLoc loc (App fun arg _) = App fun arg loc
@@ -317,9 +317,11 @@ Relocatable (Elim d n) where
     CloE $ Sub (setLoc loc term) subst
   setLoc loc (DCloE (Sub term subst)) =
     DCloE $ Sub (setLoc loc term) subst
+  setLoc loc (QCloE (SubR term subst)) =
+    QCloE $ SubR (setLoc loc term) subst
 
 export
-Relocatable (Term d n) where
+Relocatable (Term q d n) where
   setLoc loc (TYPE l _) = TYPE l loc
   setLoc loc (IOState _) = IOState loc
   setLoc loc (Pi qty arg res _) = Pi qty arg res loc
@@ -341,6 +343,7 @@ Relocatable (Term d n) where
   setLoc loc (E e) = E $ setLoc loc e
   setLoc loc (CloT (Sub term subst)) = CloT $ Sub (setLoc loc term) subst
   setLoc loc (DCloT (Sub term subst)) = DCloT $ Sub (setLoc loc term) subst
+  setLoc loc (QCloT (SubR term subst)) = QCloT $ SubR (setLoc loc term) subst
 
 export
 Relocatable1 f => Relocatable (ScopedBody s f n) where
@@ -354,93 +357,93 @@ Relocatable1 f => Relocatable (Scoped s f n) where
 
 ||| more convenient Pi
 public export %inline
-PiY : (qty : Qty) -> (x : BindName) ->
-      (arg : Term d n) -> (res : Term d (S n)) -> (loc : Loc) -> Term d n
+PiY : (qty : Qty q) -> (x : BindName) ->
+      (arg : Term q d n) -> (res : Term q d (S n)) -> (loc : Loc) -> Term q d n
 PiY {qty, x, arg, res, loc} = Pi {qty, arg, res = SY [< x] res, loc}
 
 ||| more convenient Lam
 public export %inline
-LamY : (x : BindName) -> (body : Term d (S n)) -> (loc : Loc) -> Term d n
+LamY : (x : BindName) -> (body : Term q d (S n)) -> (loc : Loc) -> Term q d n
 LamY {x, body, loc} = Lam {body = SY [< x] body, loc}
 
 public export %inline
-LamN : (body : Term d n) -> (loc : Loc) -> Term d n
+LamN : (body : Term q d n) -> (loc : Loc) -> Term q d n
 LamN {body, loc} = Lam {body = SN body, loc}
 
 ||| non dependent function type
 public export %inline
-Arr : (qty : Qty) -> (arg, res : Term d n) -> (loc : Loc) -> Term d n
+Arr : (qty : Qty q) -> (arg, res : Term q d n) -> (loc : Loc) -> Term q d n
 Arr {qty, arg, res, loc} = Pi {qty, arg, res = SN res, loc}
 
 ||| more convenient Sig
 public export %inline
-SigY : (x : BindName) -> (fst : Term d n) ->
-       (snd : Term d (S n)) -> (loc : Loc) -> Term d n
+SigY : (x : BindName) -> (fst : Term q d n) ->
+       (snd : Term q d (S n)) -> (loc : Loc) -> Term q d n
 SigY {x, fst, snd, loc} = Sig {fst, snd = SY [< x] snd, loc}
 
 ||| non dependent pair type
 public export %inline
-And : (fst, snd : Term d n) -> (loc : Loc) -> Term d n
+And : (fst, snd : Term q d n) -> (loc : Loc) -> Term q d n
 And {fst, snd, loc} = Sig {fst, snd = SN snd, loc}
 
 ||| more convenient Eq
 public export %inline
-EqY : (i : BindName) -> (ty : Term (S d) n) ->
-      (l, r : Term d n) -> (loc : Loc) -> Term d n
+EqY : (i : BindName) -> (ty : Term q (S d) n) ->
+      (l, r : Term q d n) -> (loc : Loc) -> Term q d n
 EqY {i, ty, l, r, loc} = Eq {ty = SY [< i] ty, l, r, loc}
 
 ||| more convenient DLam
 public export %inline
-DLamY : (i : BindName) -> (body : Term (S d) n) -> (loc : Loc) -> Term d n
+DLamY : (i : BindName) -> (body : Term q (S d) n) -> (loc : Loc) -> Term q d n
 DLamY {i, body, loc} = DLam {body = SY [< i] body, loc}
 
 public export %inline
-DLamN : (body : Term d n) -> (loc : Loc) -> Term d n
+DLamN : (body : Term q d n) -> (loc : Loc) -> Term q d n
 DLamN {body, loc} = DLam {body = SN body, loc}
 
 ||| non dependent equality type
 public export %inline
-Eq0 : (ty, l, r : Term d n) -> (loc : Loc) -> Term d n
+Eq0 : (ty, l, r : Term q d n) -> (loc : Loc) -> Term q d n
 Eq0 {ty, l, r, loc} = Eq {ty = SN ty, l, r, loc}
 
 ||| same as `F` but as a term
 public export %inline
-FT : Name -> Universe -> Loc -> Term d n
+FT : Name -> Universe -> Loc -> Term q d n
 FT x u loc = E $ F x u loc
 
 ||| same as `B` but as a term
 public export %inline
-BT : Var n -> (loc : Loc) -> Term d n
+BT : Var n -> (loc : Loc) -> Term q d n
 BT i loc = E $ B i loc
 
 ||| abbreviation for a bound variable like `BV 4` instead of
 ||| `B (VS (VS (VS (VS VZ))))`
 public export %inline
-BV : (i : Nat) -> (0 _ : LT i n) => (loc : Loc) -> Elim d n
+BV : (i : Nat) -> (0 _ : LT i n) => (loc : Loc) -> Elim q d n
 BV i loc = B (V i) loc
 
 ||| same as `BV` but as a term
 public export %inline
-BVT : (i : Nat) -> (0 _ : LT i n) => (loc : Loc) -> Term d n
+BVT : (i : Nat) -> (0 _ : LT i n) => (loc : Loc) -> Term q d n
 BVT i loc = E $ BV i loc
 
 public export %inline
-Zero : Loc -> Term d n
+Zero : Loc -> Term q d n
 Zero = Nat 0
 
 public export %inline
-enum : List TagVal -> Loc -> Term d n
+enum : List TagVal -> Loc -> Term q d n
 enum ts loc = Enum (SortedSet.fromList ts) loc
 
 public export %inline
-typeCase : Elim d n -> Term d n ->
-           List (TypeCaseArm d n) -> Term d n -> Loc -> Elim d n
+typeCase : Elim q d n -> Term q d n ->
+           List (TypeCaseArm q d n) -> Term q d n -> Loc -> Elim q d n
 typeCase ty ret arms def loc = TypeCase ty ret (fromList arms) def loc
 
 public export %inline
-typeCase1Y : Elim d n -> Term d n ->
-             (k : TyConKind) -> BContext (arity k) -> Term d (arity k + n) ->
+typeCase1Y : Elim q d n -> Term q d n ->
+             (k : TyConKind) -> BContext (arity k) -> Term q d (arity k + n) ->
              (loc : Loc) ->
-             {default (NAT loc) def : Term d n} ->
-             Elim d n
+             {default (NAT loc) def : Term q d n} ->
+             Elim q d n
 typeCase1Y ty ret k ns body loc = typeCase ty ret [(k ** SY ns body)] def loc
diff --git a/lib/Quox/Syntax/Term/Pretty.idr b/lib/Quox/Syntax/Term/Pretty.idr
index 36d9320..d22fc19 100644
--- a/lib/Quox/Syntax/Term/Pretty.idr
+++ b/lib/Quox/Syntax/Term/Pretty.idr
@@ -5,6 +5,7 @@ import Quox.Syntax.Term.Subst
 import Quox.Context
 import Quox.Pretty
 
+import Quox.SingletonExtra
 import Data.Vect
 import Derive.Prelude
 
@@ -13,21 +14,23 @@ import Derive.Prelude
 
 
 export
-prettyUniverse : {opts : _} -> Universe -> Eff Pretty (Doc opts)
+prettyUniverse : {opts : LayoutOpts} -> Universe -> Eff Pretty (Doc opts)
 prettyUniverse = hl Universe . text . show
 
 
 export
-prettyTerm : {opts : _} -> BContext d -> BContext n -> Term d n ->
-             Eff Pretty (Doc opts)
+prettyTerm : {opts : LayoutOpts} ->
+             NameContexts q d n -> Term q d n -> Eff Pretty (Doc opts)
 
 export
-prettyElim : {opts : _} -> BContext d -> BContext n -> Elim d n ->
-             Eff Pretty (Doc opts)
+prettyElim : {opts : LayoutOpts} ->
+             NameContexts q d n -> Elim q d n -> Eff Pretty (Doc opts)
 
-private
-BTelescope : Nat -> Nat -> Type
-BTelescope = Telescope' BindName
+
+export
+prettyQty : {opts : LayoutOpts} ->
+            NameContexts q d n -> Qty q -> Eff Pretty (Doc opts)
+prettyQty names pi = let Val q = names.qtyLen in prettyQty names.qnames pi
 
 
 private
@@ -40,109 +43,111 @@ superscript = pack . map sup . unpack where
 
 
 private
-PiBind : Nat -> Nat -> Type
-PiBind d n = (Qty, BindName, Term d n)
+PiBind : TermLike
+PiBind q d n = (Qty q, BindName, Term q d n)
 
 private
-pbname : PiBind d n -> BindName
+pbname : PiBind q d n -> BindName
 pbname (_, x, _) = x
 
 private
-record SplitPi d n where
+record SplitPi q d n where
   constructor MkSplitPi
   {0 inner : Nat}
-  binds : Telescope (PiBind d) n inner
-  cod   : Term d inner
+  binds : Telescope (PiBind q d) n inner
+  cod   : Term q d inner
 
 private
-splitPi : Telescope (PiBind d) n n' -> Term d n' -> SplitPi d n
-splitPi binds (Pi qty arg res _) =
+splitPi : {q : Nat} ->
+          Telescope (PiBind q d) n n' -> Term q d n' -> SplitPi q d n
+splitPi binds cod@(Pi qty arg res _) =
   splitPi (binds :< (qty, res.name, arg)) $
-    assert_smaller res $ pushSubsts' res.term
+    assert_smaller cod $ pushSubsts' res.term
 splitPi binds cod = MkSplitPi {binds, cod}
 
 private
-prettyPiBind1 : {opts : _} ->
-                Qty -> BindName -> BContext d -> BContext n -> Term d n ->
+prettyPiBind1 : {opts : LayoutOpts} ->
+                NameContexts q d n -> Qty q -> BindName -> Term q d n ->
                 Eff Pretty (Doc opts)
-prettyPiBind1 pi (BN Unused _) dnames tnames s =
+prettyPiBind1 names pi (BN Unused _) s =
   hcat <$> sequence
-    [prettyQty pi, dotD,
-     withPrec Arg $ assert_total prettyTerm dnames tnames s]
-prettyPiBind1 pi x dnames tnames s = hcat <$> sequence
-  [prettyQty pi, dotD,
-   hl Delim $ text "(",
-   hsep <$> sequence
-     [prettyTBind x, hl Delim $ text ":",
-      withPrec Outer $ assert_total prettyTerm dnames tnames s],
-   hl Delim $ text ")"]
+    [prettyQty names pi, dotD,
+     withPrec Arg $ assert_total prettyTerm names s]
+prettyPiBind1 names pi x s =
+  hcat <$> sequence
+    [prettyQty names pi, dotD,
+     hl Delim $ text "(",
+     hsep <$> sequence
+       [prettyTBind x, hl Delim $ text ":",
+        withPrec Outer $ assert_total prettyTerm names s],
+     hl Delim $ text ")"]
 
 private
-prettyPiBinds : {opts : _} ->
-                BContext d -> BContext n ->
-                Telescope (PiBind d) n n' ->
+prettyPiBinds : {opts : LayoutOpts} ->
+                NameContexts q d n ->
+                Telescope (PiBind q d) n n' ->
                 Eff Pretty (SnocList (Doc opts))
-prettyPiBinds _ _ [<] = pure [<]
-prettyPiBinds dnames tnames (binds :< (q, x, t)) =
-  let tnames' = tnames . map pbname binds in
-  [|prettyPiBinds dnames tnames binds :<
-    prettyPiBind1 q x dnames tnames' t|]
+prettyPiBinds _ [<] = pure [<]
+prettyPiBinds names (binds :< (q, x, t)) =
+  let names' = extendTermN' (map pbname binds) names in
+  [|prettyPiBinds names binds :<
+    prettyPiBind1 names' q x t|]
 
 
 private
-SigBind : Nat -> Nat -> Type
-SigBind d n = (BindName, Term d n)
+SigBind : TermLike
+SigBind q d n = (BindName, Term q d n)
 
 private
-record SplitSig d n where
+record SplitSig q d n where
   constructor MkSplitSig
   {0 inner : Nat}
-  binds : Telescope (SigBind d) n inner
-  last  : Term d inner
+  binds : Telescope (SigBind q d) n inner
+  last  : Term q d inner
 
 private
-splitSig : Telescope (SigBind d) n n' -> Term d n' -> SplitSig d n
+splitSig : {q : Nat} ->
+           Telescope (SigBind q d) n n' -> Term q d n' -> SplitSig q d n
 splitSig binds (Sig fst snd _) =
   splitSig (binds :< (snd.name, fst)) $
     assert_smaller snd $ pushSubsts' snd.term
 splitSig binds last = MkSplitSig {binds, last}
 
 private
-prettySigBind1 : {opts : _} ->
-                 BindName -> BContext d -> BContext n -> Term d n ->
+prettySigBind1 : {opts : LayoutOpts} ->
+                 NameContexts q d n -> BindName -> Term q d n ->
                  Eff Pretty (Doc opts)
-prettySigBind1 (BN Unused _) dnames tnames s =
-  withPrec InTimes $ assert_total prettyTerm dnames tnames s
-prettySigBind1 x dnames tnames s = hcat <$> sequence
+prettySigBind1 names (BN Unused _) s =
+  withPrec InTimes $ assert_total prettyTerm names s
+prettySigBind1 names x s = hcat <$> sequence
   [hl Delim $ text "(",
    hsep <$> sequence
      [prettyTBind x, hl Delim $ text ":",
-      withPrec Outer $ assert_total prettyTerm dnames tnames s],
+      withPrec Outer $ assert_total prettyTerm names s],
    hl Delim $ text ")"]
 
 private
-prettySigBinds : {opts : _} ->
-                 BContext d -> BContext n ->
-                 Telescope (SigBind d) n n' ->
+prettySigBinds : {opts : LayoutOpts} ->
+                 NameContexts q d n -> Telescope (SigBind q d) n n' ->
                  Eff Pretty (SnocList (Doc opts))
-prettySigBinds _ _ [<] = pure [<]
-prettySigBinds dnames tnames (binds :< (x, t)) =
-  let tnames' = tnames . map fst binds in
-  [|prettySigBinds dnames tnames binds :<
-    prettySigBind1 x dnames tnames' t|]
+prettySigBinds _ [<] = pure [<]
+prettySigBinds names (binds :< (x, t)) =
+  let names' = extendTermN' (map fst binds) names in
+  [|prettySigBinds names binds :<
+    prettySigBind1 names' x t|]
 
 
 private
-prettyTypeLine : {opts : _} ->
-                 BContext d -> BContext n ->
-                 DScopeTerm d n ->
+prettyTypeLine : {opts : LayoutOpts} ->
+                 NameContexts q d n -> DScopeTerm q d n ->
                  Eff Pretty (Doc opts)
-prettyTypeLine dnames tnames (S _ (N body)) =
-  withPrec Arg (prettyTerm dnames tnames body)
-prettyTypeLine dnames tnames (S [< i] (Y body)) =
+prettyTypeLine names (S _ (N body)) =
+  withPrec Arg (prettyTerm names body)
+prettyTypeLine names (S [< i] (Y body)) =
   parens =<< do
+    let names' = extendDim i names
     i'  <- prettyDBind i
-    ty' <- withPrec Outer $ prettyTerm (dnames :< i) tnames body
+    ty' <- withPrec Outer $ prettyTerm names' body
     pure $ sep [hsep [i', !darrowD], ty']
 
 
@@ -155,16 +160,16 @@ NameChunks : Type
 NameChunks = SnocList (NameSort, SnocList BindName)
 
 private
-record SplitLams d n where
+record SplitLams q d n where
   constructor MkSplitLams
   {0 dinner, ninner : Nat}
   dnames : BTelescope d dinner
   tnames : BTelescope n ninner
   chunks : NameChunks
-  body   : Term dinner ninner
+  body   : Term q dinner ninner
 
 private
-splitLams : Term d n -> SplitLams d n
+splitLams : {q : Nat} -> Term q d n -> SplitLams q d n
 splitLams s = go [<] [<] [<] (pushSubsts' s)
 where
   push : NameSort -> BindName -> NameChunks -> NameChunks
@@ -175,7 +180,7 @@ where
 
   go : BTelescope d d' -> BTelescope n n' ->
        SnocList (NameSort, SnocList BindName) ->
-       Term d' n' -> SplitLams d n
+       Term q d' n' -> SplitLams q d n
   go dnames tnames chunks (Lam b _) =
     go dnames (tnames :< b.name) (push T b.name chunks) $
        assert_smaller b $ pushSubsts' b.term
@@ -187,28 +192,31 @@ where
 
 
 private
-splitTuple : SnocList (Term d n) -> Term d n -> SnocList (Term d n)
+splitTuple : {q : Nat} ->
+             SnocList (Term q d n) -> Term q d n -> SnocList (Term q d n)
 splitTuple ss p@(Pair t1 t2 _) =
   splitTuple (ss :< t1) $ assert_smaller p $ pushSubsts' t2
 splitTuple ss t = ss :< t
 
 
 private
-prettyTArg : {opts : _} -> BContext d -> BContext n ->
-             Term d n -> Eff Pretty (Doc opts)
-prettyTArg dnames tnames s =
-  withPrec Arg $ assert_total prettyTerm dnames tnames s
+prettyTArg : {opts : LayoutOpts} ->
+             NameContexts q d n -> Term q d n -> Eff Pretty (Doc opts)
+prettyTArg names s =
+  withPrec Arg $ assert_total prettyTerm names s
 
 private
-prettyDArg : {opts : _} -> BContext d -> Dim d -> Eff Pretty (Doc opts)
-prettyDArg dnames p = [|atD <+> withPrec Arg (prettyDim dnames p)|]
+prettyDArg : {opts : LayoutOpts} ->
+             NameContexts _ d _ -> Dim d -> Eff Pretty (Doc opts)
+prettyDArg names p = [|atD <+> withPrec Arg (prettyDim names.dnames p)|]
 
 private
-splitApps : Elim d n -> (Elim d n, List (Either (Dim d) (Term d n)))
+splitApps : {q : Nat} ->
+            Elim q d n -> (Elim q d n, List (Either (Dim d) (Term q d n)))
 splitApps e = go [] (pushSubsts' e)
 where
-  go : List (Either (Dim d) (Term d n)) -> Elim d n ->
-       (Elim d n, List (Either (Dim d) (Term d n)))
+  go : List (Either (Dim d) (Term q d n)) -> Elim q d n ->
+       (Elim q d n, List (Either (Dim d) (Term q d n)))
   go xs e@(App  f s _) =
     go (Right s :: xs) $ assert_smaller e $ pushSubsts' f
   go xs e@(DApp f p _) =
@@ -216,49 +224,53 @@ where
   go xs s = (s, xs)
 
 private
-prettyDTApps : {opts : _} ->
-               BContext d -> BContext n ->
-               Elim d n -> List (Either (Dim d) (Term d n)) ->
+prettyDTApps : {opts : LayoutOpts} ->
+               NameContexts q d n ->
+               Elim q d n -> List (Either (Dim d) (Term q d n)) ->
                Eff Pretty (Doc opts)
-prettyDTApps dnames tnames f xs = do
-  f  <- withPrec Arg $ assert_total prettyElim dnames tnames f
-  xs <- for xs $ either (prettyDArg dnames) (prettyTArg dnames tnames)
-  parensIfM App =<< prettyAppD f xs
+prettyDTApps names f xs = do
+  f  <- withPrec Arg $ assert_total prettyElim names f
+  xs <- for xs $ either (prettyDArg names) (prettyTArg names)
+  prettyAppD f xs
 
 
 private
-record CaseArm opts d n where
+record CaseArm opts q d n where
   constructor MkCaseArm
   pat    : Doc opts
   dbinds : BTelescope d dinner -- 🍴
   tbinds : BTelescope n ninner
-  body   : Term dinner ninner
-
-parameters {opts : LayoutOpts} (dnames : BContext d) (tnames : BContext n)
-  private
-  prettyCaseArm : CaseArm opts d n -> Eff Pretty (Doc opts)
-  prettyCaseArm (MkCaseArm pat dbinds tbinds body) = do
-    body <- withPrec Outer $ assert_total
-            prettyTerm (dnames . dbinds) (tnames . tbinds) body
-    header <- (pat <++>) <$> darrowD
-    pure $ ifMultiline (header <++> body) (vsep [header, !(indentD body)])
-
-  private
-  prettyCaseBody : List (CaseArm opts d n) -> Eff Pretty (List (Doc opts))
-  prettyCaseBody xs = traverse prettyCaseArm xs
+  body   : Term q dinner ninner
 
 private
-prettyCompPat : {opts : _} -> DimConst -> BindName -> Eff Pretty (Doc opts)
+prettyCaseArm : {opts : LayoutOpts} ->
+                NameContexts q d n -> CaseArm opts q d n ->
+                Eff Pretty (Doc opts)
+prettyCaseArm names (MkCaseArm pat dbinds tbinds body) = do
+  let names' = extendDimN' dbinds $ extendTermN' tbinds names
+  body <- withPrec Outer $ assert_total prettyTerm names' body
+  header <- (pat <++>) <$> darrowD
+  pure $ ifMultiline (header <++> body) (vsep [header, !(indentD body)])
+
+private
+prettyCaseBody : {opts : LayoutOpts} ->
+                 NameContexts q d n -> List (CaseArm opts q d n) ->
+                 Eff Pretty (List (Doc opts))
+prettyCaseBody names xs = traverse (prettyCaseArm names) xs
+
+private
+prettyCompPat : {opts : LayoutOpts} ->
+                DimConst -> BindName -> Eff Pretty (Doc opts)
 prettyCompPat e x = [|prettyDimConst e <++> prettyDBind x|]
 
 private
-prettyCompArm : {opts : _} -> BContext d -> BContext n ->
-                DimConst -> DScopeTerm d n -> Eff Pretty (Doc opts)
-prettyCompArm dnames tnames e s = prettyCaseArm dnames tnames $
+prettyCompArm : {opts : LayoutOpts} -> NameContexts q d n ->
+                DimConst -> DScopeTerm q d n -> Eff Pretty (Doc opts)
+prettyCompArm names e s = prettyCaseArm names $
   MkCaseArm !(prettyCompPat e s.name) [< s.name] [<] s.term
 
 private
-layoutComp : {opts : _} ->
+layoutComp : {opts : LayoutOpts} ->
              (typq : List (Doc opts)) -> (val, r : Doc opts) ->
              (arms : List (Doc opts)) -> Eff Pretty (Doc opts)
 layoutComp typq val r arms = do
@@ -273,32 +285,33 @@ layoutComp typq val r arms = do
 
 
 export
-prettyEnum : {opts : _} -> List String -> Eff Pretty (Doc opts)
+prettyEnum : {opts : LayoutOpts} -> List String -> Eff Pretty (Doc opts)
 prettyEnum cases =
   tightBraces =<<
   fillSeparateTight !commaD <$>
   traverse (hl Constant . Doc.text . quoteTag) cases
 
 private
-prettyCaseRet : {opts : _} ->
-                BContext d -> BContext n ->
-                ScopeTerm d n -> Eff Pretty (Doc opts)
-prettyCaseRet dnames tnames body = withPrec Outer $ case body of
-  S _     (N tm) => assert_total prettyTerm dnames tnames tm
+prettyCaseRet : {opts : LayoutOpts} ->
+                NameContexts q d n -> ScopeTerm q d n -> Eff Pretty (Doc opts)
+prettyCaseRet names body = withPrec Outer $ case body of
+  S _     (N tm) => assert_total prettyTerm names tm
   S [< x] (Y tm) => do
+    let names' = extendTerm x names
     header <- [|prettyTBind x <++> darrowD|]
-    body   <- assert_total prettyTerm dnames (tnames :< x) tm
+    body   <- assert_total prettyTerm names' tm
     hangDSingle header body
 
 private
-prettyCase_ : {opts : _} ->
-              BContext d -> BContext n ->
-              Doc opts -> Elim d n -> ScopeTerm d n -> List (CaseArm opts d n) ->
+prettyCase_ : {opts : LayoutOpts} ->
+              NameContexts q d n ->
+              Doc opts -> Elim q d n -> ScopeTerm q d n ->
+              List (CaseArm opts q d n) ->
               Eff Pretty (Doc opts)
-prettyCase_ dnames tnames intro head ret body = do
-  head   <- withPrec Outer $ assert_total prettyElim dnames tnames head
-  ret    <- prettyCaseRet dnames tnames ret
-  bodys  <- prettyCaseBody dnames tnames body
+prettyCase_ names intro head ret body = do
+  head   <- withPrec Outer $ assert_total prettyElim names head
+  ret    <- prettyCaseRet names ret
+  bodys  <- prettyCaseBody names body
   return <- returnD; of_ <- ofD
   lb     <- hl Delim "{"; rb <- hl Delim "}"; semi <- semiD
   ind    <- askAt INDENT
@@ -308,25 +321,27 @@ prettyCase_ dnames tnames intro head ret body = do
            indent ind $ vseparateTight semi bodys, rb])
 
 private
-prettyCase : {opts : _} ->
-             BContext d -> BContext n ->
-             Qty -> Elim d n -> ScopeTerm d n -> List (CaseArm opts d n) ->
+prettyCase : {opts : LayoutOpts} ->
+             NameContexts q d n ->
+             Qty q -> Elim q d n -> ScopeTerm q d n ->
+             List (CaseArm opts q d n) ->
              Eff Pretty (Doc opts)
-prettyCase dnames tnames qty head ret body =
-  prettyCase_ dnames tnames ![|caseD <+> prettyQty qty|] head ret body
+prettyCase names qty head ret body =
+  prettyCase_ names ![|caseD <+> prettyQty names qty|] head ret body
 
 
 private
-LetBinder : Nat -> Nat -> Type
-LetBinder d n = (Qty, BindName, Elim d n)
+LetBinder : TermLike
+LetBinder q d n = (Qty q, BindName, Elim q d n)
 
 private
-LetExpr : Nat -> Nat -> Nat -> Type
-LetExpr d n n' = (Telescope (LetBinder d) n n', Term d n')
+LetExpr : (q, d, n, n' : Nat) -> Type
+LetExpr q d n n' = (Telescope (LetBinder q d) n n', Term q d n')
 
 -- [todo] factor out this and the untyped version somehow
 export
-splitLet : Telescope (LetBinder d) n n' -> Term d n' -> Exists (LetExpr d n)
+splitLet : Telescope (LetBinder q d) n n' -> Term q d n' ->
+           Exists (LetExpr q d n)
 splitLet ys t@(Let qty rhs body _) =
   splitLet (ys :< (qty, body.name, rhs)) (assert_smaller t body.term)
 splitLet ys t =
@@ -334,38 +349,40 @@ splitLet ys t =
 
 private covering
 prettyLets : {opts : LayoutOpts} ->
-             BContext d -> BContext a -> Telescope (LetBinder d) a b ->
+             NameContexts q d a -> Telescope (LetBinder q d) a b ->
              Eff Pretty (SnocList (Doc opts))
-prettyLets dnames xs lets = snd <$> go lets where
-  peelAnn : forall d, n. Elim d n -> Maybe (Term d n, Term d n)
+prettyLets (MkNameContexts qnames dnames tnames) lets = snd <$> go lets where
+  peelAnn : forall d, n. Elim q d n -> Maybe (Term q d n, Term q d n)
   peelAnn (Ann tm ty _) = Just (tm, ty)
   peelAnn e             = Nothing
 
-  letHeader : Qty -> BindName -> Eff Pretty (Doc opts)
+  letHeader : Qty q -> BindName -> Eff Pretty (Doc opts)
   letHeader qty x = do
-    lett <- [|letD <+> prettyQty qty|]
+    lett <- [|letD <+> prettyQty qnames qty|]
     x    <- prettyTBind x
     pure $ lett <++> x
 
   letBody : forall n. BContext n ->
-            Doc opts -> Elim d n -> Eff Pretty (Doc opts)
-  letBody tnames hdr e = case peelAnn e of
-    Just (tm, ty) => do
-      ty <- withPrec Outer $ assert_total prettyTerm dnames tnames ty
-      tm <- withPrec Outer $ assert_total prettyTerm dnames tnames tm
-      colon <- colonD; eq <- cstD; d <- askAt INDENT
-      pure $ hangSingle d (hangSingle d hdr (colon <++> ty)) (eq <++> tm)
-    Nothing => do
-      e <- withPrec Outer $ assert_total prettyElim dnames tnames e
-      eq <- cstD; d <- askAt INDENT
-      inn <- inD
-      pure $ ifMultiline
-        (hsep [hdr, eq, e, inn])
-        (vsep [hdr, indent d $ hsep [eq, e, inn]])
+            Doc opts -> Elim q d n -> Eff Pretty (Doc opts)
+  letBody tnames hdr e =
+    let names = MkNameContexts' qnames dnames tnames in
+    case peelAnn e of
+      Just (tm, ty) => do
+        ty <- withPrec Outer $ assert_total prettyTerm names ty
+        tm <- withPrec Outer $ assert_total prettyTerm names tm
+        colon <- colonD; eq <- cstD; d <- askAt INDENT
+        pure $ hangSingle d (hangSingle d hdr (colon <++> ty)) (eq <++> tm)
+      Nothing => do
+        e <- withPrec Outer $ assert_total prettyElim names e
+        eq <- cstD; d <- askAt INDENT
+        inn <- inD
+        pure $ ifMultiline
+          (hsep [hdr, eq, e, inn])
+          (vsep [hdr, indent d $ hsep [eq, e, inn]])
 
-  go : forall b. Telescope (LetBinder d) a b ->
+  go : forall b. Telescope (LetBinder q d) a b ->
        Eff Pretty (BContext b, SnocList (Doc opts))
-  go [<] = pure (xs, [<])
+  go [<] = pure (tnames, [<])
   go (lets :< (qty, x, rhs)) = do
     (ys, docs) <- go lets
     doc        <- letBody ys !(letHeader qty x) rhs
@@ -385,7 +402,7 @@ toTel [<]        = [<]
 toTel (ctx :< x) = toTel ctx :< x
 
 private
-prettyTyCasePat : {opts : _} ->
+prettyTyCasePat : {opts : LayoutOpts} ->
                   (k : TyConKind) -> BContext (arity k) ->
                   Eff Pretty (Doc opts)
 prettyTyCasePat KTYPE [<] = typeD
@@ -402,13 +419,14 @@ prettyTyCasePat KString [<] = stringD
 prettyTyCasePat KBOX [< a] = bracks =<< prettyTBind a
 
 
-prettyLambda : {opts : _} -> BContext d -> BContext n ->
-               Term d n -> Eff Pretty (Doc opts)
-prettyLambda dnames tnames s =
-  parensIfM Outer =<< do
-    let MkSplitLams {dnames = ds, tnames = ts, chunks, body} = splitLams s
-    hangDSingle !(header chunks)
-      !(assert_total prettyTerm (dnames . ds) (tnames . ts) body)
+prettyLambda : {opts : LayoutOpts} ->
+               NameContexts q d n -> Term q d n -> Eff Pretty (Doc opts)
+prettyLambda names s =
+  let Val q = names.qtyLen
+      MkSplitLams {dnames = ds, tnames = ts, chunks, body} = splitLams s
+      names' = extendDimN' ds $ extendTermN' ts names in
+  parensIfM Outer =<<
+  hangDSingle !(header chunks) !(assert_total prettyTerm names' body)
 where
   introChar : NameSort -> Eff Pretty (Doc opts)
   introChar T = lamD
@@ -426,198 +444,207 @@ where
   header cs = sep <$> traverse (\(s, xs) => header1 s (toList xs)) (toList cs)
 
 
-prettyDisp : {opts : _} -> Universe -> Eff Pretty (Maybe (Doc opts))
+prettyDisp : {opts : LayoutOpts} -> Universe -> Eff Pretty (Maybe (Doc opts))
 prettyDisp 0 = pure Nothing
 prettyDisp u = map Just $ hl Universe =<<
   ifUnicode (text $ superscript $ show u) (text $ "^" ++ show u)
 
 
-prettyTerm dnames tnames (TYPE l _) = do
+prettyTerm names (TYPE l _) = do
   type  <- hl Syntax . text =<< ifUnicode "★" "Type"
   level <- prettyDisp l
   pure $ maybe type (type <+>) level
 
-prettyTerm dnames tnames (IOState _) =
+prettyTerm _ (IOState _) =
   ioStateD
 
-prettyTerm dnames tnames (Pi qty arg res _) =
-  parensIfM Outer =<< do
-    let MkSplitPi {binds, cod} = splitPi [< (qty, res.name, arg)] res.term
-    arr   <- arrowD
-    lines <- map (<++> arr) <$> prettyPiBinds dnames tnames binds
-    let tnames = tnames . map pbname binds
-    cod <- withPrec Outer $ prettyTerm dnames tnames (assert_smaller res cod)
-    pure $ sepSingle $ toList $ lines :< cod
+prettyTerm names (Pi qty arg res _) = do
+  let Val q = names.qtyLen
+      MkSplitPi {binds, cod} = splitPi [< (qty, res.name, arg)] res.term
+  arr   <- arrowD
+  lines <- map (<++> arr) <$> prettyPiBinds names binds
+  let names' = extendTermN' (map pbname binds) names
+  cod <- withPrec Outer $ prettyTerm names' (assert_smaller res cod)
+  parensIfM Outer $ sepSingle $ toList $ lines :< cod
 
-prettyTerm dnames tnames s@(Lam {}) =
-  prettyLambda dnames tnames s
+prettyTerm names s@(Lam {}) =
+  prettyLambda names s
 
-prettyTerm dnames tnames (Sig fst snd _) =
-  parensIfM Times =<< do
-    let MkSplitSig {binds, last} = splitSig [< (snd.name, fst)] snd.term
-    times <- timesD
-    lines <- map (<++> times) <$> prettySigBinds dnames tnames binds
-    let tnames = tnames . map Builtin.fst binds
-    last <- withPrec InTimes $
-            prettyTerm dnames tnames (assert_smaller snd last)
-    pure $ sepSingle $ toList $ lines :< last
+prettyTerm names (Sig tfst tsnd _) = do
+  let Val q = names.qtyLen
+      MkSplitSig {binds, last} = splitSig [< (tsnd.name, tfst)] tsnd.term
+  times <- timesD
+  lines <- map (<++> times) <$> prettySigBinds names binds
+  let names' = extendTermN' (map fst binds) names
+  last <- withPrec InTimes $ prettyTerm names' (assert_smaller tsnd last)
+  parensIfM Times $ sepSingle $ toList $ lines :< last
 
-prettyTerm dnames tnames p@(Pair fst snd _) =
-  parens =<< do
-    let elems = splitTuple [< fst] snd
-    lines <- for elems $ \t =>
-      withPrec Outer $ prettyTerm dnames tnames $ assert_smaller p t
-    pure $ separateTight !commaD lines
+prettyTerm names p@(Pair s t _) = do
+  let Val q = names.qtyLen
+      elems = splitTuple [< s] t
+  lines <- for elems $ \t =>
+    withPrec Outer $ prettyTerm names $ assert_smaller p t
+  parens $ separateTight !commaD lines
 
-prettyTerm dnames tnames (Enum cases _) =
+prettyTerm _ (Enum cases _) =
   prettyEnum $ SortedSet.toList cases
 
-prettyTerm dnames tnames (Tag tag _) =
+prettyTerm _ (Tag tag _) =
   prettyTag tag
 
-prettyTerm dnames tnames (Eq (S _ (N ty)) l r _) =
-  parensIfM Eq =<< do
-    l  <- withPrec InEq $ prettyTerm dnames tnames l
-    r  <- withPrec InEq $ prettyTerm dnames tnames r
-    ty <- withPrec InEq $ prettyTerm dnames tnames ty
-    pure $ sep [l <++> !eqndD, r <++> !colonD, ty]
+prettyTerm names (Eq (S _ (N ty)) l r _) = do
+  l  <- withPrec InEq $ prettyTerm names l
+  r  <- withPrec InEq $ prettyTerm names r
+  ty <- withPrec InEq $ prettyTerm names ty
+  parensIfM Eq $ sep [l <++> !eqndD, r <++> !colonD, ty]
 
-prettyTerm dnames tnames (Eq ty l r _) =
-  parensIfM App =<< do
-    ty <- prettyTypeLine dnames tnames ty
-    l  <- withPrec Arg $ prettyTerm dnames tnames l
-    r  <- withPrec Arg $ prettyTerm dnames tnames r
-    prettyAppD !eqD [ty, l, r]
+prettyTerm names (Eq ty l r _) = do
+  ty <- prettyTypeLine names ty
+  l  <- withPrec Arg $ prettyTerm names l
+  r  <- withPrec Arg $ prettyTerm names r
+  prettyAppD !eqD [ty, l, r]
 
-prettyTerm dnames tnames s@(DLam {}) =
-  prettyLambda dnames tnames s
+prettyTerm names s@(DLam {}) =
+  prettyLambda names s
 
-prettyTerm dnames tnames (NAT _) = natD
-prettyTerm dnames tnames (Nat n _) = hl Syntax $ pshow n
-prettyTerm dnames tnames (Succ p _) =
-  parensIfM App =<<
-  prettyAppD !succD [!(withPrec Arg $ prettyTerm dnames tnames p)]
+prettyTerm _ (NAT _) = natD
+prettyTerm _ (Nat n _) = hl Syntax $ pshow n
+prettyTerm names (Succ p _) =
+  prettyAppD !succD [!(withPrec Arg $ prettyTerm names p)]
 
-prettyTerm dnames tnames (STRING _) = stringD
-prettyTerm dnames tnames (Str s _) = prettyStrLit s
+prettyTerm _ (STRING _) = stringD
+prettyTerm _ (Str s _) = prettyStrLit s
 
-prettyTerm dnames tnames (BOX qty ty _) =
+prettyTerm names (BOX qty ty _) =
   bracks . hcat =<<
-    sequence [prettyQty qty, dotD,
-              withPrec Outer $ prettyTerm dnames tnames ty]
+  sequence [prettyQty names qty, dotD,
+            withPrec Outer $ prettyTerm names ty]
 
-prettyTerm dnames tnames (Box val _) =
-  bracks =<< withPrec Outer (prettyTerm dnames tnames val)
+prettyTerm names (Box val _) =
+  bracks =<< withPrec Outer (prettyTerm names val)
 
-prettyTerm dnames tnames (Let qty rhs body _) = do
+prettyTerm names (Let qty rhs body _) = do
   let Evidence _ (lets, body) = splitLet [< (qty, body.name, rhs)] body.term
-  heads <- prettyLets dnames tnames lets
-  let tnames = tnames . map (\(_, x, _) => x) lets
-  body <- withPrec Outer $ assert_total prettyTerm dnames tnames body
+  heads <- prettyLets names lets
+  let names' = extendTermN' (map (fst . snd) lets) names
+  body <- withPrec Outer $ assert_total prettyTerm names' body
   let lines = toList $ heads :< body
   pure $ ifMultiline (hsep lines) (vsep lines)
 
-prettyTerm dnames tnames (E e) =
-  case the (Elim d n) (pushSubsts' e) of
-    Ann tm _ _ => assert_total prettyTerm dnames tnames tm
-    _          => assert_total prettyElim dnames tnames e
+prettyTerm names (E e) = do
+  -- [fixme] do this stuff somewhere else!!!
+  let Val q = names.qtyLen
+  case pushSubsts' e {tm = Elim} of
+    Ann tm _ _ => assert_total prettyTerm names tm
+    _          => assert_total prettyElim names e
 
-prettyTerm dnames tnames t0@(CloT (Sub t ph)) =
-  prettyTerm dnames tnames $ assert_smaller t0 $ pushSubstsWith' id ph t
+prettyTerm names t0@(CloT (Sub t ph)) = do
+  let Val q = names.qtyLen
+  prettyTerm names $ assert_smaller t0 $ pushSubstsWith' id id ph t
 
-prettyTerm dnames tnames t0@(DCloT (Sub t ph)) =
-  prettyTerm dnames tnames $ assert_smaller t0 $ pushSubstsWith' ph id t
+prettyTerm names t0@(DCloT (Sub t ph)) = do
+  let Val q = names.qtyLen
+  prettyTerm names $ assert_smaller t0 $ pushSubstsWith' id ph id t
 
-prettyElim dnames tnames (F x u _) = do
+prettyTerm names t0@(QCloT (SubR t ph)) = do
+  let Val q = names.qtyLen
+  prettyTerm names $ assert_smaller t0 $ pushSubstsWith' ph id id t
+
+prettyElim names (F x u _) = do
   x <- prettyFree x
   u <- prettyDisp u
   pure $ maybe x (x <+>) u
 
-prettyElim dnames tnames (B i _) =
-  prettyTBind $ tnames !!! i
+prettyElim names (B i _) =
+  prettyTBind $ names.tnames !!! i
 
-prettyElim dnames tnames e@(App {}) =
-  let (f, xs) = splitApps e in
-  prettyDTApps dnames tnames f xs
+prettyElim names e@(App {}) = do
+  let Val q = names.qtyLen
+      (f, xs) = splitApps e
+  prettyDTApps names f xs
 
-prettyElim dnames tnames (CasePair qty pair ret body _) = do
+prettyElim names (CasePair qty pair ret body _) = do
   let [< x, y] = body.names
-  pat <- parens . hsep =<< sequence
-         [[|prettyTBind x <+> commaD|], prettyTBind y]
-  prettyCase dnames tnames qty pair ret
+  pat <- parens $ !(prettyTBind x) <+> !commaD <++> !(prettyTBind y)
+  prettyCase names qty pair ret
     [MkCaseArm pat [<] [< x, y] body.term]
 
-prettyElim dnames tnames (Fst pair _) =
-  parensIfM App =<< do
-    pair <- prettyTArg dnames tnames (E pair)
-    prettyAppD !fstD [pair]
+prettyElim names (Fst pair _) = do
+  pair <- prettyTArg names (E pair)
+  prettyAppD !fstD [pair]
 
-prettyElim dnames tnames (Snd pair _) =
-  parensIfM App =<< do
-    pair <- prettyTArg dnames tnames (E pair)
-    prettyAppD !sndD [pair]
+prettyElim names (Snd pair _) = do
+  pair <- prettyTArg names (E pair)
+  prettyAppD !sndD [pair]
 
-prettyElim dnames tnames (CaseEnum qty tag ret arms _) = do
+prettyElim names (CaseEnum qty tag ret arms _) = do
   arms <- for (SortedMap.toList arms) $ \(tag, body) =>
     pure $ MkCaseArm !(prettyTag tag) [<] [<] body
-  prettyCase dnames tnames qty tag ret arms
+  prettyCase names qty tag ret arms
 
-prettyElim dnames tnames (CaseNat qty qtyIH nat ret zero succ _) = do
+prettyElim names (CaseNat qty qtyIH nat ret zero succ _) = do
   let zarm = MkCaseArm !zeroD [<] [<] zero
       [< p, ih] = succ.names
   spat0 <- [|succD <++> prettyTBind p|]
-  ihpat0 <- map hcat $ sequence [prettyQty qtyIH, dotD, prettyTBind ih]
+  ihpat0 <- map hcat $ sequence [prettyQty names qtyIH, dotD, prettyTBind ih]
   spat <- if ih.val == Unused
           then pure spat0
-          else pure $ hsep [spat0 <+> !commaD, ihpat0]
+          else pure $ spat0 <+> !commaD <++> ihpat0
   let sarm = MkCaseArm spat [<] [< p, ih] succ.term
-  prettyCase dnames tnames qty nat ret [zarm, sarm]
+  prettyCase names qty nat ret [zarm, sarm]
 
-prettyElim dnames tnames (CaseBox qty box ret body _) = do
+prettyElim names (CaseBox qty box ret body _) = do
   pat <- bracks =<< prettyTBind body.name
   let arm = MkCaseArm pat [<] [< body.name] body.term
-  prettyCase dnames tnames qty box ret [arm]
+  prettyCase names qty box ret [arm]
 
-prettyElim dnames tnames e@(DApp {}) =
-  let (f, xs) = splitApps e in
-  prettyDTApps dnames tnames f xs
+prettyElim names e@(DApp {}) = do
+  let Val q = names.qtyLen
+      (f, xs) = splitApps e
+  prettyDTApps names f xs
 
-prettyElim dnames tnames (Ann tm ty _) =
-  case the (Term d n) (pushSubsts' tm) of
-    E e => assert_total prettyElim dnames tnames e
+prettyElim names (Ann tm ty _) = do
+  -- [fixme] do this stuff somewhere else!!!
+  let Val q = names.qtyLen
+  case pushSubsts' tm {tm = Term} of
+    E e => assert_total prettyElim names e
     _   => do
-      tm <- withPrec AnnL  $ assert_total prettyTerm dnames tnames tm
-      ty <- withPrec Outer $ assert_total prettyTerm dnames tnames ty
+      tm <- withPrec AnnL  $ assert_total prettyTerm names tm
+      ty <- withPrec Outer $ assert_total prettyTerm names ty
       parensIfM Outer =<< hangDSingle (tm <++> !annD) ty
 
-prettyElim dnames tnames (Coe ty p q val _) =
-  parensIfM App =<< do
-    ty  <- prettyTypeLine dnames tnames ty
-    p   <- prettyDArg dnames p
-    q   <- prettyDArg dnames q
-    val <- prettyTArg dnames tnames val
-    prettyAppD !coeD [ty, sep [p, q], val]
+prettyElim names (Coe ty p p' val _) = do
+  ty  <- prettyTypeLine names ty
+  p   <- prettyDArg names p
+  p'  <- prettyDArg names p'
+  val <- prettyTArg names val
+  prettyAppD !coeD [ty, p <++> p', val]
 
-prettyElim dnames tnames e@(Comp ty p q val r zero one _) =
-  parensIfM App =<< do
-    ty   <- assert_total $ prettyTypeLine dnames tnames $ SN ty
-    pq   <- sep <$> sequence [prettyDArg dnames p, prettyDArg dnames q]
-    val  <- prettyTArg dnames tnames val
-    r    <- prettyDArg dnames r
-    arm0 <- [|prettyCompArm dnames tnames Zero zero <+> semiD|]
-    arm1 <- prettyCompArm dnames tnames One one
-    ind  <- askAt INDENT
-    layoutComp [ty, pq] val r [arm0, arm1]
+prettyElim names e@(Comp ty p p' val r zero one _) = do
+  ty   <- assert_total $ prettyTypeLine names $ SN ty
+  pp   <- [|prettyDArg names p <++> prettyDArg names p'|]
+  val  <- prettyTArg names val
+  r    <- prettyDArg names r
+  arm0 <- [|prettyCompArm names Zero zero <+> semiD|]
+  arm1 <- prettyCompArm names One one
+  ind  <- askAt INDENT
+  parensIfM App =<< layoutComp [ty, pp] val r [arm0, arm1]
 
-prettyElim dnames tnames (TypeCase ty ret arms def _) = do
+prettyElim names (TypeCase ty ret arms def _) = do
   arms <- for (toList arms) $ \(k ** body) => do
     pat <- prettyTyCasePat k body.names
     pure $ MkCaseArm pat [<] (toTel body.names) body.term
   let darm = MkCaseArm !undD [<] [<] def
-  prettyCase_ dnames tnames !typecaseD ty (SN ret) $ arms ++ [darm]
+  prettyCase_ names !typecaseD ty (SN ret) $ arms ++ [darm]
 
-prettyElim dnames tnames e0@(CloE (Sub e ph)) =
-  prettyElim dnames tnames $ assert_smaller e0 $ pushSubstsWith' id ph e
+prettyElim names e0@(CloE (Sub e ph)) = do
+  let Val q = names.qtyLen
+  prettyElim names $ assert_smaller e0 $ pushSubstsWith' id id ph e
 
-prettyElim dnames tnames e0@(DCloE (Sub e ph)) =
-  prettyElim dnames tnames $ assert_smaller e0 $ pushSubstsWith' ph id e
+prettyElim names e0@(DCloE (Sub e ph)) = do
+  let Val q = names.qtyLen
+  prettyElim names $ assert_smaller e0 $ pushSubstsWith' id ph id e
+
+prettyElim names e0@(QCloE (SubR e ph)) = do
+  let Val q = names.qtyLen
+  prettyElim names $ assert_smaller e0 $ pushSubstsWith' ph id id e
diff --git a/lib/Quox/Syntax/Term/Subst.idr b/lib/Quox/Syntax/Term/Subst.idr
index bb13d38..da90850 100644
--- a/lib/Quox/Syntax/Term/Subst.idr
+++ b/lib/Quox/Syntax/Term/Subst.idr
@@ -6,10 +6,42 @@ import Data.SnocVect
 
 %default total
 
+namespace CanQSubst
+  public export
+  interface CanQSubst (0 tm : TermLike) where
+    (//) : {q1, q2 : Nat} -> tm q1 d n -> Lazy (QSubst q1 q2) -> tm q2 d n
+
+||| does the minimal reasonable work:
+||| - deletes the closure around an atomic constant like `TYPE`
+||| - deletes an identity substitution
+||| - composes (lazily) with an existing top-level dim-closure
+||| - otherwise, wraps in a new closure
+export
+CanQSubst Term where
+  s                 // Shift SZ = s
+  TYPE l loc        // _        = TYPE l loc
+  QCloT (SubR s ph) // th       = QCloT $ SubR s $ ph .? th
+  s                 // th       = QCloT $ SubR s th
+
+||| does the minimal reasonable work:
+||| - deletes the closure around a term variable
+||| - deletes an identity substitution
+||| - composes (lazily) with an existing top-level dim-closure
+||| - immediately looks up bound variables in a
+|||   top-level sequence of dimension applications
+||| - otherwise, wraps in a new closure
+export
+CanQSubst Elim where
+  e                 // Shift SZ = e
+  F x u loc         // _        = F x u loc -- [todo] q args
+  B i loc           // _        = B i loc
+  QCloE (SubR e ph) // th       = QCloE $ SubR e $ ph .? th
+  e                 // th       = QCloE $ SubR e th
+
 namespace CanDSubst
   public export
   interface CanDSubst (0 tm : TermLike) where
-    (//) : tm d1 n -> Lazy (DSubst d1 d2) -> tm d2 n
+    (//) : tm q d1 n -> Lazy (DSubst d1 d2) -> tm q d2 n
 
 ||| does the minimal reasonable work:
 ||| - deletes the closure around an atomic constant like `TYPE`
@@ -24,7 +56,7 @@ CanDSubst Term where
   s                // th       = DCloT $ Sub s th
 
 private
-subDArgs : Elim d1 n -> DSubst d1 d2 -> Elim d2 n
+subDArgs : Elim q d1 n -> DSubst d1 d2 -> Elim q d2 n
 subDArgs (DApp f d loc) th = DApp (subDArgs f th) (d // th) loc
 subDArgs e              th = DCloE $ Sub e th
 
@@ -44,40 +76,54 @@ CanDSubst Elim where
   DCloE (Sub e ph) // th       = DCloE $ Sub e $ ph . th
   e                // th       = DCloE $ Sub e th
 
+namespace QSubst.ScopeTermN
+  export %inline
+  (//) : {q1, q2 : Nat} -> ScopeTermN s q1 d n -> Lazy (QSubst q1 q2) ->
+         ScopeTermN s q2 d n
+  S ns (Y body) // th = S ns $ Y $ body // th
+  S ns (N body) // th = S ns $ N $ body // th
+
 namespace DSubst.ScopeTermN
   export %inline
-  (//) : ScopeTermN s d1 n -> Lazy (DSubst d1 d2) ->
-         ScopeTermN s d2 n
+  (//) : ScopeTermN s q d1 n -> Lazy (DSubst d1 d2) ->
+         ScopeTermN s q d2 n
+  S ns (Y body) // th = S ns $ Y $ body // th
+  S ns (N body) // th = S ns $ N $ body // th
+
+namespace QSubst.DScopeTermN
+  export %inline
+  (//) : {q1, q2 : Nat} -> DScopeTermN s q1 d n -> Lazy (QSubst q1 q2) ->
+         DScopeTermN s q2 d n
   S ns (Y body) // th = S ns $ Y $ body // th
   S ns (N body) // th = S ns $ N $ body // th
 
 namespace DSubst.DScopeTermN
   export %inline
   (//) : {s : Nat} ->
-         DScopeTermN s d1 n -> Lazy (DSubst d1 d2) ->
-         DScopeTermN s d2 n
+         DScopeTermN s q d1 n -> Lazy (DSubst d1 d2) ->
+         DScopeTermN s q d2 n
   S ns (Y body) // th = S ns $ Y $ body // pushN s (locs $ toList' ns) th
   S ns (N body) // th = S ns $ N $ body // th
 
 
 export %inline
-FromVarR (Elim d) where fromVarR = B
+FromVarR (Elim q d) where fromVarR = B
 
 export %inline
-FromVar (Elim d) where fromVar = B; fromVarSame _ _ = Refl
+FromVar (Elim q d) where fromVar = B; fromVarSame _ _ = Refl
 
 export %inline
-FromVarR (Term d) where fromVarR = E .: fromVarR
+FromVarR (Term q d) where fromVarR = E .: fromVarR
 
 export %inline
-FromVar (Term d) where fromVar = E .: fromVar; fromVarSame _ _ = Refl
+FromVar (Term q d) where fromVar = E .: fromVar; fromVarSame _ _ = Refl
 
 
 export
-CanSubstSelf (Elim d)
+CanSubstSelf (Elim q d)
 
 private
-tsubstElim : Elim d from -> Lazy (TSubst d from to) -> Elim d to
+tsubstElim : Elim q d from -> Lazy (TSubst q d from to) -> Elim q d to
 tsubstElim (F x u loc)       _  = F x u loc
 tsubstElim (B i loc)         th = get th i loc
 tsubstElim (CloE (Sub e ph)) th = assert_total CloE $ Sub e $ ph . th
@@ -92,15 +138,15 @@ tsubstElim e                 th =
 ||| - composes (lazily) with an existing top-level closure
 ||| - immediately looks up a bound variable
 ||| - otherwise, wraps in a new closure
-CanSubstSelfR (Elim d) where (//?) = tsubstElim
+CanSubstSelfR (Elim q d) where (//?) = tsubstElim
 
 export
-CanSubstSelf (Elim d) where (//) = tsubstElim; substSame _ _ = Refl
+CanSubstSelf (Elim q d) where (//) = tsubstElim; substSame _ _ = Refl
 
 namespace CanTSubst
   public export
   interface CanTSubst (0 tm : TermLike) where
-    (//) : tm d n1 -> Lazy (TSubst d n1 n2) -> tm d n2
+    (//) : tm q d n1 -> Lazy (TSubst q d n1 n2) -> tm q d n2
 
 ||| does the minimal reasonable work:
 ||| - deletes the closure around an atomic constant like `TYPE`
@@ -120,69 +166,89 @@ CanTSubst Term where
 namespace ScopeTermN
   export %inline
   (//) : {s : Nat} ->
-         ScopeTermN s d n1 -> Lazy (TSubst d n1 n2) ->
-         ScopeTermN s d n2
+         ScopeTermN s q d n1 -> Lazy (TSubst q d n1 n2) ->
+         ScopeTermN s q d n2
   S ns (Y body) // th = S ns $ Y $ body // pushN s (locs $ toList' ns) th
   S ns (N body) // th = S ns $ N $ body // th
 
 namespace DScopeTermN
   export %inline
   (//) : {s : Nat} ->
-         DScopeTermN s d n1 -> Lazy (TSubst d n1 n2) -> DScopeTermN s d n2
+         DScopeTermN s q d n1 -> Lazy (TSubst q d n1 n2) ->
+         DScopeTermN s q d n2
   S ns (Y body) // th = S ns $ Y $ body // map (// shift s) th
   S ns (N body) // th = S ns $ N $ body // th
 
-export %inline CanShift (Term d) where s // by = s // Shift by
-export %inline CanShift (Elim d) where e // by = e // Shift by
+export %inline CanShift (Term q d) where s // by = s // Shift by
+export %inline CanShift (Elim q d) where e // by = e // Shift by
 
-export %inline CanShift (flip Term n) where s // by = s // Shift by
-export %inline CanShift (flip Elim n) where e // by = e // Shift by
+-- -- from is not accessible in this context
+-- export %inline CanShift (\q => Term q d n) where s // by = s // Shift by
+-- export %inline CanShift (\q => Elim q d n) where e // by = e // Shift by
+
+export %inline CanShift (\d => Term q d n) where s // by = s // Shift by
+export %inline CanShift (\d => Elim q d n) where e // by = e // Shift by
 
 export %inline
-{s : Nat} -> CanShift (ScopeTermN s d) where
+{s : Nat} -> CanShift (ScopeTermN s q d) where
   b // by = b // Shift by
 
 
 export %inline
-comp : DSubst d1 d2 -> TSubst d1 n1 mid -> TSubst d2 mid n2 -> TSubst d2 n1 n2
-comp th ps ph = map (// th) ps . ph
+comp : {q1, q2 : Nat} ->
+       QSubst q1 q2 -> DSubst d1 d2 ->
+       TSubst q1 d1 n1 mid -> TSubst q2 d2 mid n2 -> TSubst q2 d2 n1 n2
+comp th ph ps ps' = map (\t => t // th // ph) ps . ps'
+
+-- export %inline
+-- compD : DSubst d1 d2 -> TSubst q d1 n1 mid ->
+--         TSubst q d2 mid n2 -> TSubst q d2 n1 n2
+-- compD th ps ph = map (// th) ps . ph
+
+-- export %inline
+-- compQ : {q1, q2 : Nat} -> QSubst q1 q2 -> TSubst q1 d n1 mid ->
+--         TSubst q2 d mid n2 -> TSubst q2 d n1 n2
+-- compQ th ps ph = map (// th) ps . ph
 
 
 public export %inline
-dweakT : (by : Nat) -> Term d n -> Term (by + d) n
+dweakT : (by : Nat) -> Term q d n -> Term q (by + d) n
 dweakT by t = t // shift by
 
 public export %inline
-dweakS : (by : Nat) -> ScopeTermN s d n -> ScopeTermN s (by + d) n
+dweakS : (by : Nat) -> ScopeTermN s q d n -> ScopeTermN s q (by + d) n
 dweakS by t = t // shift by
 
 public export %inline
 dweakDS : {s : Nat} -> (by : Nat) ->
-          DScopeTermN s d n -> DScopeTermN s (by + d) n
+          DScopeTermN s q d n -> DScopeTermN s q (by + d) n
 dweakDS by t = t // shift by
 
 public export %inline
-dweakE : (by : Nat) -> Elim d n -> Elim (by + d) n
+dweakE : (by : Nat) -> Elim q d n -> Elim q (by + d) n
 dweakE by t = t // shift by
 
 
 public export %inline
-weakT : (by : Nat) -> Term d n -> Term d (by + n)
+weakT : (by : Nat) -> Term q d n -> Term q d (by + n)
 weakT by t = t // shift by
 
 public export %inline
-weakS : {s : Nat} -> (by : Nat) -> ScopeTermN s d n -> ScopeTermN s d (by + n)
+weakS : {s : Nat} -> (by : Nat) ->
+        ScopeTermN s q d n -> ScopeTermN s q d (by + n)
 weakS by t = t // shift by
 
 public export %inline
 weakDS : {s : Nat} -> (by : Nat) ->
-         DScopeTermN s d n -> DScopeTermN s d (by + n)
+         DScopeTermN s q d n -> DScopeTermN s q d (by + n)
 weakDS by t = t // shift by
 
 public export %inline
-weakE : (by : Nat) -> Elim d n -> Elim d (by + n)
+weakE : (by : Nat) -> Elim q d n -> Elim q d (by + n)
 weakE by t = t // shift by
 
+-- no weakQ etc because no first-class binder to push under
+
 
 parameters {auto _ : CanShift f} {s : Nat}
   export %inline
@@ -206,69 +272,74 @@ namespace ScopeTermN
   t.term0 = getTerm0 t.body
 
 export %inline
-subN : ScopeTermN s d n -> SnocVect s (Elim d n) -> Term d n
+subN : ScopeTermN s q d n -> SnocVect s (Elim q d n) -> Term q d n
 subN (S _ (Y body)) es = body // fromSnocVect es
 subN (S _ (N body)) _  = body
 
 export %inline
-sub1 : ScopeTerm d n -> Elim d n -> Term d n
+sub1 : ScopeTerm q d n -> Elim q d n -> Term q d n
 sub1 t e = subN t [< e]
 
 export %inline
-dsubN : DScopeTermN s d n -> SnocVect s (Dim d) -> Term d n
+dsubN : DScopeTermN s q d n -> SnocVect s (Dim d) -> Term q d n
 dsubN (S _ (Y body)) ps = body // fromSnocVect ps
 dsubN (S _ (N body)) _  = body
 
 export %inline
-dsub1 : DScopeTerm d n -> Dim d -> Term d n
+dsub1 : DScopeTerm q d n -> Dim d -> Term q d n
 dsub1 t p = dsubN t [< p]
 
 
 public export %inline
-(.zero) : (body : DScopeTerm d n) -> {default body.loc loc : Loc} -> Term d n
+(.zero) : (body : DScopeTerm q d n) -> {default body.loc loc : Loc} ->
+          Term q d n
 body.zero = dsub1 body $ K Zero loc
 
 public export %inline
-(.one) : (body : DScopeTerm d n) -> {default body.loc loc : Loc} -> Term d n
+(.one) : (body : DScopeTerm q d n) -> {default body.loc loc : Loc} ->
+         Term q d n
 body.one = dsub1 body $ K One loc
 
 
 public export
 0 CloTest : TermLike -> Type
-CloTest tm = forall d, n. tm d n -> Bool
+CloTest tm = forall q, d, n. tm q d n -> Bool
 
 public export
 interface PushSubsts (0 tm : TermLike) (0 isClo : CloTest tm) | tm where
-  pushSubstsWith : DSubst d1 d2 -> TSubst d2 n1 n2 ->
-                   tm d1 n1 -> Subset (tm d2 n2) (No . isClo)
+  pushSubstsWith : {q1, q2 : Nat} ->
+                   QSubst q1 q2 -> DSubst d1 d2 -> TSubst q2 d2 n1 n2 ->
+                   tm q1 d1 n1 -> Subset (tm q2 d2 n2) (No . isClo)
 
 public export
-0 NotClo : {isClo : CloTest tm} -> PushSubsts tm isClo => Pred (tm d n)
+0 NotClo : {isClo : CloTest tm} -> PushSubsts tm isClo => Pred (tm q d n)
 NotClo = No . isClo
 
 public export
 0 NonClo : (tm : TermLike) -> {isClo : CloTest tm} ->
            PushSubsts tm isClo => TermLike
-NonClo tm d n = Subset (tm d n) NotClo
+NonClo tm q d n = Subset (tm q d n) NotClo
 
 public export %inline
 nclo : {isClo : CloTest tm} -> (0 _ : PushSubsts tm isClo) =>
-       (t : tm d n) -> (0 nc : NotClo t) => NonClo tm d n
+       (t : tm q d n) -> (0 nc : NotClo t) => NonClo tm q d n
 nclo t = Element t nc
 
 parameters {0 isClo : CloTest tm} {auto _ : PushSubsts tm isClo}
   ||| if the input term has any top-level closures, push them under one layer of
   ||| syntax
   export %inline
-  pushSubsts : tm d n -> NonClo tm d n
-  pushSubsts s = pushSubstsWith id id s
+  pushSubsts : {q : Nat} -> tm q d n -> NonClo tm q d n
+  pushSubsts s = pushSubstsWith id id id s
 
   export %inline
-  pushSubstsWith' : DSubst d1 d2 -> TSubst d2 n1 n2 -> tm d1 n1 -> tm d2 n2
-  pushSubstsWith' th ph x = fst $ pushSubstsWith th ph x
+  pushSubstsWith' : {q1, q2 : Nat} ->
+                    QSubst q1 q2 -> DSubst d1 d2 -> TSubst q2 d2 n1 n2 ->
+                    tm q1 d1 n1 -> tm q2 d2 n2
+  pushSubstsWith' th ph ps x = fst $ pushSubstsWith th ph ps x
 
   export %inline
-  pushSubsts' : tm d n -> tm d n
+  pushSubsts' : {q : Nat} -> tm q d n -> tm q d n
   pushSubsts' s = fst $ pushSubsts s
 
 mutual
@@ -276,6 +347,7 @@ mutual
   isCloT : CloTest Term
   isCloT (CloT  {}) = True
   isCloT (DCloT {}) = True
+  isCloT (QCloT {}) = True
   isCloT (E e)      = isCloE e
   isCloT _          = False
 
@@ -283,92 +355,118 @@ mutual
   isCloE : CloTest Elim
   isCloE (CloE  {}) = True
   isCloE (DCloE {}) = True
+  isCloE (QCloE {}) = True
   isCloE _          = False
 
 export
 PushSubsts Elim Subst.isCloE where
-  pushSubstsWith th ph (F x u loc) =
+  pushSubstsWith th ph ps (F x u loc) =
     nclo $ F x u loc
-  pushSubstsWith th ph (B i loc) =
-    let res = get ph i loc in
+  pushSubstsWith th ph ps (B i loc) =
+    let res = get ps i loc in
     case nchoose $ isCloE res of
       Left  yes => assert_total pushSubsts res
       Right no  => Element res no
-  pushSubstsWith th ph (App f s loc) =
-    nclo $ App (f // th // ph) (s // th // ph) loc
-  pushSubstsWith th ph (CasePair pi p r b loc) =
-    nclo $ CasePair pi (p // th // ph) (r // th // ph) (b // th // ph) loc
-  pushSubstsWith th ph (Fst pair loc) =
-    nclo $ Fst (pair // th // ph) loc
-  pushSubstsWith th ph (Snd pair loc) =
-    nclo $ Snd (pair // th // ph) loc
-  pushSubstsWith th ph (CaseEnum pi t r arms loc) =
-    nclo $ CaseEnum pi (t // th // ph) (r // th // ph)
-             (map (\b => b // th // ph) arms) loc
-  pushSubstsWith th ph (CaseNat pi pi' n r z s loc) =
-    nclo $ CaseNat pi pi' (n // th // ph) (r // th // ph)
-             (z // th // ph) (s // th // ph) loc
-  pushSubstsWith th ph (CaseBox pi x r b loc) =
-    nclo $ CaseBox pi (x // th // ph) (r // th // ph) (b // th // ph) loc
-  pushSubstsWith th ph (DApp f d loc) =
-    nclo $ DApp (f // th // ph) (d // th) loc
-  pushSubstsWith th ph (Ann s a loc) =
-    nclo $ Ann (s // th // ph) (a // th // ph) loc
-  pushSubstsWith th ph (Coe ty p q val loc) =
-    nclo $ Coe (ty // th // ph) (p // th) (q // th) (val // th // ph) loc
-  pushSubstsWith th ph (Comp ty p q val r zero one loc) =
-    nclo $ Comp (ty // th // ph) (p // th) (q // th)
-                (val // th // ph) (r // th)
-                (zero // th // ph) (one // th // ph) loc
-  pushSubstsWith th ph (TypeCase ty ret arms def loc) =
-    nclo $ TypeCase (ty // th // ph) (ret  // th // ph)
-      (map (\t => t // th // ph) arms) (def // th // ph) loc
-  pushSubstsWith th ph (CloE (Sub e ps)) =
-    pushSubstsWith th (comp th ps ph) e
-  pushSubstsWith th ph (DCloE (Sub e ps)) =
-    pushSubstsWith (ps . th) ph e
+  pushSubstsWith th ph ps (App f s loc) =
+    nclo $ App (f // th // ph // ps) (s // th // ph // ps) loc
+  pushSubstsWith th ph ps (CasePair pi p r b loc) =
+    nclo $ CasePair (pi //? th)
+        (p // th // ph // ps)
+        (r // th // ph // ps)
+        (b // th // ph // ps) loc
+  pushSubstsWith th ph ps (Fst pair loc) =
+    nclo $ Fst (pair // th // ph // ps) loc
+  pushSubstsWith th ph ps (Snd pair loc) =
+    nclo $ Snd (pair // th // ph // ps) loc
+  pushSubstsWith th ph ps (CaseEnum pi t r arms loc) =
+    nclo $ CaseEnum (pi //? th)
+        (t // th // ph // ps)
+        (r // th // ph // ps)
+        (map (\b => b // th // ph // ps) arms) loc
+  pushSubstsWith th ph ps (CaseNat pi pi' n r z s loc) =
+    nclo $ CaseNat (pi //? th) (pi' //? th)
+        (n // th // ph // ps)
+        (r // th // ph // ps)
+        (z // th // ph // ps)
+        (s // th // ph // ps) loc
+  pushSubstsWith th ph ps (CaseBox pi x r b loc) =
+    nclo $ CaseBox (pi //? th)
+        (x // th // ph // ps)
+        (r // th // ph // ps)
+        (b // th // ph // ps) loc
+  pushSubstsWith th ph ps (DApp f d loc) =
+    nclo $ DApp (f // th // ph // ps) (d // ph) loc
+  pushSubstsWith th ph ps (Ann s a loc) =
+    nclo $ Ann (s // th // ph // ps) (a // th // ph // ps) loc
+  pushSubstsWith th ph ps (Coe ty p q val loc) =
+    nclo $ Coe
+        (ty // th // ph // ps)
+        (p // ph) (q // ph)
+        (val // th // ph // ps) loc
+  pushSubstsWith th ph ps (Comp ty p q val r zero one loc) =
+    nclo $ Comp (ty // th // ph // ps) (p // ph) (q // ph)
+                (val // th // ph // ps) (r // ph)
+                (zero // th // ph // ps) (one // th // ph // ps) loc
+  pushSubstsWith th ph ps (TypeCase ty ret arms def loc) =
+    nclo $ TypeCase (ty // th // ph // ps) (ret // th // ph // ps)
+      (map (\t => t // th // ph // ps) arms) (def // th // ph // ps) loc
+  pushSubstsWith th ph ps (CloE (Sub e ps')) =
+    pushSubstsWith th ph (comp th ph ps' ps) e
+  pushSubstsWith th ph ps (DCloE (Sub e ph')) =
+    pushSubstsWith th (ph' . ph) ps e
+  pushSubstsWith th ph ps (QCloE (SubR e th')) =
+    pushSubstsWith (th' .? th) ph ps e
 
 export
 PushSubsts Term Subst.isCloT where
-  pushSubstsWith th ph (TYPE l loc) =
+  pushSubstsWith th ph ps (TYPE l loc) =
     nclo $ TYPE l loc
-  pushSubstsWith th ph (IOState loc) =
+  pushSubstsWith _ _ _ (IOState loc) =
     nclo $ IOState loc
-  pushSubstsWith th ph (Pi qty a body loc) =
-    nclo $ Pi qty (a // th // ph) (body // th // ph) loc
-  pushSubstsWith th ph (Lam body loc) =
-    nclo $ Lam (body // th // ph) loc
-  pushSubstsWith th ph (Sig a b loc) =
-    nclo $ Sig (a // th // ph) (b // th // ph) loc
-  pushSubstsWith th ph (Pair s t loc) =
-    nclo $ Pair (s // th // ph) (t // th // ph) loc
-  pushSubstsWith th ph (Enum tags loc) =
+  pushSubstsWith th ph ps (Pi qty a body loc) =
+    nclo $ Pi (qty //? th)
+        (a // th // ph // ps)
+        (body // th // ph // ps) loc
+  pushSubstsWith th ph ps (Lam body loc) =
+    nclo $ Lam (body // th // ph // ps) loc
+  pushSubstsWith th ph ps (Sig a b loc) =
+    nclo $ Sig (a // th // ph // ps) (b // th // ph // ps) loc
+  pushSubstsWith th ph ps (Pair s t loc) =
+    nclo $ Pair (s // th // ph // ps) (t // th // ph // ps) loc
+  pushSubstsWith th ph ps (Enum tags loc) =
     nclo $ Enum tags loc
-  pushSubstsWith th ph (Tag tag loc) =
+  pushSubstsWith th ph ps (Tag tag loc) =
     nclo $ Tag tag loc
-  pushSubstsWith th ph (Eq ty l r loc) =
-    nclo $ Eq (ty // th // ph) (l // th // ph) (r // th // ph) loc
-  pushSubstsWith th ph (DLam body loc) =
-    nclo $ DLam (body // th // ph) loc
-  pushSubstsWith _ _ (NAT loc) =
+  pushSubstsWith th ph ps (Eq ty l r loc) =
+    nclo $ Eq
+        (ty // th // ph // ps)
+        (l // th // ph // ps)
+        (r // th // ph // ps) loc
+  pushSubstsWith th ph ps (DLam body loc) =
+    nclo $ DLam (body // th // ph // ps) loc
+  pushSubstsWith _ _ _ (NAT loc) =
     nclo $ NAT loc
-  pushSubstsWith _ _ (Nat n loc) =
+  pushSubstsWith _ _ _ (Nat n loc) =
     nclo $ Nat n loc
-  pushSubstsWith th ph (Succ n loc) =
-    nclo $ Succ (n // th // ph) loc
-  pushSubstsWith _ _ (STRING loc) =
+  pushSubstsWith th ph ps (Succ n loc) =
+    nclo $ Succ (n // th // ph // ps) loc
+  pushSubstsWith _ _ _ (STRING loc) =
     nclo $ STRING loc
-  pushSubstsWith _ _ (Str s loc) =
+  pushSubstsWith _ _ _ (Str s loc) =
     nclo $ Str s loc
-  pushSubstsWith th ph (BOX pi ty loc) =
-    nclo $ BOX pi (ty // th // ph) loc
-  pushSubstsWith th ph (Box val loc) =
-    nclo $ Box (val // th // ph) loc
-  pushSubstsWith th ph (E e) =
-    let Element e nc = pushSubstsWith th ph e in nclo $ E e
-  pushSubstsWith th ph (Let qty rhs body loc) =
-    nclo $ Let qty (rhs // th // ph) (body // th // ph) loc
-  pushSubstsWith th ph (CloT (Sub s ps)) =
-    pushSubstsWith th (comp th ps ph) s
-  pushSubstsWith th ph (DCloT (Sub s ps)) =
-    pushSubstsWith (ps . th) ph s
+  pushSubstsWith th ph ps (BOX pi ty loc) =
+    nclo $ BOX (pi //? th) (ty // th // ph // ps) loc
+  pushSubstsWith th ph ps (Box val loc) =
+    nclo $ Box (val // th // ph // ps) loc
+  pushSubstsWith th ph ps (E e) =
+    let Element e nc = pushSubstsWith th ph ps e in nclo $ E e
+  pushSubstsWith th ph ps (Let qty rhs body loc) =
+    nclo $ Let (qty //? th)
+        (rhs // th // ph // ps)
+        (body // th // ph // ps) loc
+  pushSubstsWith th ph ps (CloT (Sub s ps')) =
+    pushSubstsWith th ph (comp th ph ps' ps) s
+  pushSubstsWith th ph ps (DCloT (Sub s ph')) =
+    pushSubstsWith th (ph' . ph) ps s
+  pushSubstsWith th ph ps (QCloT (SubR s th')) =
+    pushSubstsWith (th' .? th) ph ps s
diff --git a/lib/Quox/Syntax/Term/Tighten.idr b/lib/Quox/Syntax/Term/Tighten.idr
index 0709684..2244666 100644
--- a/lib/Quox/Syntax/Term/Tighten.idr
+++ b/lib/Quox/Syntax/Term/Tighten.idr
@@ -29,20 +29,20 @@ tightenDScope f p (S names (N body)) = S names . N <$> f p body
 
 mutual
   private
-  tightenT : OPE n1 n2 -> Term d n2 -> Maybe (Term d n1)
+  tightenT : {q : Nat} -> OPE n1 n2 -> Term q d n2 -> Maybe (Term q d n1)
   tightenT p s =
     let Element s' _ = pushSubsts s in
     tightenT' p $ assert_smaller s s'
 
   private
-  tightenE : OPE n1 n2 -> Elim d n2 -> Maybe (Elim d n1)
+  tightenE : {q : Nat} -> OPE n1 n2 -> Elim q d n2 -> Maybe (Elim q d n1)
   tightenE p e =
     let Element e' _ = pushSubsts e in
     tightenE' p $ assert_smaller e e'
 
   private
-  tightenT' : OPE n1 n2 -> (t : Term d n2) -> (0 nt : NotClo t) =>
-              Maybe (Term d n1)
+  tightenT' : {q : Nat} -> OPE n1 n2 -> (t : Term q d n2) -> (0 nt : NotClo t) =>
+              Maybe (Term q d n1)
   tightenT' p (TYPE l loc) = pure $ TYPE l loc
   tightenT' p (IOState loc) = pure $ IOState loc
   tightenT' p (Pi qty arg res loc) =
@@ -81,8 +81,9 @@ mutual
     E <$> assert_total tightenE p e
 
   private
-  tightenE' : OPE n1 n2 -> (e : Elim d n2) -> (0 ne : NotClo e) =>
-              Maybe (Elim d n1)
+  tightenE' : {q : Nat} ->
+              OPE n1 n2 -> (e : Elim q d n2) -> (0 ne : NotClo e) =>
+              Maybe (Elim q d n1)
   tightenE' p (F x u loc) =
     pure $ F x u loc
   tightenE' p (B i loc) =
@@ -140,34 +141,35 @@ mutual
              <*> pure loc
 
   export
-  tightenS : {s : Nat} -> OPE m n ->
-             ScopeTermN s f n -> Maybe (ScopeTermN s f m)
+  tightenS : {q, s : Nat} -> OPE m n ->
+             ScopeTermN s q d n -> Maybe (ScopeTermN s q d m)
   tightenS = assert_total $ tightenScope tightenT
 
   export
-  tightenDS : OPE m n -> DScopeTermN s f n -> Maybe (DScopeTermN s f m)
-  tightenDS = assert_total $ tightenDScope tightenT {f = \n, d => Term d n}
+  tightenDS : {q : Nat} ->
+              OPE m n -> DScopeTermN s q d n -> Maybe (DScopeTermN s q d m)
+  tightenDS = assert_total $ tightenDScope tightenT {f = \n, d => Term q d n}
 
-export Tighten (Elim d) where tighten p e = tightenE p e
-export Tighten (Term d) where tighten p t = tightenT p t
+export {q : Nat} -> Tighten (Elim q d) where tighten p e = tightenE p e
+export {q : Nat} -> Tighten (Term q d) where tighten p t = tightenT p t
 
 
 mutual
   export
-  dtightenT : OPE d1 d2 -> Term d2 n -> Maybe (Term d1 n)
+  dtightenT : {q : Nat} -> OPE d1 d2 -> Term q d2 n -> Maybe (Term q d1 n)
   dtightenT p s =
     let Element s' _ = pushSubsts s in
     dtightenT' p $ assert_smaller s s'
 
   export
-  dtightenE : OPE d1 d2 -> Elim d2 n -> Maybe (Elim d1 n)
+  dtightenE : {q : Nat} -> OPE d1 d2 -> Elim q d2 n -> Maybe (Elim q d1 n)
   dtightenE p e =
     let Element e' _ = pushSubsts e in
     dtightenE' p $ assert_smaller e e'
 
   private
-  dtightenT' : OPE d1 d2 -> (t : Term d2 n) -> (0 nt : NotClo t) =>
-               Maybe (Term d1 n)
+  dtightenT' : {q : Nat} -> OPE d1 d2 -> (t : Term q d2 n) -> (0 nt : NotClo t) =>
+               Maybe (Term q d1 n)
   dtightenT' p (TYPE l loc) =
     pure $ TYPE l loc
   dtightenT' p (IOState loc) =
@@ -208,8 +210,8 @@ mutual
     E <$> assert_total dtightenE p e
 
   export
-  dtightenE' : OPE d1 d2 -> (e : Elim d2 n) -> (0 ne : NotClo e) =>
-               Maybe (Elim d1 n)
+  dtightenE' : {q : Nat} -> OPE d1 d2 -> (e : Elim q d2 n) -> (0 ne : NotClo e) =>
+               Maybe (Elim q d1 n)
   dtightenE' p (F x u loc) =
     pure $ F x u loc
   dtightenE' p (B i loc) =
@@ -258,17 +260,18 @@ mutual
                (traverse (dtightenS p) arms) (dtightenT p def) (pure loc)|]
 
   export
-  dtightenS : OPE d1 d2 -> ScopeTermN s d2 n -> Maybe (ScopeTermN s d1 n)
-  dtightenS = assert_total $ tightenDScope dtightenT {f = Term}
+  dtightenS : {q : Nat} -> OPE d1 d2 -> ScopeTermN s q d2 n ->
+              Maybe (ScopeTermN s q d1 n)
+  dtightenS = assert_total $ tightenDScope dtightenT {f = Term q}
 
   export
-  dtightenDS : {s : Nat} -> OPE d1 d2 ->
-               DScopeTermN s d2 n -> Maybe (DScopeTermN s d1 n)
+  dtightenDS : {q, s : Nat} -> OPE d1 d2 ->
+               DScopeTermN s q d2 n -> Maybe (DScopeTermN s q d1 n)
   dtightenDS = assert_total $ tightenScope dtightenT
 
 
-export Tighten (\d => Term d n) where tighten p t = dtightenT p t
-export Tighten (\d => Elim d n) where tighten p e = dtightenE p e
+export {q : Nat} -> Tighten (\d => Term q d n) where tighten p t = dtightenT p t
+export {q : Nat} -> Tighten (\d => Elim q d n) where tighten p e = dtightenE p e
 
 
 parameters {auto _ : Tighten f} {s : Nat}
@@ -300,59 +303,64 @@ ST : Tighten f => {s : Nat} -> BContext s -> f (s + n) -> Scoped s f n
 ST names body = squeeze' $ SY names body
 
 public export %inline
-DST : {s : Nat} -> BContext s -> Term (s + d) n -> DScopeTermN s d n
-DST names body = dsqueeze' {f = Term} $ SY names body
+DST : {s, q : Nat} -> BContext s -> Term q (s + d) n -> DScopeTermN s q d n
+DST names body = dsqueeze' {f = Term q} $ SY names body
 
 public export %inline
-PiT : (qty : Qty) -> (x : BindName) ->
-      (arg : Term d n) -> (res : Term d (S n)) -> (loc : Loc) -> Term d n
+PiT : {q : Nat} -> (qty : Qty q) -> (x : BindName) ->
+      (arg : Term q d n) -> (res : Term q d (S n)) -> (loc : Loc) -> Term q d n
 PiT {qty, x, arg, res, loc} = Pi {qty, arg, res = ST [< x] res, loc}
 
 public export %inline
-LamT : (x : BindName) -> (body : Term d (S n)) -> (loc : Loc) -> Term d n
+LamT : {q : Nat} ->
+       (x : BindName) -> (body : Term q d (S n)) -> (loc : Loc) -> Term q d n
 LamT {x, body, loc} = Lam {body = ST [< x] body, loc}
 
 public export %inline
-SigT : (x : BindName) -> (fst : Term d n) ->
-       (snd : Term d (S n)) -> (loc : Loc) -> Term d n
+SigT : {q : Nat} -> (x : BindName) -> (fst : Term q d n) ->
+       (snd : Term q d (S n)) -> (loc : Loc) -> Term q d n
 SigT {x, fst, snd, loc} = Sig {fst, snd = ST [< x] snd, loc}
 
 public export %inline
-EqT : (i : BindName) -> (ty : Term (S d) n) ->
-      (l, r : Term d n) -> (loc : Loc) -> Term d n
+EqT : {q : Nat} -> (i : BindName) -> (ty : Term q (S d) n) ->
+      (l, r : Term q d n) -> (loc : Loc) -> Term q d n
 EqT {i, ty, l, r, loc} = Eq {ty = DST [< i] ty, l, r, loc}
 
 public export %inline
-DLamT : (i : BindName) -> (body : Term (S d) n) -> (loc : Loc) -> Term d n
+DLamT : {q : Nat} ->
+        (i : BindName) -> (body : Term q (S d) n) -> (loc : Loc) -> Term q d n
 DLamT {i, body, loc} = DLam {body = DST [< i] body, loc}
 
 public export %inline
-CoeT : (i : BindName) -> (ty : Term (S d) n) ->
-       (p, q : Dim d) -> (val : Term d n) -> (loc : Loc) -> Elim d n
-CoeT {i, ty, p, q, val, loc} = Coe {ty = DST [< i] ty, p, q, val, loc}
+CoeT : {q : Nat} -> (i : BindName) -> (ty : Term q (S d) n) ->
+       (p, p' : Dim d) -> (val : Term q d n) -> (loc : Loc) -> Elim q d n
+CoeT {i, ty, p, p', val, loc} = Coe {ty = DST [< i] ty, p, p', val, loc}
 
 public export %inline
-typeCase1T : Elim d n -> Term d n ->
-             (k : TyConKind) -> BContext (arity k) -> Term d (arity k + n) ->
+typeCase1T : {q : Nat} ->
+             Elim q d n -> Term q d n ->
+             (k : TyConKind) -> BContext (arity k) -> Term q d (arity k + n) ->
              (loc : Loc) ->
-             {default (NAT loc) def : Term d n} ->
-             Elim d n
+             {default (NAT loc) def : Term q d n} ->
+             Elim q d n
 typeCase1T ty ret k ns body loc {def} =
   typeCase ty ret [(k ** ST ns body)] def loc
 
 
 public export %inline
-CompH' : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
-         (r : Dim d) -> (zero, one : DScopeTerm d n) -> (loc : Loc) -> Elim d n
-CompH' {ty, p, q, val, r, zero, one, loc} =
+CompH' : {q : Nat} ->
+         (ty : DScopeTerm q d n) -> (p, p' : Dim d) -> (val : Term q d n) ->
+         (r : Dim d) -> (zero, one : DScopeTerm q d n) -> (loc : Loc) ->
+         Elim q d n
+CompH' {ty, p, p', val, r, zero, one, loc} =
   let ty' = DST ty.names $ ty.term // (B VZ ty.name.loc ::: shift 2) in
   Comp {
-    ty = dsub1 ty q, p, q,
-    val = E $ Coe ty p q val val.loc, r,
+    ty = dsub1 ty p', p, p',
+    val = E $ Coe ty p p' val val.loc, r,
     zero = DST zero.names $ E $
-      Coe ty' (B VZ zero.loc) (weakD 1 q) zero.term zero.loc,
+      Coe ty' (B VZ zero.loc) (weakD 1 p') zero.term zero.loc,
     one = DST one.names $ E $
-      Coe ty' (B VZ one.loc) (weakD 1 q) one.term one.loc,
+      Coe ty' (B VZ one.loc) (weakD 1 p') one.term one.loc,
     loc
   }
 
@@ -365,12 +373,12 @@ CompH' {ty, p, q, val, r, zero, one, loc} =
 |||   1 j ⇒ coe [i ⇒ A] @j @q t₁
 ||| }
 public export %inline
-CompH : (i : BindName) -> (ty : Term (S d) n) ->
-        (p, q : Dim d) -> (val : Term d n) -> (r : Dim d) ->
-        (j0 : BindName) -> (zero : Term (S d) n) ->
-        (j1 : BindName) -> (one : Term (S d) n) ->
+CompH : {q : Nat} -> (i : BindName) -> (ty : Term q (S d) n) ->
+        (p, p' : Dim d) -> (val : Term q d n) -> (r : Dim d) ->
+        (j0 : BindName) -> (zero : Term q (S d) n) ->
+        (j1 : BindName) -> (one : Term q (S d) n) ->
         (loc : Loc) ->
-        Elim d n
-CompH {i, ty, p, q, val, r, j0, zero, j1, one, loc} =
-  CompH' {ty = DST [< i] ty, p, q, val, r,
+        Elim q d n
+CompH {i, ty, p, p', val, r, j0, zero, j1, one, loc} =
+  CompH' {ty = DST [< i] ty, p, p', val, r,
           zero = DST [< j0] zero, one = DST [< j1] one, loc}
diff --git a/lib/Quox/Typing.idr b/lib/Quox/Typing.idr
index 2ebed73..8885245 100644
--- a/lib/Quox/Typing.idr
+++ b/lib/Quox/Typing.idr
@@ -21,22 +21,22 @@ TTName = TT.Name
 
 
 public export
-CheckResult' : Nat -> Type
+CheckResult' : Nat -> Nat -> Type
 CheckResult' = QOutput
 
 public export
-CheckResult : DimEq d -> Nat -> Type
-CheckResult eqs n = IfConsistent eqs $ CheckResult' n
+CheckResult : DimEq d -> Nat -> Nat -> Type
+CheckResult eqs q n = IfConsistent eqs $ CheckResult' q n
 
 public export
-record InferResult' d n where
+record InferResult' q d n where
   constructor InfRes
-  type : Term d n
-  qout : QOutput n
+  type : Term q d n
+  qout : QOutput q n
 
 public export
 InferResult : DimEq d -> TermLike
-InferResult eqs d n = IfConsistent eqs $ InferResult' d n
+InferResult eqs q d n = IfConsistent eqs $ InferResult' q d n
 
 
 export
@@ -45,21 +45,22 @@ lookupFree x loc defs = maybe (throw $ NotInScope loc x) pure $ lookup x defs
 
 
 public export
-substCasePairRet : BContext 2 -> Term d n -> ScopeTerm d n -> Term d (2 + n)
+substCasePairRet : BContext 2 -> Term q d n -> ScopeTerm q d n ->
+                   Term q d (2 + n)
 substCasePairRet [< x, y] dty retty =
   let tm  = Pair (BVT 1 x.loc) (BVT 0 y.loc) $ x.loc `extendL` y.loc
       arg = Ann tm (dty // fromNat 2) tm.loc in
   retty.term // (arg ::: shift 2)
 
 public export
-substCaseSuccRet : BContext 2 -> ScopeTerm d n -> Term d (2 + n)
+substCaseSuccRet : BContext 2 -> ScopeTerm q d n -> Term q d (2 + n)
 substCaseSuccRet [< p, ih] retty =
   let loc = p.loc `extendL` ih.loc
       arg = Ann (Succ (BVT 1 p.loc) p.loc) (NAT p.loc) loc in
   retty.term // (arg ::: shift 2)
 
 public export
-substCaseBoxRet : BindName -> Term d n -> ScopeTerm d n -> Term d (S n)
+substCaseBoxRet : BindName -> Term q d n -> ScopeTerm q d n -> Term q d (S n)
 substCaseBoxRet x dty retty =
   let arg = Ann (Box (BVT 0 x.loc) x.loc) (weakT 1 dty) x.loc in
   retty.term // (arg ::: shift 1)
@@ -68,15 +69,15 @@ substCaseBoxRet x dty retty =
 private
 0 ExpectErrorConstructor : Type
 ExpectErrorConstructor =
-  forall d, n. Loc -> NameContexts d n -> Term d n -> Error
+  forall q, d, n. Loc -> NameContexts q d n -> Term q d n -> Error
 
 parameters (defs : Definitions)
            {auto _ : (Has ErrorEff fs, Has NameGen fs, Has Log fs)}
   namespace TyContext
-   parameters (ctx : TyContext d n) (sg : SQty) (loc : Loc)
+   parameters (ctx : TyContext q d n) (sg : SQty) (loc : Loc)
     export covering
     whnf : {0 isRedex : RedexTest tm} -> CanWhnf tm isRedex =>
-           tm d n -> Eff fs (NonRedex tm d n defs (toWhnfContext ctx) sg)
+           tm q d n -> Eff fs (NonRedex tm q d n defs (toWhnfContext ctx) sg)
     whnf tm = do
       let Val n = ctx.termLen; Val d = ctx.dimLen
       res <- lift $ runExcept $ whnf defs (toWhnfContext ctx) sg tm
@@ -84,7 +85,7 @@ parameters (defs : Definitions)
 
     private covering %macro
     expect : ExpectErrorConstructor -> TTImp -> TTImp ->
-             Elab (Term d n -> Eff fs a)
+             Elab (Term q d n -> Eff fs a)
     expect err pat rhs = Prelude.do
       match <- check `(\case ~(pat) => Just ~(rhs); _ => Nothing)
       pure $ \term => do
@@ -92,54 +93,54 @@ parameters (defs : Definitions)
         maybe (throw $ err loc ctx.names term) pure $ match $ fst res
 
     export covering %inline
-    expectTYPE : Term d n -> Eff fs Universe
+    expectTYPE : Term q d n -> Eff fs Universe
     expectTYPE = expect ExpectedTYPE `(TYPE {l, _}) `(l)
 
     export covering %inline
-    expectPi : Term d n -> Eff fs (Qty, Term d n, ScopeTerm d n)
+    expectPi : Term q d n -> Eff fs (Qty q, Term q d n, ScopeTerm q d n)
     expectPi = expect ExpectedPi `(Pi {qty, arg, res, _}) `((qty, arg, res))
 
     export covering %inline
-    expectSig : Term d n -> Eff fs (Term d n, ScopeTerm d n)
+    expectSig : Term q d n -> Eff fs (Term q d n, ScopeTerm q d n)
     expectSig = expect ExpectedSig `(Sig {fst, snd, _}) `((fst, snd))
 
     export covering %inline
-    expectEnum : Term d n -> Eff fs (SortedSet TagVal)
+    expectEnum : Term q d n -> Eff fs (SortedSet TagVal)
     expectEnum = expect ExpectedEnum `(Enum {cases, _}) `(cases)
 
     export covering %inline
-    expectEq : Term d n -> Eff fs (DScopeTerm d n, Term d n, Term d n)
+    expectEq : Term q d n -> Eff fs (DScopeTerm q d n, Term q d n, Term q d n)
     expectEq = expect ExpectedEq `(Eq {ty, l, r, _}) `((ty, l, r))
 
     export covering %inline
-    expectNAT : Term d n -> Eff fs ()
+    expectNAT : Term q d n -> Eff fs ()
     expectNAT = expect ExpectedNAT `(NAT {}) `(())
 
     export covering %inline
-    expectSTRING : Term d n -> Eff fs ()
+    expectSTRING : Term q d n -> Eff fs ()
     expectSTRING = expect ExpectedSTRING `(STRING {}) `(())
 
     export covering %inline
-    expectBOX : Term d n -> Eff fs (Qty, Term d n)
+    expectBOX : Term q d n -> Eff fs (Qty q, Term q d n)
     expectBOX = expect ExpectedBOX `(BOX {qty, ty, _}) `((qty, ty))
 
     export covering %inline
-    expectIOState : Term d n -> Eff fs ()
+    expectIOState : Term q d n -> Eff fs ()
     expectIOState = expect ExpectedIOState `(IOState {}) `(())
 
 
   namespace EqContext
-   parameters (ctx : EqContext n) (sg : SQty) (loc : Loc)
+   parameters (ctx : EqContext q n) (sg : SQty) (loc : Loc)
     export covering
     whnf : {0 isRedex : RedexTest tm} -> CanWhnf tm isRedex =>
-           tm 0 n -> Eff fs (NonRedex tm 0 n defs (toWhnfContext ctx) sg)
+           tm q 0 n -> Eff fs (NonRedex tm q 0 n defs (toWhnfContext ctx) sg)
     whnf tm = do
       res <- lift $ runExcept $ whnf defs (toWhnfContext ctx) sg tm
       rethrow res
 
     private covering %macro
     expect : ExpectErrorConstructor -> TTImp -> TTImp ->
-             Elab (Term 0 n -> Eff fs a)
+             Elab (Term q 0 n -> Eff fs a)
     expect err pat rhs = do
       match <- check `(\case ~(pat) => Just ~(rhs); _ => Nothing)
       pure $ \term => do
@@ -148,37 +149,37 @@ parameters (defs : Definitions)
         maybe (throw $ err loc ctx.names t0) pure $ match $ fst res
 
     export covering %inline
-    expectTYPE : Term 0 n -> Eff fs Universe
+    expectTYPE : Term q 0 n -> Eff fs Universe
     expectTYPE = expect ExpectedTYPE `(TYPE {l, _}) `(l)
 
     export covering %inline
-    expectPi : Term 0 n -> Eff fs (Qty, Term 0 n, ScopeTerm 0 n)
+    expectPi : Term q 0 n -> Eff fs (Qty q, Term q 0 n, ScopeTerm q 0 n)
     expectPi = expect ExpectedPi `(Pi {qty, arg, res, _}) `((qty, arg, res))
 
     export covering %inline
-    expectSig : Term 0 n -> Eff fs (Term 0 n, ScopeTerm 0 n)
+    expectSig : Term q 0 n -> Eff fs (Term q 0 n, ScopeTerm q 0 n)
     expectSig = expect ExpectedSig `(Sig {fst, snd, _}) `((fst, snd))
 
     export covering %inline
-    expectEnum : Term 0 n -> Eff fs (SortedSet TagVal)
+    expectEnum : Term q 0 n -> Eff fs (SortedSet TagVal)
     expectEnum = expect ExpectedEnum `(Enum {cases, _}) `(cases)
 
     export covering %inline
-    expectEq : Term 0 n -> Eff fs (DScopeTerm 0 n, Term 0 n, Term 0 n)
+    expectEq : Term q 0 n -> Eff fs (DScopeTerm q 0 n, Term q 0 n, Term q 0 n)
     expectEq = expect ExpectedEq `(Eq {ty, l, r, _}) `((ty, l, r))
 
     export covering %inline
-    expectNAT : Term 0 n -> Eff fs ()
+    expectNAT : Term q 0 n -> Eff fs ()
     expectNAT = expect ExpectedNAT `(NAT {}) `(())
 
     export covering %inline
-    expectSTRING : Term 0 n -> Eff fs ()
+    expectSTRING : Term q 0 n -> Eff fs ()
     expectSTRING = expect ExpectedSTRING `(STRING {}) `(())
 
     export covering %inline
-    expectBOX : Term 0 n -> Eff fs (Qty, Term 0 n)
+    expectBOX : Term q 0 n -> Eff fs (Qty q, Term q 0 n)
     expectBOX = expect ExpectedBOX `(BOX {qty, ty, _}) `((qty, ty))
 
     export covering %inline
-    expectIOState : Term 0 n -> Eff fs ()
+    expectIOState : Term q 0 n -> Eff fs ()
     expectIOState = expect ExpectedIOState `(IOState {}) `(())
diff --git a/lib/Quox/Typing/Context.idr b/lib/Quox/Typing/Context.idr
index d231694..11c51c6 100644
--- a/lib/Quox/Typing/Context.idr
+++ b/lib/Quox/Typing/Context.idr
@@ -3,7 +3,7 @@ module Quox.Typing.Context
 import Quox.Syntax
 import Quox.Context
 import Quox.Pretty
-import public Data.Singleton
+import public Quox.SingletonExtra
 import Derive.Prelude
 
 %default total
@@ -11,48 +11,60 @@ import Derive.Prelude
 
 
 public export
-QContext : Nat -> Type
-QContext = Context' Qty
+QContext : (q, n : Nat) -> Type
+QContext q n = Context' (Qty q) n
 
 public export
-record LocalVar d n where
+record LocalVar q d n where
   constructor MkLocal
-  type : Term d n
-  term : Maybe (Term d n) -- if from a `let`
-%runElab deriveIndexed "LocalVar" [Show]
+  type : Term q d n
+  term : Maybe (Term q d n) -- if from a `let`
+-- %runElab deriveIndexed "LocalVar" [Show]
+
+export
+[LocateVarType] Located (LocalVar q d n) where x.loc = x.type.loc
 
 namespace LocalVar
   export %inline
-  letVar : (type, term : Term d n) -> LocalVar d n
+  letVar : (type, term : Term q d n) -> LocalVar q d n
   letVar type term = MkLocal {type, term = Just term}
 
   export %inline
-  lamVar : (type : Term d n) -> LocalVar d n
+  lamVar : (type : Term q d n) -> LocalVar q d n
   lamVar type = MkLocal {type, term = Nothing}
 
   export %inline
-  mapVar : (Term d n -> Term d' n') -> LocalVar d n -> LocalVar d' n'
+  mapVar : (Term q d n -> Term q' d' n') -> LocalVar q d n -> LocalVar q' d' n'
   mapVar f = {type $= f, term $= map f}
 
   export %inline
-  subD : DSubst d1 d2 -> LocalVar d1 n -> LocalVar d2 n
+  subQ : {q1, q2 : Nat} -> QSubst q1 q2 -> LocalVar q1 d n -> LocalVar q2 d n
+  subQ th = mapVar (// th)
+
+  export %inline
+  weakQ : {q : Nat} -> LocalVar q d n -> LocalVar (S q) d n
+  weakQ = subQ $ shift 1
+
+  export %inline
+  subD : DSubst d1 d2 -> LocalVar q d1 n -> LocalVar q d2 n
   subD th = mapVar (// th)
 
   export %inline
-  weakD : LocalVar d n -> LocalVar (S d) n
+  weakD : LocalVar q d n -> LocalVar q (S d) n
   weakD = subD $ shift 1
 
-export %inline CanShift  (LocalVar d) where l // by = mapVar (// by) l
-export %inline CanDSubst LocalVar     where l // by = mapVar (// by) l
-export %inline CanTSubst LocalVar     where l // by = mapVar (// by) l
+export %inline CanShift  (LocalVar q d) where l // by = mapVar (// by) l
+export %inline CanQSubst LocalVar       where l // th = mapVar (// th) l
+export %inline CanDSubst LocalVar       where l // th = mapVar (// th) l
+export %inline CanTSubst LocalVar       where l // th = mapVar (// th) l
 
 public export
 TContext : TermLike
-TContext d = Context (LocalVar d)
+TContext q d = Context (LocalVar q d)
 
 public export
-QOutput : Nat -> Type
-QOutput = Context' Qty
+QOutput : (q, n : Nat) -> Type
+QOutput = QContext
 
 public export
 DimAssign : Nat -> Type
@@ -60,48 +72,54 @@ DimAssign = Context' DimConst
 
 
 public export
-record TyContext d n where
+record TyContext q d n where
   constructor MkTyContext
+  {auto qtyLen  : Singleton q}
   {auto dimLen  : Singleton d}
   {auto termLen : Singleton n}
+  qnames : BContext q -- only used for printing
   dctx   : DimEq d
   dnames : BContext d -- only used for printing
-  tctx   : TContext d n
+  tctx   : TContext q d n
   tnames : BContext n -- only used for printing
-  qtys   : QContext n -- only used for printing
+  qtys   : QContext q n -- only used for printing
 %name TyContext ctx
-%runElab deriveIndexed "TyContext" [Show]
+-- %runElab deriveIndexed "TyContext" [Show]
 
 
 public export
-record EqContext n where
+record EqContext q n where
   constructor MkEqContext
+  {auto qtyLen : Singleton q}
   {dimLen : Nat}
   {auto termLen : Singleton n}
+  qnames  : BContext q -- only used for printing
   dassign : DimAssign dimLen -- only used for printing
   dnames  : BContext dimLen -- only used for printing
-  tctx    : TContext 0 n
+  tctx    : TContext q 0 n
   tnames  : BContext n -- only used for printing
-  qtys    : QContext n -- only used for printing
+  qtys    : QContext q n -- only used for printing
 %name EqContext ctx
-%runElab deriveIndexed "EqContext" [Show]
+-- %runElab deriveIndexed "EqContext" [Show]
 
 
 public export
-record WhnfContext d n where
+record WhnfContext q d n where
   constructor MkWhnfContext
+  {auto qtyLen  : Singleton q}
   {auto dimLen  : Singleton d}
   {auto termLen : Singleton n}
+  qnames : BContext q -- only used for printing
   dnames : BContext d
   tnames : BContext n
-  tctx   : TContext d n
+  tctx   : TContext q d n
 %name WhnfContext ctx
-%runElab deriveIndexed "WhnfContext" [Show]
+-- %runElab deriveIndexed "WhnfContext" [Show]
 
 namespace TContext
   export %inline
-  zeroFor : Context tm n -> QOutput n
-  zeroFor ctx = Zero <$ ctx
+  zeroFor : {q : Nat} -> Located1 tm => Context tm n -> QOutput q n
+  zeroFor = map $ \x => zero x.loc
 
 public export
 extendLen : Telescope a n1 n2 -> Singleton n1 -> Singleton n2
@@ -110,38 +128,40 @@ extendLen (tel :< _) x = [|S $ extendLen tel x|]
 
 
 public export
-CtxExtension : Nat -> Nat -> Nat -> Type
-CtxExtension d = Telescope ((Qty, BindName,) . Term d)
+CtxExtension : (q, d, n1, n2 : Nat) -> Type
+CtxExtension q d = Telescope $ \n => (Qty q, BindName, Term q d n)
 
 public export
-CtxExtension0 : Nat -> Nat -> Nat -> Type
-CtxExtension0 d = Telescope ((BindName,) . Term d)
+CtxExtension0 : (q, d, n1, n2 : Nat) -> Type
+CtxExtension0 q d = Telescope $ \n => (BindName, Term q d n)
 
 public export
-CtxExtensionLet : Nat -> Nat -> Nat -> Type
-CtxExtensionLet d = Telescope ((Qty, BindName,) . LocalVar d)
+CtxExtensionLet : (q, d, n1, n2 : Nat) -> Type
+CtxExtensionLet q d = Telescope $ \n => (Qty q, BindName, LocalVar q d n)
 
 public export
-CtxExtensionLet0 : Nat -> Nat -> Nat -> Type
-CtxExtensionLet0 d = Telescope ((BindName,) . LocalVar d)
+CtxExtensionLet0 : (q, d, n1, n2 : Nat) -> Type
+CtxExtensionLet0 q d = Telescope $ \n => (BindName, LocalVar q d n)
 
 namespace TyContext
   public export %inline
-  empty : TyContext 0 0
+  empty : TyContext 0 0 0
   empty = MkTyContext {
-    dctx = new, dnames = [<], tctx = [<], tnames = [<], qtys = [<]
+    qnames = [<], dctx = new, dnames = [<], tctx = [<], tnames = [<], qtys = [<]
   }
 
   public export %inline
-  null : TyContext d n -> Bool
-  null ctx = null ctx.dnames && null ctx.tnames
+  null : TyContext q d n -> Bool
+  null ctx = null ctx.qnames && null ctx.dnames && null ctx.tnames
 
   export %inline
-  extendTyLetN : CtxExtensionLet d n1 n2 -> TyContext d n1 -> TyContext d n2
-  extendTyLetN xss (MkTyContext {termLen, dctx, dnames, tctx, tnames, qtys}) =
+  extendTyLetN : CtxExtensionLet q d n1 n2 ->
+                 TyContext q d n1 -> TyContext q d n2
+  extendTyLetN xss
+      (MkTyContext {termLen, qnames, dctx, dnames, tctx, tnames, qtys}) =
     let (qs, xs, ls) = unzip3 xss in
     MkTyContext {
-      dctx, dnames,
+      qnames, dctx, dnames,
       termLen = extendLen xss termLen,
       tctx    = tctx . ls,
       tnames  = tnames . xs,
@@ -149,63 +169,78 @@ namespace TyContext
     }
 
   export %inline
-  extendTyN : CtxExtension d n1 n2 -> TyContext d n1 -> TyContext d n2
+  extendTyN : CtxExtension q d n1 n2 -> TyContext q d n1 -> TyContext q d n2
   extendTyN = extendTyLetN . map (\(q, x, s) => (q, x, lamVar s))
 
   export %inline
-  extendTyLetN0 : CtxExtensionLet0 d n1 n2 -> TyContext d n1 -> TyContext d n2
-  extendTyLetN0 xss = extendTyLetN (map (Zero,) xss)
+  extendTyLetN0 : CtxExtensionLet0 q d n1 n2 ->
+                  TyContext q d n1 -> TyContext q d n2
+  extendTyLetN0 xss ctx =
+    let Val q = ctx.qtyLen in
+    extendTyLetN (map (\(x, t) => (zero x.loc, x, t)) xss) ctx
 
   export %inline
-  extendTyN0 : CtxExtension0 d n1 n2 -> TyContext d n1 -> TyContext d n2
-  extendTyN0 xss = extendTyN (map (Zero,) xss)
+  extendTyN0 : CtxExtension0 q d n1 n2 ->
+               TyContext q d n1 -> TyContext q d n2
+  extendTyN0 xss ctx =
+    let Val q = ctx.qtyLen in
+    extendTyN (map (\(x, t) => (zero x.loc, x, t)) xss) ctx
 
   export %inline
-  extendTyLet : Qty -> BindName -> Term d n -> Term d n ->
-                TyContext d n -> TyContext d (S n)
+  extendTyLet : Qty q -> BindName -> Term q d n -> Term q d n ->
+                TyContext q d n -> TyContext q d (S n)
   extendTyLet q x s e = extendTyLetN [< (q, x, letVar s e)]
 
   export %inline
-  extendTy : Qty -> BindName -> Term d n -> TyContext d n -> TyContext d (S n)
+  extendTy : Qty q -> BindName -> Term q d n ->
+             TyContext q d n -> TyContext q d (S n)
   extendTy q x s = extendTyN [< (q, x, s)]
 
   export %inline
-  extendTy0 : BindName -> Term d n -> TyContext d n -> TyContext d (S n)
-  extendTy0 = extendTy Zero
+  extendTy0 : BindName -> Term q d n ->
+              TyContext q d n -> TyContext q d (S n)
+  extendTy0 x t ctx = let Val q = ctx.qtyLen in extendTy (zero x.loc) x t ctx
 
   export %inline
-  extendDim : BindName -> TyContext d n -> TyContext (S d) n
-  extendDim x (MkTyContext {dimLen, dctx, dnames, tctx, tnames, qtys}) =
+  extendDim : BindName -> TyContext q d n -> TyContext q (S d) n
+  extendDim x (MkTyContext {dimLen, dctx, dnames, qnames, tctx, tnames, qtys}) =
     MkTyContext {
       dctx   = dctx :<? Nothing,
       dnames = dnames :< x,
       dimLen = [|S dimLen|],
       tctx   = map weakD tctx,
-      tnames, qtys
+      qnames, tnames, qtys
     }
 
   export %inline
-  eqDim : Dim d -> Dim d -> TyContext d n -> TyContext d n
-  eqDim p q = {dctx $= set p q, dimLen $= id, termLen $= id}
+  eqDim : Dim d -> Dim d -> TyContext q d n -> TyContext q d n
+  eqDim p q = {dctx $= set p q}
 
   export
-  toWhnfContext : TyContext d n -> WhnfContext d n
-  toWhnfContext (MkTyContext {dnames, tnames, tctx, _}) =
-    MkWhnfContext {dnames, tnames, tctx}
+  toWhnfContext : TyContext q d n -> WhnfContext q d n
+  toWhnfContext (MkTyContext {qnames, dnames, tnames, tctx, _}) =
+    MkWhnfContext {qnames, dnames, tnames, tctx}
+
+  public export
+  (.names) : TyContext q d n -> NameContexts q d n
+  (MkTyContext {qnames, dnames, tnames, _}).names =
+    MkNameContexts {qnames, dnames, tnames}
 
 
 namespace QOutput
   export %inline
-  (+) : QOutput n -> QOutput n -> QOutput n
+  (+) : QOutput q n -> QOutput q n -> QOutput q n
   (+) = zipWith (+)
 
   export %inline
-  (*) : Qty -> QOutput n -> QOutput n
+  (*) : Qty q -> QOutput q n -> QOutput q n
   (*) pi = map (pi *)
 
   export %inline
-  zeroFor : TyContext _ n -> QOutput n
-  zeroFor ctx = zeroFor ctx.tctx
+  zeroFor : TyContext q _ n -> QOutput q n
+  zeroFor ctx =
+    let Val q = ctx.qtyLen in
+    zeroFor ctx.tctx @{LocateVarType}
 
 
 export
@@ -214,8 +249,10 @@ makeDAssign (Shift SZ)     = [<]
 makeDAssign (K e _ ::: th) = makeDAssign th :< e
 
 export
-makeEqContext' : {d : Nat} -> TyContext d n -> DSubst d 0 -> EqContext n
+makeEqContext' : {d : Nat} -> TyContext q d n -> DSubst d 0 -> EqContext q n
 makeEqContext' ctx th = MkEqContext {
+  qtyLen  = ctx.qtyLen,
+  qnames  = ctx.qnames,
   termLen = ctx.termLen,
   dassign = makeDAssign th,
   dnames  = ctx.dnames,
@@ -225,134 +262,160 @@ makeEqContext' ctx th = MkEqContext {
 }
 
 export
-makeEqContext : TyContext d n -> DSubst d 0 -> EqContext n
+makeEqContext : TyContext q d n -> DSubst d 0 -> EqContext q n
 makeEqContext ctx@(MkTyContext {dnames, _}) th =
   let Val d = lengthPrf0 dnames in makeEqContext' ctx th
 
 namespace EqContext
   public export %inline
-  empty : EqContext 0
+  empty : EqContext 0 0
   empty = MkEqContext {
-    dassign = [<], dnames = [<], tctx = [<], tnames = [<], qtys = [<]
+    qnames = [<], dassign = [<], dnames = [<],
+    tctx = [<], tnames = [<], qtys = [<]
   }
 
   public export %inline
-  null : EqContext n -> Bool
-  null ctx = null ctx.dnames && null ctx.tnames
+  null : EqContext q n -> Bool
+  null ctx = null ctx.qnames && null ctx.dnames && null ctx.tnames
 
   export %inline
-  extendTyLetN : CtxExtensionLet 0 n1 n2 -> EqContext n1 -> EqContext n2
-  extendTyLetN xss (MkEqContext {termLen, dassign, dnames, tctx, tnames, qtys}) =
+  extendTyLetN : CtxExtensionLet q 0 n1 n2 -> EqContext q n1 -> EqContext q n2
+  extendTyLetN xss
+      (MkEqContext {termLen, qnames, dassign, dnames, tctx, tnames, qtys}) =
     let (qs, xs, ls) = unzip3 xss in
     MkEqContext {
       termLen = extendLen xss termLen,
       tctx    = tctx . ls,
       tnames  = tnames . xs,
       qtys    = qtys . qs,
-      dassign, dnames
+      dassign, dnames, qnames
     }
 
   export %inline
-  extendTyN : CtxExtension 0 n1 n2 -> EqContext n1 -> EqContext n2
+  extendTyN : CtxExtension q 0 n1 n2 -> EqContext q n1 -> EqContext q n2
   extendTyN = extendTyLetN . map (\(q, x, s) => (q, x, lamVar s))
 
   export %inline
-  extendTyLetN0 : CtxExtensionLet0 0 n1 n2 -> EqContext n1 -> EqContext n2
-  extendTyLetN0 xss = extendTyLetN (map (Zero,) xss)
+  extendTyLetN0 : CtxExtensionLet0 q 0 n1 n2 -> EqContext q n1 -> EqContext q n2
+  extendTyLetN0 xss ctx =
+    let Val q = ctx.qtyLen in
+    extendTyLetN (map (\(x, t) => (zero x.loc, x, t)) xss) ctx
 
   export %inline
-  extendTyN0 : CtxExtension0 0 n1 n2 -> EqContext n1 -> EqContext n2
-  extendTyN0 xss = extendTyN (map (Zero,) xss)
+  extendTyN0 : CtxExtension0 q 0 n1 n2 -> EqContext q n1 -> EqContext q n2
+  extendTyN0 xss ctx =
+    let Val q = ctx.qtyLen in
+    extendTyN (map (\(x, t) => (zero x.loc, x, t)) xss) ctx
 
   export %inline
-  extendTyLet : Qty -> BindName -> Term 0 n -> Term 0 n ->
-                EqContext n -> EqContext (S n)
+  extendTyLet : Qty q -> BindName -> Term q 0 n -> Term q 0 n ->
+                EqContext q n -> EqContext q (S n)
   extendTyLet q x s e = extendTyLetN [< (q, x, letVar s e)]
 
   export %inline
-  extendTy : Qty -> BindName -> Term 0 n -> EqContext n -> EqContext (S n)
+  extendTy : Qty q -> BindName -> Term q 0 n ->
+             EqContext q n -> EqContext q (S n)
   extendTy q x s = extendTyN [< (q, x, s)]
 
   export %inline
-  extendTy0 : BindName -> Term 0 n -> EqContext n -> EqContext (S n)
-  extendTy0 = extendTy Zero
+  extendTy0 : BindName -> Term q 0 n -> EqContext q n -> EqContext q (S n)
+  extendTy0 x t ctx = let Val q = ctx.qtyLen in extendTy (zero x.loc) x t ctx
 
   export %inline
-  extendDim : BindName -> DimConst -> EqContext n -> EqContext n
-  extendDim x e (MkEqContext {dassign, dnames, tctx, tnames, qtys}) =
+  extendDim : BindName -> DimConst -> EqContext q n -> EqContext q n
+  extendDim x e (MkEqContext {dassign, dnames, qnames, tctx, tnames, qtys}) =
     MkEqContext {dassign = dassign :< e, dnames = dnames :< x,
-                 tctx, tnames, qtys}
+                 qnames, tctx, tnames, qtys}
 
   export
-  toTyContext : (e : EqContext n) -> TyContext e.dimLen n
-  toTyContext (MkEqContext {dimLen, dassign, dnames, tctx, tnames, qtys}) =
+  toTyContext : (e : EqContext q n) -> TyContext q e.dimLen n
+  toTyContext
+      (MkEqContext {dimLen, dassign, dnames, qnames, tctx, tnames, qtys}) =
     MkTyContext {
       dctx = fromGround dnames dassign,
       tctx = map (subD $ shift0 dimLen) tctx,
-      dnames, tnames, qtys
+      dnames, qnames, tnames, qtys
     }
 
   export
-  toWhnfContext : (ectx : EqContext n) -> WhnfContext 0 n
-  toWhnfContext (MkEqContext {tnames, tctx, _}) =
-    MkWhnfContext {dnames = [<], tnames, tctx}
+  toWhnfContext : (ectx : EqContext q n) -> WhnfContext q 0 n
+  toWhnfContext (MkEqContext {qnames, tnames, tctx, _}) =
+    MkWhnfContext {dnames = [<], qnames, tnames, tctx}
 
   export
-  injElim : WhnfContext d n -> Elim 0 0 -> Elim d n
+  injElim : WhnfContext q d n -> Elim q 0 0 -> Elim q d n
   injElim ctx e =
     let Val d = ctx.dimLen; Val n = ctx.termLen in
     e // shift0 d // shift0 n
 
+  public export
+  (.names) : (e : EqContext q n) -> NameContexts q e.dimLen n
+  (MkEqContext {qnames, dnames, tnames, _}).names =
+    MkNameContexts {qnames, dnames, tnames}
+
+  public export
+  (.names0) : EqContext q n -> NameContexts q 0 n
+  (MkEqContext {qnames, tnames, _}).names0 =
+    MkNameContexts {qnames, dnames = [<], tnames}
+
 namespace WhnfContext
   public export %inline
-  empty : WhnfContext 0 0
-  empty = MkWhnfContext [<] [<] [<]
+  empty : WhnfContext 0 0 0
+  empty = MkWhnfContext [<] [<] [<] [<]
 
   export
-  extendTy' : BindName -> LocalVar d n -> WhnfContext d n -> WhnfContext d (S n)
-  extendTy' x var (MkWhnfContext {termLen, dnames, tnames, tctx}) =
+  extendTy' : BindName -> LocalVar q d n ->
+              WhnfContext q d n -> WhnfContext q d (S n)
+  extendTy' x var (MkWhnfContext {termLen, qnames, dnames, tnames, tctx}) =
     MkWhnfContext {
-      dnames,
+      dnames, qnames,
       termLen = [|S termLen|],
       tnames  = tnames :< x,
       tctx    = tctx   :< var
     }
 
   export %inline
-  extendTy : BindName -> Term d n -> WhnfContext d n -> WhnfContext d (S n)
+  extendTy : BindName -> Term q d n ->
+             WhnfContext q d n -> WhnfContext q d (S n)
   extendTy x ty ctx = extendTy' x (lamVar ty) ctx
 
   export %inline
-  extendTyLet : BindName -> (type, term : Term d n) ->
-                WhnfContext d n -> WhnfContext d (S n)
+  extendTyLet : BindName -> (type, term : Term q d n) ->
+                WhnfContext q d n -> WhnfContext q d (S n)
   extendTyLet x type term ctx = extendTy' x (letVar {type, term}) ctx
 
   export
-  extendDimN : {s : Nat} -> BContext s -> WhnfContext d n ->
-               WhnfContext (s + d) n
-  extendDimN ns (MkWhnfContext {dnames, tnames, tctx, dimLen}) =
+  extendDimN : {s : Nat} -> BContext s -> WhnfContext q d n ->
+               WhnfContext q (s + d) n
+  extendDimN ns (MkWhnfContext {qnames, dnames, tnames, tctx, dimLen}) =
     MkWhnfContext {
       dimLen = [|Val s + dimLen|],
       dnames = dnames ++ toSnocVect' ns,
       tctx   = map (subD $ shift s) tctx,
-      tnames
+      qnames, tnames
     }
 
   export
-  extendDim : BindName -> WhnfContext d n -> WhnfContext (S d) n
+  extendDim : BindName -> WhnfContext q d n -> WhnfContext q (S d) n
   extendDim i = extendDimN [< i]
 
+  public export
+  (.names) : WhnfContext q d n -> NameContexts q d n
+  (MkWhnfContext {qnames, dnames, tnames, _}).names =
+    MkNameContexts {qnames, dnames, tnames}
+
 
 private
 prettyTContextElt : {opts : _} ->
-                    BContext d -> BContext n ->
-                    Doc opts -> BindName -> LocalVar d n ->
+                    NameContexts q d n ->
+                    Doc opts -> BindName -> LocalVar q d n ->
                     Eff Pretty (Doc opts)
-prettyTContextElt dnames tnames q x s = do
+prettyTContextElt names q x s = do
+  let Val _ = lengthPrf0 names.qnames
   dot <- dotD
   x  <- prettyTBind x; colon <- colonD
-  ty <- withPrec Outer $ prettyTerm dnames tnames s.type; eq <- cstD
-  tm <- traverse (withPrec Outer . prettyTerm dnames tnames) s.term
+  ty <- withPrec Outer $ prettyTerm names s.type; eq <- cstD
+  tm <- traverse (withPrec Outer . prettyTerm names) s.term
   d  <- askAt INDENT
   let qx = hcat [q, dot, x]
   pure $ case tm of
@@ -364,39 +427,37 @@ prettyTContextElt dnames tnames q x s = do
 
 private
 prettyTContext' : {opts : _} ->
-                  BContext d -> Context' (Doc opts) n -> BContext n ->
-                  TContext d n -> Eff Pretty (SnocList (Doc opts))
-prettyTContext' _ [<] [<] [<] = pure [<]
-prettyTContext' dnames (qtys :< q) (tnames :< x) (tys :< t) =
-  [|prettyTContext' dnames qtys tnames tys :<
-    prettyTContextElt dnames tnames q x t|]
+                  NameContexts q d n -> Context' (Doc opts) n ->
+                  TContext q d n -> Eff Pretty (SnocList (Doc opts))
+prettyTContext' _ [<] [<] = pure [<]
+prettyTContext' names (qtys :< q) (tys :< t) =
+  let names' = {tnames $= tail, termLen $= map pred} names in
+  [|prettyTContext' names' qtys tys :<
+    prettyTContextElt names' q (head names.tnames) t|]
 
 export
 prettyTContext : {opts : _} ->
-                 BContext d -> QContext n -> BContext n ->
-                 TContext d n -> Eff Pretty (Doc opts)
-prettyTContext dnames qtys tnames tys = do
-  comma <- commaD
-  qtys <- traverse prettyQty qtys
-  sepSingle . exceptLast (<+> comma) . toList <$>
-    prettyTContext' dnames qtys tnames tys
+                 NameContexts q d n -> QContext q n ->
+                 TContext q d n -> Eff Pretty (Doc opts)
+prettyTContext names qtys tys = do
+  qtys <- traverse (prettyQty names.qnames) qtys
+  sepSingleTight !commaD . toList <$> prettyTContext' names qtys tys
 
 export
-prettyTyContext : {opts : _} -> TyContext d n -> Eff Pretty (Doc opts)
-prettyTyContext (MkTyContext dctx dnames tctx tnames qtys) =
-  case dctx of
-    C [<] => prettyTContext dnames qtys tnames tctx
-    _     => pure $
-      sepSingle [!(prettyDimEq dnames dctx) <++> !pipeD,
-                 !(prettyTContext dnames qtys tnames tctx)]
+prettyTyContext : {opts : _} -> TyContext q d n -> Eff Pretty (Doc opts)
+prettyTyContext ctx = case ctx.dctx of
+  C [<] => prettyTContext ctx.names ctx.qtys ctx.tctx
+  _     => pure $
+    sepSingle [!(prettyDimEq ctx.dnames ctx.dctx) <++> !pipeD,
+               !(prettyTContext ctx.names ctx.qtys ctx.tctx)]
 
 export
-prettyEqContext : {opts : _} -> EqContext n -> Eff Pretty (Doc opts)
+prettyEqContext : {opts : _} -> EqContext q n -> Eff Pretty (Doc opts)
 prettyEqContext ctx = prettyTyContext $ toTyContext ctx
 
 export
-prettyWhnfContext : {opts : _} -> WhnfContext d n -> Eff Pretty (Doc opts)
+prettyWhnfContext : {opts : _} -> WhnfContext q d n -> Eff Pretty (Doc opts)
 prettyWhnfContext ctx =
   let Val n = ctx.termLen in
-  sepSingle . exceptLast (<+> comma) . toList <$>
-    prettyTContext' ctx.dnames (replicate n "_") ctx.tnames ctx.tctx
+  sepSingleTight !commaD . toList <$>
+    prettyTContext' ctx.names (replicate n "_") ctx.tctx
diff --git a/lib/Quox/Typing/Error.idr b/lib/Quox/Typing/Error.idr
index 502757c..b34b041 100644
--- a/lib/Quox/Typing/Error.idr
+++ b/lib/Quox/Typing/Error.idr
@@ -17,108 +17,64 @@ import Derive.Prelude
 %default total
 
 
-public export
-record NameContexts d n where
-  constructor MkNameContexts
-  dnames : BContext d
-  tnames : BContext n
-%runElab deriveIndexed "NameContexts" [Show]
-
-namespace NameContexts
-  export
-  empty : NameContexts 0 0
-  empty = MkNameContexts [<] [<]
-
-  export
-  extendDimN : BContext s -> NameContexts d n -> NameContexts (s + d) n
-  extendDimN xs = {dnames $= (++ toSnocVect' xs)}
-
-  export
-  extendDim : BindName -> NameContexts d n -> NameContexts (S d) n
-  extendDim i = extendDimN [< i]
-
-namespace TyContext
-  public export
-  (.names) : TyContext d n -> NameContexts d n
-  (MkTyContext {dnames, tnames, _}).names =
-    MkNameContexts {dnames, tnames}
-
-namespace EqContext
-  public export
-  (.names) : (e : EqContext n) -> NameContexts e.dimLen n
-  (MkEqContext {dnames, tnames, _}).names =
-    MkNameContexts {dnames, tnames}
-
-  public export
-  (.names0) : EqContext n -> NameContexts 0 n
-  (MkEqContext {tnames, _}).names0 =
-    MkNameContexts {dnames = [<], tnames}
-
-namespace WhnfContext
-  public export
-  (.names) : WhnfContext d n -> NameContexts d n
-  (MkWhnfContext {dnames, tnames, _}).names =
-    MkNameContexts {dnames, tnames}
-
-
 public export
 data Error
-= ExpectedTYPE    Loc (NameContexts d n) (Term d n)
-| ExpectedPi      Loc (NameContexts d n) (Term d n)
-| ExpectedSig     Loc (NameContexts d n) (Term d n)
-| ExpectedEnum    Loc (NameContexts d n) (Term d n)
-| ExpectedEq      Loc (NameContexts d n) (Term d n)
-| ExpectedNAT     Loc (NameContexts d n) (Term d n)
-| ExpectedSTRING  Loc (NameContexts d n) (Term d n)
-| ExpectedBOX     Loc (NameContexts d n) (Term d n)
-| ExpectedIOState Loc (NameContexts d n) (Term d n)
+= ExpectedTYPE    Loc (NameContexts q d n) (Term q d n)
+| ExpectedPi      Loc (NameContexts q d n) (Term q d n)
+| ExpectedSig     Loc (NameContexts q d n) (Term q d n)
+| ExpectedEnum    Loc (NameContexts q d n) (Term q d n)
+| ExpectedEq      Loc (NameContexts q d n) (Term q d n)
+| ExpectedNAT     Loc (NameContexts q d n) (Term q d n)
+| ExpectedSTRING  Loc (NameContexts q d n) (Term q d n)
+| ExpectedBOX     Loc (NameContexts q d n) (Term q d n)
+| ExpectedIOState Loc (NameContexts q d n) (Term q d n)
 | BadUniverse     Loc Universe Universe
 | TagNotIn        Loc TagVal (SortedSet TagVal)
 | BadCaseEnum     Loc (SortedSet TagVal) (SortedSet TagVal)
-| BadQtys         Loc String (TyContext d n) (List (QOutput n, Term d n))
+| BadQtys         Loc String (TyContext q d n) (List (QOutput q n, Term q d n))
 
 -- first term arg of ClashT is the type
-| ClashT  Loc (EqContext n) EqMode (Term 0 n) (Term 0 n) (Term 0 n)
-| ClashTy Loc (EqContext n) EqMode (Term 0 n) (Term 0 n)
-| ClashE  Loc (EqContext n) EqMode (Elim 0 n) (Elim 0 n)
+| ClashT  Loc (EqContext q n) EqMode (Term q 0 n) (Term q 0 n) (Term q 0 n)
+| ClashTy Loc (EqContext q n) EqMode (Term q 0 n) (Term q 0 n)
+| ClashE  Loc (EqContext q n) EqMode (Elim q 0 n) (Elim q 0 n)
 | ClashU  Loc EqMode Universe Universe
-| ClashQ  Loc Qty Qty
+| ClashQ  Loc (BContext q) (Qty q) (Qty q)
 | NotInScope Loc Name
 
-| NotType Loc (TyContext d n) (Term d n)
-| WrongType Loc (EqContext n) (Term 0 n) (Term 0 n)
+| NotType Loc (TyContext q d n) (Term q d n)
+| WrongType Loc (EqContext q n) (Term q 0 n) (Term q 0 n)
 
 | WrongBuiltinType Builtin Error
-| ExpectedSingleEnum Loc (NameContexts d n) (Term d n)
+| ExpectedSingleEnum Loc (NameContexts q d n) (Term q d n)
 
 | MissingEnumArm Loc TagVal (List TagVal)
 
 -- extra context
 | WhileChecking
-    (TyContext d n) SQty
-    (Term d n) -- term
-    (Term d n) -- type
+    (TyContext q d n) SQty
+    (Term q d n) -- term
+    (Term q d n) -- type
     Error
 | WhileCheckingTy
-    (TyContext d n)
-    (Term d n)
+    (TyContext q d n)
+    (Term q d n)
     (Maybe Universe)
     Error
 | WhileInferring
-    (TyContext d n) SQty
-    (Elim d n)
+    (TyContext q d n) SQty
+    (Elim q d n)
     Error
 | WhileComparingT
-    (EqContext n) EqMode SQty
-    (Term 0 n) -- type
-    (Term 0 n) (Term 0 n) -- lhs/rhs
+    (EqContext q n) EqMode SQty
+    (Term q 0 n) -- type
+    (Term q 0 n) (Term q 0 n) -- lhs/rhs
     Error
 | WhileComparingE
-    (EqContext n) EqMode SQty
-    (Elim 0 n) (Elim 0 n)
+    (EqContext q n) EqMode SQty
+    (Elim q 0 n) (Elim q 0 n)
     Error
 %name Error err
-%runElab derive "Error" [Show]
+-- %runElab derive "Error" [Show]
 
 public export
 ErrorEff : Type -> Type
@@ -144,7 +100,7 @@ Located Error where
   (ClashTy          loc _ _ _ _).loc    = loc
   (ClashE           loc _ _ _ _).loc    = loc
   (ClashU           loc _ _ _).loc      = loc
-  (ClashQ           loc _ _).loc        = loc
+  (ClashQ           loc _ _ _).loc      = loc
   (NotInScope       loc _).loc          = loc
   (NotType          loc _ _).loc        = loc
   (WrongType        loc _ _ _).loc      = loc
@@ -192,14 +148,15 @@ expect : Has (Except e) fs =>
          (a -> a -> e) -> (a -> a -> Bool) -> a -> a -> Eff fs ()
 expect err cmp x y = unless (x `cmp` y) $ throw $ err x y
 
-parameters {auto _ : Has ErrorEff fs} (loc : Loc)
+parameters {auto _ : Has ErrorEff fs} (loc : Loc) (ctx : BContext q)
   export %inline
-  expectEqualQ : Qty -> Qty -> Eff fs ()
-  expectEqualQ = expect (ClashQ loc) (==)
+  expectEqualQ : Qty q -> Qty q -> Eff fs ()
+  expectEqualQ = expect (ClashQ loc ctx) (==)
+    -- [fixme] probably replace (==)
 
   export %inline
-  expectCompatQ : Qty -> Qty -> Eff fs ()
-  expectCompatQ = expect (ClashQ loc) compat
+  expectCompatQ : Qty q -> Qty q -> Eff fs ()
+  expectCompatQ = expect (ClashQ loc ctx) compat
 
   export %inline
   expectModeU : EqMode -> Universe -> Universe -> Eff fs ()
@@ -225,8 +182,8 @@ isTypeInUniverse (Just k) = "is a type in universe \{show k}"
 
 
 private
-filterSameQtys : BContext n -> List (QOutput n, z) ->
-                 Exists $ \n' => (BContext n', List (QOutput n', z))
+filterSameQtys : BContext n -> List (QOutput q n, z) ->
+                 Exists $ \n' => (BContext n', List (QOutput q n', z))
 filterSameQtys [<]       qts = Evidence 0 ([<], qts)
 filterSameQtys (ns :< n) qts =
   let (qs, qts) = unzip $ map (\(qs :< q, t) => (q, qs, t)) qts
@@ -236,27 +193,29 @@ filterSameQtys (ns :< n) qts =
   then Evidence l (ns, qts)
   else Evidence (S l) (ns :< n, zipWith (\(qs, t), q => (qs :< q, t)) qts qs)
 where
-  allSame : List Qty -> Bool
+  allSame : List (Qty q) -> Bool
   allSame []        = True
   allSame (q :: qs) = all (== q) qs
 
 
 private
-printCaseQtys : {opts : _} -> TyContext d n ->
-                BContext n' -> List (QOutput n', Term d n) ->
+printCaseQtys : {opts : _} -> TyContext q d n ->
+                BContext n' -> List (QOutput q n', Term q d n) ->
                 Eff Pretty (List (Doc opts))
 printCaseQtys ctx ns qts =
   let Evidence _ (ns, qts) = filterSameQtys ns qts in
   traverse (line ns) qts
 where
-  line : BContext l -> (QOutput l, Term d n) -> Eff Pretty (Doc opts)
-  line ns (qs, t) = map (("-" <++>) . sep) $ sequence
+  line : BContext l -> (QOutput q l, Term q d n) -> Eff Pretty (Doc opts)
+  line ns (qs, t) =
+    let Val q = ctx.qtyLen; names = ctx.names in
+    map (("-" <++>) . sep) $ sequence
     [hangDSingle "the term"
-      !(prettyTerm ctx.dnames ctx.tnames t),
+      !(prettyTerm names t),
      hangDSingle "uses variables" $
       separateTight !commaD $ toSnocList' !(traverse prettyTBind ns),
      hangDSingle "with quantities" $
-      separateTight !commaD $ toSnocList' !(traverse prettyQty qs)]
+      separateTight !commaD $ toSnocList' !(traverse (prettyQty names) qs)]
 
 parameters {opts : LayoutOpts} (showContext : Bool)
   export
@@ -268,11 +227,11 @@ parameters {opts : LayoutOpts} (showContext : Bool)
     else pure doc
 
   export %inline
-  inTContext : TyContext d n -> Doc opts -> Eff Pretty (Doc opts)
+  inTContext : TyContext q d n -> Doc opts -> Eff Pretty (Doc opts)
   inTContext ctx = inContext' (null ctx) ctx prettyTyContext
 
   export %inline
-  inEContext : EqContext n -> Doc opts -> Eff Pretty (Doc opts)
+  inEContext : EqContext q n -> Doc opts -> Eff Pretty (Doc opts)
   inEContext ctx = inContext' (null ctx) ctx prettyEqContext
 
   export
@@ -280,43 +239,43 @@ parameters {opts : LayoutOpts} (showContext : Bool)
   prettyErrorNoLoc err0 = case err0 of
     ExpectedTYPE _ ctx s =>
       hangDSingle "expected a type universe, but got"
-        !(prettyTerm ctx.dnames ctx.tnames s)
+        !(prettyTerm ctx s)
 
     ExpectedPi _ ctx s =>
       hangDSingle "expected a function type, but got"
-        !(prettyTerm ctx.dnames ctx.tnames s)
+        !(prettyTerm ctx s)
 
     ExpectedSig _ ctx s =>
       hangDSingle "expected a pair type, but got"
-        !(prettyTerm ctx.dnames ctx.tnames s)
+        !(prettyTerm ctx s)
 
     ExpectedEnum _ ctx s =>
       hangDSingle "expected an enumeration type, but got"
-        !(prettyTerm ctx.dnames ctx.tnames s)
+        !(prettyTerm ctx s)
 
     ExpectedEq _ ctx s =>
       hangDSingle "expected an equality type, but got"
-        !(prettyTerm ctx.dnames ctx.tnames s)
+        !(prettyTerm ctx s)
 
     ExpectedNAT _ ctx s =>
       hangDSingle
         ("expected the type" <++>
-          !(prettyTerm [<] [<] $ NAT noLoc) <+> ", but got")
-        !(prettyTerm ctx.dnames ctx.tnames s)
+          !(prettyTerm ctx $ NAT noLoc) <+> ", but got")
+        !(prettyTerm ctx s)
 
     ExpectedSTRING _ ctx s =>
       hangDSingle
         ("expected the type" <++>
-          !(prettyTerm [<] [<] $ STRING noLoc) <+> ", but got")
-        !(prettyTerm ctx.dnames ctx.tnames s)
+          !(prettyTerm ctx $ STRING noLoc) <+> ", but got")
+        !(prettyTerm ctx s)
 
     ExpectedBOX _ ctx s =>
       hangDSingle "expected a box type, but got"
-        !(prettyTerm ctx.dnames ctx.tnames s)
+        !(prettyTerm ctx s)
 
     ExpectedIOState _ ctx s =>
       hangDSingle "expected IOState, but got"
-        !(prettyTerm ctx.dnames ctx.tnames s)
+        !(prettyTerm ctx s)
 
     BadUniverse _ k l => pure $
       sep ["the universe level" <++> !(prettyUniverse k),
@@ -324,57 +283,58 @@ parameters {opts : LayoutOpts} (showContext : Bool)
 
     TagNotIn _ tag set =>
       hangDSingle (hsep ["the tag", !(prettyTag tag), "is not contained in"])
-        !(prettyTerm [<] [<] $ Enum set noLoc)
+        !(prettyTerm empty $ Enum set noLoc)
 
     BadCaseEnum _ head body => sep <$> sequence
       [hangDSingle "case expression has head of type"
-         !(prettyTerm [<] [<] $ Enum head noLoc),
+         !(prettyTerm empty $ Enum head noLoc),
        hangDSingle "but cases for"
-         !(prettyTerm [<] [<] $ Enum body noLoc)]
+         !(prettyTerm empty $ Enum body noLoc)]
 
     BadQtys _ what ctx arms =>
       hangDSingle (text "inconsistent variable usage in \{what}") $
         sep !(printCaseQtys ctx ctx.tnames arms)
 
     ClashT _ ctx mode ty s t =>
+      let names = ctx.names0 in
       inEContext ctx . sep =<< sequence
-      [hangDSingle "the term" !(prettyTerm [<] ctx.tnames s),
-       hangDSingle (text "is not \{prettyMode mode}")
-          !(prettyTerm [<] ctx.tnames t),
-       hangDSingle "at type" !(prettyTerm [<] ctx.tnames ty)]
+      [hangDSingle "the term" !(prettyTerm names s),
+       hangDSingle (text "is not \{prettyMode mode}") !(prettyTerm names t),
+       hangDSingle "at type" !(prettyTerm names ty)]
 
     ClashTy _ ctx mode a b =>
+      let names = ctx.names0 in
       inEContext ctx . sep =<< sequence
-      [hangDSingle "the type" !(prettyTerm [<] ctx.tnames a),
-       hangDSingle (text "is not \{prettyMode mode}")
-          !(prettyTerm [<] ctx.tnames b)]
+      [hangDSingle "the type" !(prettyTerm names a),
+       hangDSingle (text "is not \{prettyMode mode}") !(prettyTerm names b)]
 
     ClashE _ ctx mode e f =>
+      let names = ctx.names0 in
       inEContext ctx . sep =<< sequence
-      [hangDSingle "the term" !(prettyElim [<] ctx.tnames e),
-       hangDSingle (text "is not \{prettyMode mode}")
-          !(prettyElim [<] ctx.tnames f)]
+      [hangDSingle "the term" !(prettyElim names e),
+       hangDSingle (text "is not \{prettyMode mode}") !(prettyElim names f)]
 
     ClashU _ mode k l => pure $
       sep ["the universe level" <++> !(prettyUniverse k),
            text "is not \{prettyModeU mode}" <++> !(prettyUniverse l)]
 
-    ClashQ _ pi rh => pure $
-      sep ["the quantity" <++> !(prettyQty pi),
-           "is not equal to" <++> !(prettyQty rh)]
+    ClashQ _ ctx pi rh => pure $
+      sep ["the quantity" <++> !(prettyQty ctx pi),
+           "is not equal to" <++> !(prettyQty ctx rh)]
 
     NotInScope _ x => pure $
       hsep [!(prettyFree x), "is not in scope"]
 
     NotType _ ctx s =>
       inTContext ctx . sep =<< sequence
-      [hangDSingle "the term" !(prettyTerm ctx.dnames ctx.tnames s),
+      [hangDSingle "the term" !(prettyTerm ctx.names s),
        pure "is not a type"]
 
     WrongType _ ctx ty s =>
+      let names = ctx.names0 in
       inEContext ctx . sep =<< sequence
-      [hangDSingle "the term" !(prettyTerm [<] ctx.tnames s),
-       hangDSingle "cannot have type" !(prettyTerm [<] ctx.tnames ty)]
+      [hangDSingle "the term" !(prettyTerm names s),
+       hangDSingle "cannot have type" !(prettyTerm names ty)]
 
     WrongBuiltinType b err => pure $
       vappend
@@ -384,24 +344,25 @@ parameters {opts : LayoutOpts} (showContext : Bool)
 
     ExpectedSingleEnum _ ctx s =>
       hangDSingle "expected an enumeration type with one case, but got"
-        !(prettyTerm ctx.dnames ctx.tnames s)
+        !(prettyTerm ctx s)
 
     MissingEnumArm _ tag tags => pure $
       sep [hsep ["the tag", !(prettyTag tag), "is not contained in"],
-           !(prettyTerm [<] [<] $ Enum (fromList tags) noLoc)]
+           !(prettyTerm empty $ Enum (fromList tags) noLoc)]
 
     WhileChecking ctx sg s a err =>
+      let names = ctx.names in
       [|vappendBlank
           (inTContext ctx . sep =<< sequence
-            [hangDSingle "while checking" !(prettyTerm ctx.dnames ctx.tnames s),
-             hangDSingle "has type"       !(prettyTerm ctx.dnames ctx.tnames a),
-             hangDSingle "with quantity"  !(prettyQty sg.qty)])
+            [hangDSingle "while checking" !(prettyTerm names s),
+             hangDSingle "has type"       !(prettyTerm names a),
+             hangDSingle "with quantity"  !(prettyQConst sg.qconst)])
           (prettyErrorNoLoc err)|]
 
     WhileCheckingTy ctx a k err =>
       [|vappendBlank
           (inTContext ctx . sep =<< sequence
-            [hangDSingle "while checking" !(prettyTerm ctx.dnames ctx.tnames a),
+            [hangDSingle "while checking" !(prettyTerm ctx.names a),
              pure $ text $ isTypeInUniverse k])
           (prettyErrorNoLoc err)|]
 
@@ -409,27 +370,27 @@ parameters {opts : LayoutOpts} (showContext : Bool)
       [|vappendBlank
           (inTContext ctx . sep =<< sequence
             [hangDSingle "while inferring the type of"
-                !(prettyElim ctx.dnames ctx.tnames e),
-             hangDSingle "with quantity" !(prettyQty sg.qty)])
+                !(prettyElim ctx.names e),
+             hangDSingle "with quantity" !(prettyQConst sg.qconst)])
           (prettyErrorNoLoc err)|]
 
     WhileComparingT ctx mode sg a s t err =>
+      let names = ctx.names0 in
       [|vappendBlank
           (inEContext ctx . sep =<< sequence
-            [hangDSingle "while checking that" !(prettyTerm [<] ctx.tnames s),
-             hangDSingle (text "is \{prettyMode mode}")
-                !(prettyTerm [<] ctx.tnames t),
-             hangDSingle "at type" !(prettyTerm [<] ctx.tnames a),
-             hangDSingle "with quantity" !(prettyQty sg.qty)])
+            [hangDSingle "while checking that" !(prettyTerm names s),
+             hangDSingle (text "is \{prettyMode mode}") !(prettyTerm names t),
+             hangDSingle "at type" !(prettyTerm names a),
+             hangDSingle "with quantity" !(prettyQConst sg.qconst)])
           (prettyErrorNoLoc err)|]
 
     WhileComparingE ctx mode sg e f err =>
+      let names = ctx.names0 in
       [|vappendBlank
           (inEContext ctx . sep =<< sequence
-            [hangDSingle "while checking that" !(prettyElim [<] ctx.tnames e),
-             hangDSingle (text "is \{prettyMode mode}")
-                !(prettyElim [<] ctx.tnames f),
-             hangDSingle "with quantity" !(prettyQty sg.qty)])
+            [hangDSingle "while checking that" !(prettyElim names e),
+             hangDSingle (text "is \{prettyMode mode}") !(prettyElim names f),
+             hangDSingle "with quantity" !(prettyQConst sg.qconst)])
           (prettyErrorNoLoc err)|]
 
   where
diff --git a/lib/Quox/Whnf/Coercion.idr b/lib/Quox/Whnf/Coercion.idr
index 91d94d2..1e3f532 100644
--- a/lib/Quox/Whnf/Coercion.idr
+++ b/lib/Quox/Whnf/Coercion.idr
@@ -9,140 +9,147 @@ import Quox.Whnf.TypeCase
 
 
 private
-coeScoped : {s : Nat} -> DScopeTerm d n -> Dim d -> Dim d -> Loc ->
-            ScopeTermN s d n -> ScopeTermN s d n
-coeScoped ty p q loc (S names (N body)) =
-  S names $ N $ E $ Coe ty p q body loc
-coeScoped ty p q loc (S names (Y body)) =
-  ST names $ E $ Coe (weakDS s ty) p q body loc
+coeScoped : {s, q : Nat} -> DScopeTerm q d n -> Dim d -> Dim d -> Loc ->
+            ScopeTermN s q d n -> ScopeTermN s q d n
+coeScoped ty p p' loc (S names (N body)) =
+  S names $ N $ E $ Coe ty p p' body loc
+coeScoped ty p p' loc (S names (Y body)) =
+  ST names $ E $ Coe (weakDS s ty) p p' body loc
 where
-  weakDS : (by : Nat) -> DScopeTerm d n -> DScopeTerm d (by + n)
+  weakDS : (by : Nat) -> DScopeTerm q d n -> DScopeTerm q d (by + n)
   weakDS by (S names (Y body)) = S names $ Y $ weakT by body
   weakDS by (S names (N body)) = S names $ N $ weakT by body
 
 
 parameters {auto _ : CanWhnf Term Interface.isRedexT}
            {auto _ : CanWhnf Elim Interface.isRedexE}
-           (defs : Definitions) (ctx : WhnfContext d n) (sg : SQty)
-  ||| reduce a function application `App (Coe ty p q val) s loc`
+           (defs : Definitions) (ctx : WhnfContext q d n) (sg : SQty)
+  ||| reduce a function application `App (Coe ty p p' val) s loc`
   export covering
-  piCoe : (ty : DScopeTerm d n) -> (p, q : Dim d) ->
-          (val, s : Term d n) -> Loc ->
-          Eff Whnf (Subset (Elim d n) (No . isRedexE defs ctx sg))
-  piCoe sty@(S [< i] ty) p q val s loc = do
-    -- (coe [i ⇒ π.(x : A) → B] @p @q t) s ⇝
-    -- coe [i ⇒ B[𝒔‹i›/x] @p @q ((t ∷ (π.(x : A) → B)‹p/i›) 𝒔‹p›)
-    --   where 𝒔‹j› ≔ coe [i ⇒ A] @q @j s
+  piCoe : (ty : DScopeTerm q d n) -> (p, p' : Dim d) ->
+          (val, s : Term q d n) -> Loc ->
+          Eff Whnf (Subset (Elim q d n) (No . isRedexE defs ctx sg))
+  piCoe sty@(S [< i] ty) p p' val s loc = do
+    -- (coe [i ⇒ π.(x : A) → B] @p @p' t) s ⇝
+    -- coe [i ⇒ B[𝒔‹i›/x] @p @p' ((t ∷ (π.(x : A) → B)‹p/i›) 𝒔‹p›)
+    --   where 𝒔‹j› ≔ coe [i ⇒ A] @p' @j s
     --
     -- type-case is used to expose A,B if the type is neutral
     let ctx1 = extendDim i ctx
     Element ty tynf <- whnf defs ctx1 SZero $ getTerm ty
     (arg, res) <- tycasePi defs ctx1 ty
-    let s0   = CoeT i arg q p s s.loc
-        body = E $ App (Ann val (ty // one p) val.loc) (E s0) loc
-        s1   = CoeT i (arg // (BV 0 i.loc ::: shift 2)) (weakD 1 q) (BV 0 i.loc)
-                    (s // shift 1) s.loc
-    whnf defs ctx sg $ CoeT i (sub1 res s1) p q body loc
+    let Val q = ctx.qtyLen
+        s0    = CoeT i arg p' p s s.loc
+        body  = E $ App (Ann val (ty // one p) val.loc) (E s0) loc
+        s1    = CoeT i (arg // (BV 0 i.loc ::: shift 2))
+                  (weakD 1 p') (BV 0 i.loc)
+                  (s // shift 1) s.loc
+    whnf defs ctx sg $ CoeT i (sub1 res s1) p p' body loc
 
-  ||| reduce a pair elimination `CasePair pi (Coe ty p q val) ret body loc`
+  ||| reduce a pair elimination `CasePair pi (Coe ty p p' val) ret body loc`
   export covering
-  sigCoe : (qty : Qty) ->
-           (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
-           (ret : ScopeTerm d n) -> (body : ScopeTermN 2 d n) -> Loc ->
-           Eff Whnf (Subset (Elim d n) (No . isRedexE defs ctx sg))
-  sigCoe qty sty@(S [< i] ty) p q val ret body loc = do
-    -- caseπ (coe [i ⇒ (x : A) × B] @p @q s) return z ⇒ C of { (a, b) ⇒ e }
+  sigCoe : (qty : Qty q) ->
+           (ty : DScopeTerm q d n) -> (p, p' : Dim d) -> (val : Term q d n) ->
+           (ret : ScopeTerm q d n) -> (body : ScopeTermN 2 q d n) -> Loc ->
+           Eff Whnf (Subset (Elim q d n) (No . isRedexE defs ctx sg))
+  sigCoe qty sty@(S [< i] ty) p p' val ret body loc = do
+    -- caseπ (coe [i ⇒ (x : A) × B] @p @p' s) return z ⇒ C of { (a, b) ⇒ e }
     --   ⇝
     -- caseπ s ∷ ((x : A) × B)‹p/i› return z ⇒ C
     -- of { (a, b) ⇒
-    --   e[(coe [i ⇒ A] @p @q a)/a,
-    --     (coe [i ⇒ B[(coe [j ⇒ A‹j/i›] @p @i a)/x]] @p @q b)/b] }
+    --   e[(coe [i ⇒ A] @p @p' a)/a,
+    --     (coe [i ⇒ B[(coe [j ⇒ A‹j/i›] @p @i a)/x]] @p @p' b)/b] }
     --
     -- type-case is used to expose A,B if the type is neutral
     let ctx1 = extendDim i ctx
     Element ty tynf <- whnf defs ctx1 SZero $ getTerm ty
     (tfst, tsnd) <- tycaseSig defs ctx1 ty
-    let [< x, y] = body.names
-        a' = CoeT i (weakT 2 tfst) p q (BVT 1 x.loc) x.loc
+    let Val q = ctx.qtyLen
+        [< x, y] = body.names
+        a' = CoeT i (weakT 2 tfst) p p' (BVT 1 x.loc) x.loc
         tsnd' = tsnd.term //
           (CoeT i (weakT 2 $ tfst // (B VZ tsnd.loc ::: shift 2))
             (weakD 1 p) (B VZ i.loc) (BVT 1 tsnd.loc) y.loc ::: shift 2)
-        b' = CoeT i tsnd' p q (BVT 0 y.loc) y.loc
+        b' = CoeT i tsnd' p p' (BVT 0 y.loc) y.loc
     whnf defs ctx sg $ CasePair qty (Ann val (ty // one p) val.loc) ret
       (ST body.names $ body.term // (a' ::: b' ::: shift 2)) loc
 
-  ||| reduce a pair projection `Fst (Coe ty p q val) loc`
+  ||| reduce a pair projection `Fst (Coe ty p p' val) loc`
   export covering
-  fstCoe : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
-           Loc -> Eff Whnf (Subset (Elim d n) (No . isRedexE defs ctx sg))
-  fstCoe sty@(S [< i] ty) p q val loc = do
-    -- fst (coe (𝑖 ⇒ (x : A) × B) @p @q s)
+  fstCoe : (ty : DScopeTerm q d n) -> (p, p' : Dim d) -> (val : Term q d n) ->
+           Loc -> Eff Whnf (Subset (Elim q d n) (No . isRedexE defs ctx sg))
+  fstCoe sty@(S [< i] ty) p p' val loc = do
+    -- fst (coe (𝑖 ⇒ (x : A) × B) @p @p' s)
     --   ⇝
-    -- coe (𝑖 ⇒ A) @p @q (fst (s ∷ (x : A‹p/𝑖›) × B‹p/𝑖›))
+    -- coe (𝑖 ⇒ A) @p @p' (fst (s ∷ (x : A‹p/𝑖›) × B‹p/𝑖›))
     --
     -- type-case is used to expose A,B if the type is neutral
     let ctx1 = extendDim i ctx
     Element ty tynf <- whnf defs ctx1 SZero $ getTerm ty
     (tfst, _) <- tycaseSig defs ctx1 ty
+    let Val q = ctx.qtyLen
     whnf defs ctx sg $
-      Coe (ST [< i] tfst) p q
+      Coe (ST [< i] tfst) p p'
           (E (Fst (Ann val (ty // one p) val.loc) val.loc)) loc
 
   ||| reduce a pair projection `Snd (Coe ty p q val) loc`
   export covering
-  sndCoe : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
-           Loc -> Eff Whnf (Subset (Elim d n) (No . isRedexE defs ctx sg))
-  sndCoe sty@(S [< i] ty) p q val loc = do
-    -- snd (coe (𝑖 ⇒ (x : A) × B) @p @q s)
+  sndCoe : (ty : DScopeTerm q d n) -> (p, p' : Dim d) -> (val : Term q d n) ->
+           Loc -> Eff Whnf (Subset (Elim q d n) (No . isRedexE defs ctx sg))
+  sndCoe sty@(S [< i] ty) p p' val loc = do
+    -- snd (coe (𝑖 ⇒ (x : A) × B) @p @p' s)
     --   ⇝
-    -- coe (𝑖 ⇒ B[coe (𝑗 ⇒ A‹𝑗/𝑖›) @p @𝑖 (fst (s ∷ (x : A) × B))/x]) @p @q
+    -- coe (𝑖 ⇒ B[coe (𝑗 ⇒ A‹𝑗/𝑖›) @p @𝑖 (fst (s ∷ (x : A) × B))/x]) @p @p'
     --     (snd (s ∷ (x : A‹p/𝑖›) × B‹p/𝑖›))
     --
     -- type-case is used to expose A,B if the type is neutral
     let ctx1 = extendDim i ctx
     Element ty tynf <- whnf defs ctx1 SZero $ getTerm ty
     (tfst, tsnd) <- tycaseSig defs ctx1 ty
+    let Val q = ctx.qtyLen
     whnf defs ctx sg $
       Coe (ST [< i] $ sub1 tsnd $
             Coe (ST [< !(fresh i)] $ tfst // (BV 0 i.loc ::: shift 2))
                 (weakD 1 p) (BV 0 loc)
                 (E (Fst (Ann (dweakT 1 val) ty val.loc) val.loc)) loc)
-          p q
+          p p'
           (E (Snd (Ann val (ty // one p) val.loc) val.loc))
           loc
 
   ||| reduce a dimension application `DApp (Coe ty p q val) r loc`
   export covering
-  eqCoe : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
+  eqCoe : (ty : DScopeTerm q d n) -> (p, p' : Dim d) -> (val : Term q d n) ->
           (r : Dim d) -> Loc ->
-          Eff Whnf (Subset (Elim d n) (No . isRedexE defs ctx sg))
-  eqCoe sty@(S [< j] ty) p q val r loc = do
-    -- (coe [j ⇒ Eq [i ⇒ A] L R] @p @q eq) @r
+          Eff Whnf (Subset (Elim q d n) (No . isRedexE defs ctx sg))
+  eqCoe sty@(S [< j] ty) p p' val r loc = do
+    -- (coe [j ⇒ Eq [i ⇒ A] L R] @p @p' eq) @r
     --   ⇝
-    -- comp [j ⇒ A‹r/i›] @p @q ((eq ∷ (Eq [i ⇒ A] L R)‹p/j›) @r)
+    -- comp [j ⇒ A‹r/i›] @p @p' ((eq ∷ (Eq [i ⇒ A] L R)‹p/j›) @r)
     --   @r { 0 j ⇒ L; 1 j ⇒ R }
     let ctx1 = extendDim j ctx
     Element ty tynf <- whnf defs ctx1 SZero $ getTerm ty
     (a0, a1, a, s, t) <- tycaseEq defs ctx1 ty
-    let a'   = dsub1 a (weakD 1 r)
-        val' = E $ DApp (Ann val (ty // one p) val.loc) r loc
-    whnf defs ctx sg $ CompH j a' p q val' r j s j t loc
+    let Val q = ctx.qtyLen
+        a'    = dsub1 a (weakD 1 r)
+        val'  = E $ DApp (Ann val (ty // one p) val.loc) r loc
+    whnf defs ctx sg $ CompH j a' p p' val' r j s j t loc
 
   ||| reduce a pair elimination `CaseBox pi (Coe ty p q val) ret body`
   export covering
-  boxCoe : (qty : Qty) ->
-           (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
-           (ret : ScopeTerm d n) -> (body : ScopeTerm d n) -> Loc ->
-           Eff Whnf (Subset (Elim d n) (No . isRedexE defs ctx sg))
-  boxCoe qty sty@(S [< i] ty) p q val ret body loc = do
-    -- caseπ (coe [i ⇒ [ρ. A]] @p @q s) return z ⇒ C of { [a] ⇒ e }
+  boxCoe : (qty : Qty q) ->
+           (ty : DScopeTerm q d n) -> (p, p' : Dim d) -> (val : Term q d n) ->
+           (ret : ScopeTerm q d n) -> (body : ScopeTerm q d n) -> Loc ->
+           Eff Whnf (Subset (Elim q d n) (No . isRedexE defs ctx sg))
+  boxCoe qty sty@(S [< i] ty) p p' val ret body loc = do
+    -- caseπ (coe [i ⇒ [ρ. A]] @p @p' s) return z ⇒ C of { [a] ⇒ e }
     --   ⇝
-    -- caseπ s ∷ [ρ. A]‹p/i› return z ⇒ C of { [a] ⇒ e[(coe [i ⇒ A] p q a)/a] }
-    let ctx1 = extendDim i ctx
+    -- caseπ s ∷ [ρ. A]‹p/i› return z ⇒ C of { [a] ⇒ e[(coe [i ⇒ A] p p' a)/a] }
+    let ctx1  = extendDim i ctx
+        Val q = ctx.qtyLen
     Element ty tynf <- whnf defs ctx1 SZero $ getTerm ty
     ta <- tycaseBOX defs ctx1 ty
     let xloc = body.name.loc
-    let a' = CoeT i (weakT 1 ta) p q (BVT 0 xloc) xloc
+    let a' = CoeT i (weakT 1 ta) p p' (BVT 0 xloc) xloc
     whnf defs ctx sg $ CaseBox qty (Ann val (ty // one p) val.loc) ret
       (ST body.names $ body.term // (a' ::: shift 1)) loc
 
@@ -150,14 +157,14 @@ parameters {auto _ : CanWhnf Term Interface.isRedexT}
 -- new params block to call the above functions at different `n`
 parameters {auto _ : CanWhnf Term Interface.isRedexT}
            {auto _ : CanWhnf Elim Interface.isRedexE}
-           (defs : Definitions) (ctx : WhnfContext d n) (sg : SQty)
+           (defs : Definitions) (ctx : WhnfContext q d n) (sg : SQty)
   ||| pushes a coercion inside a whnf-ed term
   export covering
   pushCoe : BindName ->
-            (ty : Term (S d) n) -> (p, q : Dim d) -> (s : Term d n) -> Loc ->
-            (0 pc : So (canPushCoe sg ty s)) =>
-            Eff Whnf (NonRedex Elim d n defs ctx sg)
-  pushCoe i ty p q s loc =
+            (ty : Term q (S d) n) -> (p, p' : Dim d) -> (s : Term q d n) ->
+            Loc -> (0 pc : So (canPushCoe sg ty s)) =>
+            Eff Whnf (NonRedex Elim q d n defs ctx sg)
+  pushCoe i ty p p' s loc =
     case ty of
       -- (coe ★ᵢ @_ @_ s) ⇝ (s ∷ ★ᵢ)
       TYPE l tyLoc =>
@@ -169,40 +176,40 @@ parameters {auto _ : CanWhnf Term Interface.isRedexT}
 
       -- η expand, then simplify the Coe/App in the body
       --
-      -- (coe (𝑖 ⇒ π.(x : A) → B) @p @q s)
+      -- (coe (𝑖 ⇒ π.(x : A) → B) @p @p' s)
       --   ⇝
-      -- (λ y ⇒ (coe (𝑖 ⇒ π.(x : A) → B) @p @q s) y) ∷ (π.(x : A) → B)‹q/𝑖›
-      --   ⇝     ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
-      -- (λ y ⇒ ⋯) ∷ (π.(x : A) → B)‹q/𝑖›   -- see `piCoe`
+      -- (λ y ⇒ (coe (𝑖 ⇒ π.(x : A) → B) @p @p' s) y) ∷ (π.(x : A) → B)‹p'/𝑖›
+      --   ⇝     ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
+      -- (λ y ⇒ ⋯) ∷ (π.(x : A) → B)‹p'/𝑖›   -- see `piCoe`
       --
       -- do the piCoe step here because otherwise equality checking keeps
       -- doing the η forever
       Pi {arg, res = S [< x] _, _} => do
         let ctx' = extendTy x (arg // one p) ctx
         body <- piCoe defs ctx' sg
-          (weakDS 1 $ SY [< i] ty) p q (weakT 1 s) (BVT 0 loc) loc
+          (weakDS 1 $ SY [< i] ty) p p' (weakT 1 s) (BVT 0 loc) loc
         whnf defs ctx sg $
-          Ann (LamY x (E body.fst) loc) (ty // one q) loc
+          Ann (LamY x (E body.fst) loc) (ty // one p') loc
 
-      -- no η!!!
       -- push into a pair constructor, otherwise still stuck
       --
       --   s̃‹𝑘› ≔ coe (𝑗 ⇒ A‹𝑗/𝑖›) @p @𝑘 s
       -- -----------------------------------------------
-      --   (coe (𝑖 ⇒ (x : A) × B) @p @q (s, t))
+      --   (coe (𝑖 ⇒ (x : A) × B) @p @p' (s, t))
       --     ⇝
-      --   (s̃‹q›, coe (𝑖 ⇒ B[s̃‹𝑖›/x]) @p @q t)
-      --     ∷ ((x : A) × B)‹q/𝑖›
+      --   (s̃‹p'›, coe (𝑖 ⇒ B[s̃‹𝑖›/x]) @p @p' t)
+      --     ∷ ((x : A) × B)‹p'/𝑖›
       Sig tfst tsnd tyLoc => do
-        let Pair fst snd sLoc = s
-            fst' = CoeT i tfst p q fst fst.loc
+        let Val q = ctx.qtyLen
+            Pair fst snd sLoc = s
+            fst' = CoeT i tfst p p' fst fst.loc
             fstInSnd =
               CoeT !(fresh i)
                    (tfst // (BV 0 loc ::: shift 2))
                    (weakD 1 p) (BV 0 loc) (dweakT 1 fst) fst.loc
-            snd' = CoeT i (sub1 tsnd fstInSnd) p q snd snd.loc
+            snd' = CoeT i (sub1 tsnd fstInSnd) p p' snd snd.loc
         whnf defs ctx sg $
-          Ann (Pair (E fst') (E snd') sLoc) (ty // one q) loc
+          Ann (Pair (E fst') (E snd') sLoc) (ty // one p') loc
 
       -- (coe {𝐚̄} @_ @_ s) ⇝ (s ∷ {𝐚̄})
       Enum cases tyLoc =>
@@ -210,21 +217,21 @@ parameters {auto _ : CanWhnf Term Interface.isRedexT}
 
       -- η expand/simplify, same as for Π
       --
-      -- (coe (𝑖 ⇒ Eq (𝑗 ⇒ A) l r) @p @q s)
+      -- (coe (𝑖 ⇒ Eq (𝑗 ⇒ A) l r) @p @p' s)
       --   ⇝
-      -- (δ 𝑘 ⇒ (coe (𝑖 ⇒ Eq (𝑗 ⇒ A) l r) @p @q s) @𝑘) ∷ (Eq (𝑗 ⇒ A) l r)‹q/𝑖›
-      --   ⇝     ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
-      -- (δ 𝑘 ⇒ ⋯) ∷ (Eq (𝑗 ⇒ A) l r)‹q/𝑖›   -- see `eqCoe`
+      -- (δ 𝑘 ⇒ (coe (𝑖 ⇒ Eq (𝑗 ⇒ A) l r) @p @p' s) @𝑘) ∷ (Eq (𝑗 ⇒ A) l r)‹p'/𝑖›
+      --   ⇝     ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
+      -- (δ 𝑘 ⇒ ⋯) ∷ (Eq (𝑗 ⇒ A) l r)‹p'/𝑖›   -- see `eqCoe`
       --
       -- do the eqCoe step here because otherwise equality checking keeps
       -- doing the η forever
       Eq {ty = S [< j] _, _} => do
         let ctx' = extendDim j ctx
         body <- eqCoe defs ctx' sg
-          (dweakDS 1 $ S [< i] $ Y ty) (weakD 1 p) (weakD 1 q)
+          (dweakDS 1 $ S [< i] $ Y ty) (weakD 1 p) (weakD 1 p')
           (dweakT 1 s) (BV 0 loc) loc
         whnf defs ctx sg $
-          Ann (DLamY i (E body.fst) loc) (ty // one q) loc
+          Ann (DLamY i (E body.fst) loc) (ty // one p') loc
 
       -- (coe ℕ @_ @_ s) ⇝ (s ∷ ℕ)
       NAT tyLoc =>
@@ -236,17 +243,17 @@ parameters {auto _ : CanWhnf Term Interface.isRedexT}
 
       -- η expand/simplify
       --
-      -- (coe (𝑖 ⇒ [π.A]) @p @q s)
+      -- (coe (𝑖 ⇒ [π.A]) @p @p' s)
       --   ⇝
-      -- [case coe (𝑖 ⇒ [π.A]) @p @q s return A‹q/𝑖› of {[x] ⇒ x}]
+      -- [case coe (𝑖 ⇒ [π.A]) @p @p' s return A‹p'/𝑖› of {[x] ⇒ x}]
       --   ⇝
-      -- [case1 s ∷ [π.A]‹p/𝑖› ⋯] ∷ [π.A]‹q/𝑖›   -- see `boxCoe`
+      -- [case1 s ∷ [π.A]‹p/𝑖› ⋯] ∷ [π.A]‹p'/𝑖›   -- see `boxCoe`
       --
-      -- do the eqCoe step here because otherwise equality checking keeps
+      -- do the boxCoe step here because otherwise equality checking keeps
       -- doing the η forever
       BOX qty inner tyLoc => do
         body <- boxCoe defs ctx sg qty
-          (SY [< i] ty) p q s
-          (SN $ inner // one q)
+          (SY [< i] ty) p p' s
+          (SN $ inner // one p')
           (SY [< !(mnb "inner" loc)] (BVT 0 loc)) loc
-        whnf defs ctx sg $ Ann (Box (E body.fst) loc) (ty // one q) loc
+        whnf defs ctx sg $ Ann (Box (E body.fst) loc) (ty // one p') loc
diff --git a/lib/Quox/Whnf/ComputeElimType.idr b/lib/Quox/Whnf/ComputeElimType.idr
index 3661c12..2994d69 100644
--- a/lib/Quox/Whnf/ComputeElimType.idr
+++ b/lib/Quox/Whnf/ComputeElimType.idr
@@ -15,46 +15,44 @@ export covering
 computeElimType :
   CanWhnf Term Interface.isRedexT =>
   CanWhnf Elim Interface.isRedexE =>
-  (defs : Definitions) -> (ctx : WhnfContext d n) -> (0 sg : SQty) ->
-  (e : Elim d n) -> (0 ne : No (isRedexE defs ctx sg e)) =>
-  Eff Whnf (Term d n)
+  (defs : Definitions) -> (ctx : WhnfContext q d n) -> (0 sg : SQty) ->
+  (e : Elim q d n) -> (0 ne : No (isRedexE defs ctx sg e)) =>
+  Eff Whnf (Term q d n)
 
 ||| computes a type and then reduces it to whnf
 export covering
 computeWhnfElimType0 :
   CanWhnf Term Interface.isRedexT =>
   CanWhnf Elim Interface.isRedexE =>
-  (defs : Definitions) -> (ctx : WhnfContext d n) -> (0 sg : SQty) ->
-  (e : Elim d n) -> (0 ne : No (isRedexE defs ctx sg e)) =>
-  Eff Whnf (Term d n)
+  (defs : Definitions) -> (ctx : WhnfContext q d n) -> (0 sg : SQty) ->
+  (e : Elim q d n) -> (0 ne : No (isRedexE defs ctx sg e)) =>
+  Eff Whnf (Term q d n)
 
 
 private covering
 computeElimTypeNoLog, computeWhnfElimType0NoLog :
   CanWhnf Term Interface.isRedexT =>
   CanWhnf Elim Interface.isRedexE =>
-  (defs : Definitions) -> WhnfContext d n -> (0 sg : SQty) ->
-  (e : Elim d n) -> (0 ne : No (isRedexE defs ctx sg e)) =>
-  Eff Whnf (Term d n)
+  (defs : Definitions) -> WhnfContext q d n -> (0 sg : SQty) ->
+  (e : Elim q d n) -> (0 ne : No (isRedexE defs ctx sg e)) =>
+  Eff Whnf (Term q d n)
 
 computeElimTypeNoLog defs ctx sg e =
   case e of
     F x u loc => do
       let Just def = lookup x defs
         | Nothing => throw $ NotInScope loc x
-      pure $ def.typeWithAt ctx.dimLen ctx.termLen u
+      let polyTy = def.typeWithAt ctx.dimLen ctx.termLen u
+          Val q  = ctx.qtyLen
+      pure $ polyTy.type // ?freeQSubst
 
-    B i _ =>
-      pure (ctx.tctx !! i).type
+    B i _ => pure (ctx.tctx !! i).type
 
     App f s loc =>
       case !(computeWhnfElimType0NoLog defs ctx sg f {ne = noOr1 ne}) of
         Pi {arg, res, _} => pure $ sub1 res $ Ann s arg loc
         ty               => throw $ ExpectedPi loc ctx.names ty
 
-    CasePair {pair, ret, _} =>
-      pure $ sub1 ret pair
-
     Fst pair loc =>
       case !(computeWhnfElimType0NoLog defs ctx sg pair {ne = noOr1 ne}) of
         Sig {fst, _} => pure fst
@@ -65,46 +63,34 @@ computeElimTypeNoLog defs ctx sg e =
         Sig {snd, _} => pure $ sub1 snd $ Fst pair loc
         ty           => throw $ ExpectedSig loc ctx.names ty
 
-    CaseEnum {tag, ret, _} =>
-      pure $ sub1 ret tag
-
-    CaseNat {nat, ret, _} =>
-      pure $ sub1 ret nat
-
-    CaseBox {box, ret, _} =>
-      pure $ sub1 ret box
+    CasePair {pair, ret, _} => pure $ sub1 ret pair
+    CaseEnum {tag, ret, _}  => pure $ sub1 ret tag
+    CaseNat  {nat, ret, _}  => pure $ sub1 ret nat
+    CaseBox  {box, ret, _}  => pure $ sub1 ret box
 
     DApp {fun = f, arg = p, loc} =>
       case !(computeWhnfElimType0NoLog defs ctx sg f {ne = noOr1 ne}) of
         Eq {ty, _} => pure $ dsub1 ty p
         t          => throw $ ExpectedEq loc ctx.names t
 
-    Ann {ty, _} =>
-      pure ty
-
-    Coe {ty, q, _} =>
-      pure $ dsub1 ty q
-
-    Comp {ty, _} =>
-      pure ty
-
-    TypeCase {ret, _} =>
-      pure ret
+    Ann      {ty, _}     => pure ty
+    Coe      {ty, p', _} => pure $ dsub1 ty p'
+    Comp     {ty, _}     => pure ty
+    TypeCase {ret, _}    => pure ret
 
 computeElimType defs ctx sg e {ne} = do
   let Val n = ctx.termLen
   sayMany "whnf" e.loc
     [90 :> "computeElimType",
      95 :> hsep ["ctx =", runPretty $ prettyWhnfContext ctx],
-     90 :> hsep ["e =", runPretty $ prettyElim ctx.dnames ctx.tnames e]]
+     90 :> hsep ["e =", runPretty $ prettyElim ctx.names e]]
   res <- computeElimTypeNoLog defs ctx sg e {ne}
   say "whnf" 91 e.loc $
-    hsep ["computeElimType ⇝",
-          runPretty $ prettyTerm ctx.dnames ctx.tnames res]
+    hsep ["computeElimType ⇝", runPretty $ prettyTerm ctx.names res]
   pure res
 
 computeWhnfElimType0 defs ctx sg e =
-  computeElimType defs ctx sg e >>= whnf0 defs ctx SZero
+  whnf0 defs ctx SZero !(computeElimType defs ctx sg e)
 
 computeWhnfElimType0NoLog defs ctx sg e {ne} =
-  computeElimTypeNoLog defs ctx sg e {ne} >>= whnf0 defs ctx SZero
+  whnf0 defs ctx SZero !(computeElimTypeNoLog defs ctx sg e {ne})
diff --git a/lib/Quox/Whnf/Interface.idr b/lib/Quox/Whnf/Interface.idr
index e516f62..9632cc4 100644
--- a/lib/Quox/Whnf/Interface.idr
+++ b/lib/Quox/Whnf/Interface.idr
@@ -20,14 +20,15 @@ Whnf = [Except Error, NameGen, Log]
 public export
 0 RedexTest : TermLike -> Type
 RedexTest tm =
-  {0 d, n : Nat} -> Definitions -> WhnfContext d n -> SQty -> tm d n -> Bool
+  {0 q, d, n : Nat} ->
+  Definitions -> WhnfContext q d n -> SQty -> tm q d n -> Bool
 
 public export
 interface CanWhnf (0 tm : TermLike) (0 isRedex : RedexTest tm) | tm
 where
   whnf, whnfNoLog :
-    (defs : Definitions) -> (ctx : WhnfContext d n) -> (q : SQty) ->
-    tm d n -> Eff Whnf (Subset (tm d n) (No . isRedex defs ctx q))
+    (defs : Definitions) -> (ctx : WhnfContext q d n) -> (sg : SQty) ->
+    tm q d n -> Eff Whnf (Subset (tm q d n) (No . isRedex defs ctx sg))
   -- having isRedex be part of the class header, and needing to be explicitly
   -- quantified on every use since idris can't infer its type, is a little ugly.
   -- but none of the alternatives i've thought of so far work. e.g. in some
@@ -36,26 +37,27 @@ where
 public export %inline
 whnf0, whnfNoLog0 :
   {0 isRedex : RedexTest tm} -> CanWhnf tm isRedex =>
-  Definitions -> WhnfContext d n -> SQty -> tm d n -> Eff Whnf (tm d n)
+  Definitions -> WhnfContext q d n -> SQty -> tm q d n -> Eff Whnf (tm q d n)
 whnf0      defs ctx q t = fst <$> whnf defs ctx q t
 whnfNoLog0 defs ctx q t = fst <$> whnfNoLog defs ctx q t
 
 public export
 0 IsRedex, NotRedex : {isRedex : RedexTest tm} -> CanWhnf tm isRedex =>
-                      Definitions -> WhnfContext d n -> SQty -> Pred (tm d n)
+                      Definitions -> WhnfContext q d n -> SQty ->
+                      Pred (tm q d n)
 IsRedex  defs ctx q = So . isRedex defs ctx q
 NotRedex defs ctx q = No . isRedex defs ctx q
 
 public export
 0 NonRedex : (tm : TermLike) -> {isRedex : RedexTest tm} ->
-             CanWhnf tm isRedex => (d, n : Nat) ->
-             Definitions -> WhnfContext d n -> SQty -> Type
-NonRedex tm d n defs ctx q = Subset (tm d n) (NotRedex defs ctx q)
+             CanWhnf tm isRedex => (q, d, n : Nat) ->
+             Definitions -> WhnfContext q d n -> SQty -> Type
+NonRedex tm q d n defs ctx sg = Subset (tm q d n) (NotRedex defs ctx sg)
 
 public export %inline
 nred : {0 isRedex : RedexTest tm} -> (0 _ : CanWhnf tm isRedex) =>
-       (t : tm d n) -> (0 nr : NotRedex defs ctx q t) =>
-       NonRedex tm d n defs ctx q
+       (t : tm q d n) -> (0 nr : NotRedex defs ctx sg t) =>
+       NonRedex tm q d n defs ctx sg
 nred t = Element t nr
 
 
@@ -97,7 +99,7 @@ isNatHead _                          = False
 
 ||| a natural constant, with or without an annotation
 public export %inline
-isNatConst : Term d n -> Bool
+isNatConst : Term {} -> Bool
 isNatConst (Nat {})               = True
 isNatConst (E (Ann (Nat {}) _ _)) = True
 isNatConst _                      = False
@@ -145,6 +147,7 @@ isTyCon (Let     {}) = False
 isTyCon (E       {}) = False
 isTyCon (CloT    {}) = False
 isTyCon (DCloT   {}) = False
+isTyCon (QCloT   {}) = False
 
 ||| a syntactic type, or a neutral
 public export %inline
@@ -195,6 +198,7 @@ canPushCoe sg (Let     {}) _         = False
 canPushCoe sg (E       {}) _         = False
 canPushCoe sg (CloT    {}) _         = False
 canPushCoe sg (DCloT   {}) _         = False
+canPushCoe sg (QCloT   {}) _         = False
 
 
 mutual
@@ -238,15 +242,16 @@ mutual
   isRedexE defs ctx sg (Ann {tm, ty, _}) =
     isE tm || isRedexT defs ctx sg tm || isRedexT defs ctx SZero ty
   isRedexE defs ctx sg (Coe {ty = S _ (N _), _}) = True
-  isRedexE defs ctx sg (Coe {ty = S [< i] (Y ty), p, q, val, _}) =
+  isRedexE defs ctx sg (Coe {ty = S [< i] (Y ty), p, p', val, _}) =
     isRedexT defs (extendDim i ctx) SZero ty ||
-    canPushCoe sg ty val || isYes (p `decEqv` q)
-  isRedexE defs ctx sg (Comp {ty, p, q, r, _}) =
-    isYes (p `decEqv` q) || isK r
+    canPushCoe sg ty val || isYes (p `decEqv` p')
+  isRedexE defs ctx sg (Comp {ty, p, p', r, _}) =
+    isYes (p `decEqv` p') || isK r
   isRedexE defs ctx sg (TypeCase {ty, ret, _}) =
     isRedexE defs ctx sg ty || isRedexT defs ctx sg ret || isAnnTyCon ty
   isRedexE _ _ _ (CloE  {}) = True
   isRedexE _ _ _ (DCloE {}) = True
+  isRedexE _ _ _ (QCloE {}) = True
 
   ||| a reducible term
   |||
@@ -260,6 +265,7 @@ mutual
   isRedexT : RedexTest Term
   isRedexT _    _   _  (CloT  {})  = True
   isRedexT _    _   _  (DCloT {})  = True
+  isRedexT _    _   _  (QCloT {})  = True
   isRedexT _    _   _  (Let   {})  = True
   isRedexT defs ctx sg (E {e, _})  = isAnn e || isRedexE defs ctx sg e
   isRedexT _    _   _  (Succ p {}) = isNatConst p
diff --git a/lib/Quox/Whnf/Main.idr b/lib/Quox/Whnf/Main.idr
index 1c3bcc4..ee46712 100644
--- a/lib/Quox/Whnf/Main.idr
+++ b/lib/Quox/Whnf/Main.idr
@@ -19,19 +19,19 @@ export covering CanWhnf Elim Interface.isRedexE
 private %inline
 whnfDefault :
   {0 isRedex : RedexTest tm} ->
-  (CanWhnf tm isRedex, Located2 tm) =>
+  (CanWhnf tm isRedex, Located3 tm) =>
   String ->
-  (forall d, n. WhnfContext d n -> tm d n -> Eff Pretty LogDoc) ->
+  (forall d, n. WhnfContext q d n -> tm q d n -> Eff Pretty LogDoc) ->
   (defs : Definitions) ->
-  (ctx : WhnfContext d n) ->
+  (ctx : WhnfContext q d n) ->
   (sg : SQty) ->
-  (s : tm d n) ->
-  Eff Whnf (Subset (tm d n) (No . isRedex defs ctx sg))
+  (s : tm q d n) ->
+  Eff Whnf (Subset (tm q d n) (No . isRedex defs ctx sg))
 whnfDefault name ppr defs ctx sg s = do
   sayMany "whnf" s.loc
     [10 :> "whnf",
      95 :> hsep ["ctx =", runPretty $ prettyWhnfContext ctx],
-     95 :> hsep ["sg =", runPretty $ prettyQty sg.qty],
+     95 :> hsep ["sg =", runPretty $ prettyQConst sg.qconst],
      10 :> hsep [text name, "=", runPretty $ ppr ctx s]]
   res <- whnfNoLog defs ctx sg s
   say "whnf" 11 s.loc $ hsep ["whnf ⇝", runPretty $ ppr ctx res.fst]
@@ -39,10 +39,10 @@ whnfDefault name ppr defs ctx sg s = do
 
 covering
 CanWhnf Elim Interface.isRedexE where
-  whnf = whnfDefault "e" $ \ctx, e => prettyElim ctx.dnames ctx.tnames e
+  whnf = whnfDefault "e" $ \ctx, e => prettyElim ctx.names e
 
   whnfNoLog defs ctx sg (F x u loc) with (lookupElim0 x u defs) proof eq
-    _ | Just y  = whnf defs ctx sg $ setLoc loc $ injElim ctx y
+    _ | Just y  = whnf defs ctx sg $ setLoc loc $ ?whnfFreeQSubst
     _ | Nothing = pure $ Element (F x u loc) $ rewrite eq in Ah
 
   whnfNoLog defs ctx sg (B i loc) with (ctx.tctx !! i) proof eq1
@@ -186,8 +186,8 @@ CanWhnf Elim Interface.isRedexE where
           whnf defs ctx sg $
             Ann (endsOr (setLoc appLoc l) (setLoc appLoc r) (dsub1 body p) p)
                 (dsub1 ty p) appLoc
-        Coe ty p' q' val _ =>
-          eqCoe defs ctx sg ty p' q' val p appLoc
+        Coe ty r r' val _ =>
+          eqCoe defs ctx sg ty r r' val p appLoc
       Right ndlh => case p of
         K e _ => do
           Eq {l, r, ty, _} <- computeWhnfElimType0 defs ctx sg f
@@ -206,36 +206,37 @@ CanWhnf Elim Interface.isRedexE where
         Element a anf <- whnf defs ctx SZero a
         pure $ Element (Ann s a annLoc) (ne `orNo` snf `orNo` anf)
 
-  whnfNoLog defs ctx sg (Coe sty p q val coeLoc) =
+  whnfNoLog defs ctx sg (Coe sty p p' val coeLoc) = do
     --   𝑖 ∉ fv(A)
     -- -------------------------------
-    --   coe (𝑖 ⇒ A) @p @q s ⇝ s ∷ A
+    --   coe (𝑖 ⇒ A) @p @p' s ⇝ s ∷ A
     --
     -- [fixme] needs a real equality check between A‹0/𝑖› and A‹1/𝑖›
-    case dsqueeze sty {f = Term} of
+    let Val q = ctx.qtyLen
+    case dsqueeze sty {f = Term q} of
       ([< i], Left ty) =>
-        case p `decEqv` q of
+        case p `decEqv` p' of
           -- coe (𝑖 ⇒ A) @p @p s ⇝ (s ∷ A‹p/𝑖›)
           Yes _   => whnf defs ctx sg $ Ann val (dsub1 sty p) coeLoc
           No  npq => do
             Element ty tynf <- whnf defs (extendDim i ctx) SZero ty
             case nchoose $ canPushCoe sg ty val of
-              Left  pc  => pushCoe defs ctx sg i ty p q val coeLoc
-              Right npc => pure $ Element (Coe (SY [< i] ty) p q val coeLoc)
+              Left  pc  => pushCoe defs ctx sg i ty p p' val coeLoc
+              Right npc => pure $ Element (Coe (SY [< i] ty) p p' val coeLoc)
                                           (tynf `orNo` npc `orNo` notYesNo npq)
       (_, Right ty) =>
         whnf defs ctx sg $ Ann val ty coeLoc
 
-  whnfNoLog defs ctx sg (Comp ty p q val r zero one compLoc) =
-    case p `decEqv` q of
+  whnfNoLog defs ctx sg (Comp ty p p' val r zero one compLoc) =
+    case p `decEqv` p' of
       -- comp [A] @p @p s @r { ⋯ } ⇝ s ∷ A
       Yes y   => whnf defs ctx sg $ Ann val ty compLoc
       No  npq => case r of
-        -- comp [A] @p @q s @0 { 0 𝑗 ⇒ t₀; ⋯ } ⇝ t₀‹q/𝑗› ∷ A
-        K Zero _ => whnf defs ctx sg $ Ann (dsub1 zero q) ty compLoc
-        -- comp [A] @p @q s @1 { 1 𝑗 ⇒ t₁; ⋯ } ⇝ t₁‹q/𝑗› ∷ A
-        K One  _ => whnf defs ctx sg $ Ann (dsub1 one  q) ty compLoc
-        B {}     => pure $ Element (Comp ty p q val r zero one compLoc)
+        -- comp [A] @p @p' s @0 { 0 𝑗 ⇒ t₀; ⋯ } ⇝ t₀‹p'/𝑗› ∷ A
+        K Zero _ => whnf defs ctx sg $ Ann (dsub1 zero p') ty compLoc
+        -- comp [A] @p @p' s @1 { 1 𝑗 ⇒ t₁; ⋯ } ⇝ t₁‹p'/𝑗› ∷ A
+        K One  _ => whnf defs ctx sg $ Ann (dsub1 one  p') ty compLoc
+        B {}     => pure $ Element (Comp ty p p' val r zero one compLoc)
                                    (notYesNo npq `orNo` Ah)
 
   whnfNoLog defs ctx sg (TypeCase ty ret arms def tcLoc) =
@@ -248,17 +249,23 @@ CanWhnf Elim Interface.isRedexE where
                       reduceTypeCase defs ctx ty u ret arms def tcLoc
           Right nt => pure $ Element (TypeCase ty ret arms def tcLoc)
                                      (tynf `orNo` retnf `orNo` nt)
-      No _ =>
-        throw $ ClashQ tcLoc sg.qty Zero
+      No _ => do
+        let Val q = ctx.qtyLen
+        throw $ ClashQ tcLoc ctx.qnames (toQty tcLoc sg) (zero tcLoc)
 
-  whnfNoLog defs ctx sg (CloE (Sub el th)) =
-    whnfNoLog defs ctx sg $ pushSubstsWith' id th el
-  whnfNoLog defs ctx sg (DCloE (Sub el th)) =
-    whnfNoLog defs ctx sg $ pushSubstsWith' th id el
+  whnfNoLog defs ctx sg (CloE (Sub el th)) = do
+    let Val q = ctx.qtyLen
+    whnfNoLog defs ctx sg $ pushSubstsWith' id id th el
+  whnfNoLog defs ctx sg (DCloE (Sub el th)) = do
+    let Val q = ctx.qtyLen
+    whnfNoLog defs ctx sg $ pushSubstsWith' id th id el
+  whnfNoLog defs ctx sg (QCloE (SubR el th)) = do
+    let Val q = ctx.qtyLen
+    whnfNoLog defs ctx sg $ pushSubstsWith' th id id el
 
 covering
 CanWhnf Term Interface.isRedexT where
-  whnf = whnfDefault "e" $ \ctx, s => prettyTerm ctx.dnames ctx.tnames s
+  whnf = whnfDefault "e" $ \ctx, s => prettyTerm ctx.names s
 
   whnfNoLog _ _ _ t@(TYPE    {}) = pure $ nred t
   whnfNoLog _ _ _ t@(IOState {}) = pure $ nred t
@@ -294,7 +301,14 @@ CanWhnf Term Interface.isRedexT where
       Left  _  => let Ann {tm, _} = e in pure $ Element tm $ noOr1 $ noOr2 enf
       Right na => pure $ Element (E e) $ na `orNo` enf
 
-  whnfNoLog defs ctx sg (CloT (Sub tm th)) =
-    whnfNoLog defs ctx sg $ pushSubstsWith' id th tm
-  whnfNoLog defs ctx sg (DCloT (Sub tm th)) =
-    whnfNoLog defs ctx sg $ pushSubstsWith' th id tm
+  whnfNoLog defs ctx sg (CloT (Sub tm th)) = do
+    let Val q = ctx.qtyLen
+    whnfNoLog defs ctx sg $ pushSubstsWith' id id th tm
+
+  whnfNoLog defs ctx sg (DCloT (Sub tm th)) = do
+    let Val q = ctx.qtyLen
+    whnfNoLog defs ctx sg $ pushSubstsWith' id th id tm
+
+  whnfNoLog defs ctx sg (QCloT (SubR tm th)) = do
+    let Val q = ctx.qtyLen
+    whnfNoLog defs ctx sg $ pushSubstsWith' th id id tm
diff --git a/lib/Quox/Whnf/TypeCase.idr b/lib/Quox/Whnf/TypeCase.idr
index 9b3645f..e6a4de9 100644
--- a/lib/Quox/Whnf/TypeCase.idr
+++ b/lib/Quox/Whnf/TypeCase.idr
@@ -8,44 +8,45 @@ import Data.SnocVect
 
 
 private
-tycaseRhs : (k : TyConKind) -> TypeCaseArms d n ->
-            Maybe (ScopeTermN (arity k) d n)
+tycaseRhs : (k : TyConKind) -> TypeCaseArms q d n ->
+            Maybe (ScopeTermN (arity k) q d n)
 tycaseRhs k arms = lookupPrecise k arms
 
 private
-tycaseRhsDef : Term d n -> (k : TyConKind) -> TypeCaseArms d n ->
-               ScopeTermN (arity k) d n
+tycaseRhsDef : (def : Term q d n) -> (k : TyConKind) -> TypeCaseArms q d n ->
+               ScopeTermN (arity k) q d n
 tycaseRhsDef def k arms = fromMaybe (SN def) $ tycaseRhs k arms
 
 private
-tycaseRhs0 : (k : TyConKind) -> TypeCaseArms d n ->
-             (0 eq : arity k = 0) => Maybe (Term d n)
+tycaseRhs0 : (k : TyConKind) -> TypeCaseArms q d n ->
+             (0 eq : arity k = 0) => Maybe (Term q d n)
 tycaseRhs0 k arms = map (.term0) $ rewrite sym eq in tycaseRhs k arms
 
 private
-tycaseRhsDef0 : Term d n -> (k : TyConKind) -> TypeCaseArms d n ->
-                (0 eq : arity k = 0) => Term d n
+tycaseRhsDef0 : (def : Term q d n) -> (k : TyConKind) -> TypeCaseArms q d n ->
+                (0 eq : arity k = 0) => Term q d n
 tycaseRhsDef0 def k arms = fromMaybe def $ tycaseRhs0 k arms
 
 
 parameters {auto _ : CanWhnf Term Interface.isRedexT}
            {auto _ : CanWhnf Elim Interface.isRedexE}
-           (defs : Definitions) (ctx : WhnfContext d n)
+           (defs : Definitions) (ctx : WhnfContext q d n)
   ||| for π.(x : A) → B, returns (A, B);
   ||| for an elim returns a pair of type-cases that will reduce to that;
   ||| for other intro forms error
   export covering
-  tycasePi : (t : Term d n) -> (0 tnf : No (isRedexT defs ctx SZero t)) =>
-             Eff Whnf (Term d n, ScopeTerm d n)
+  tycasePi : (t : Term q d n) -> (0 tnf : No (isRedexT defs ctx SZero t)) =>
+             Eff Whnf (Term q d n, ScopeTerm q d n)
   tycasePi (Pi {arg, res, _}) = pure (arg, res)
   tycasePi (E e) {tnf} = do
     ty <- computeElimType defs ctx SZero e {ne = noOr2 tnf}
-    let loc  = e.loc
-        narg = mnb "Arg" loc; nret = mnb "Ret" loc
-        arg  = E $ typeCase1Y e ty KPi [< !narg, !nret] (BVT 1 loc) loc
-        res' = typeCase1Y e (Arr Zero arg ty loc) KPi [< !narg, !nret]
+    let Val q = ctx.qtyLen
+        loc   = e.loc
+        narg  = mnb "Arg" loc; nret = mnb "Ret" loc
+        arg   = E $ typeCase1Y e ty KPi [< !narg, !nret] (BVT 1 loc) loc
+        res'  = typeCase1Y e (Arr (zero loc) arg ty loc) KPi [< !narg, !nret]
                  (BVT 0 loc) loc
-        res  = ST [< !narg] $ E $ App (weakE 1 res') (BVT 0 loc) loc
+        res   = ST [< !narg] $ E $ App (weakE 1 res') (BVT 0 loc) loc
     pure (arg, res)
   tycasePi t = throw $ ExpectedPi t.loc ctx.names t
 
@@ -53,17 +54,18 @@ parameters {auto _ : CanWhnf Term Interface.isRedexT}
   ||| for an elim returns a pair of type-cases that will reduce to that;
   ||| for other intro forms error
   export covering
-  tycaseSig : (t : Term d n) -> (0 tnf : No (isRedexT defs ctx SZero t)) =>
-              Eff Whnf (Term d n, ScopeTerm d n)
+  tycaseSig : (t : Term q d n) -> (0 tnf : No (isRedexT defs ctx SZero t)) =>
+              Eff Whnf (Term q d n, ScopeTerm q d n)
   tycaseSig (Sig {fst, snd, _}) = pure (fst, snd)
   tycaseSig (E e) {tnf} = do
     ty <- computeElimType defs ctx SZero e {ne = noOr2 tnf}
-    let loc  = e.loc
-        nfst = mnb "Fst" loc; nsnd = mnb "Snd" loc
-        fst  = E $ typeCase1Y e ty KSig [< !nfst, !nsnd] (BVT 1 loc) loc
-        snd' = typeCase1Y e (Arr Zero fst ty loc) KSig [< !nfst, !nsnd]
+    let Val q = ctx.qtyLen
+        loc   = e.loc
+        nfst  = mnb "Fst" loc; nsnd = mnb "Snd" loc
+        fst   = E $ typeCase1Y e ty KSig [< !nfst, !nsnd] (BVT 1 loc) loc
+        snd'  = typeCase1Y e (Arr (zero loc) fst ty loc) KSig [< !nfst, !nsnd]
                  (BVT 0 loc) loc
-        snd  = ST [< !nfst] $ E $ App (weakE 1 snd') (BVT 0 loc) loc
+        snd   = ST [< !nfst] $ E $ App (weakE 1 snd') (BVT 0 loc) loc
     pure (fst, snd)
   tycaseSig t = throw $ ExpectedSig t.loc ctx.names t
 
@@ -71,8 +73,8 @@ parameters {auto _ : CanWhnf Term Interface.isRedexT}
   ||| for an elim returns a type-case that will reduce to that;
   ||| for other intro forms error
   export covering
-  tycaseBOX : (t : Term d n) -> (0 tnf : No (isRedexT defs ctx SZero t)) =>
-              Eff Whnf (Term d n)
+  tycaseBOX : (t : Term q d n) -> (0 tnf : No (isRedexT defs ctx SZero t)) =>
+              Eff Whnf (Term q d n)
   tycaseBOX (BOX {ty, _}) = pure ty
   tycaseBOX (E e) {tnf} = do
     ty <- computeElimType defs ctx SZero e {ne = noOr2 tnf}
@@ -83,12 +85,14 @@ parameters {auto _ : CanWhnf Term Interface.isRedexT}
   ||| for an elim returns five type-cases that will reduce to that;
   ||| for other intro forms error
   export covering
-  tycaseEq : (t : Term d n) -> (0 tnf : No (isRedexT defs ctx SZero t)) =>
-             Eff Whnf (Term d n, Term d n, DScopeTerm d n, Term d n, Term d n)
+  tycaseEq : (t : Term q d n) -> (0 tnf : No (isRedexT defs ctx SZero t)) =>
+             Eff Whnf (Term q d n, Term q d n, DScopeTerm q d n,
+                       Term q d n, Term q d n)
   tycaseEq (Eq {ty, l, r, _}) = pure (ty.zero, ty.one, ty, l, r)
   tycaseEq (E e) {tnf} = do
     ty <- computeElimType defs ctx SZero e {ne = noOr2 tnf}
-    let loc   = e.loc
+    let Val q = ctx.qtyLen
+        loc   = e.loc
         names = traverse' (\x => mnb x loc) [< "A0", "A1", "A", "L", "R"]
         a0    = E $ typeCase1Y e ty KEq !names (BVT 4 loc) loc
         a1    = E $ typeCase1Y e ty KEq !names (BVT 3 loc) loc
@@ -104,10 +108,10 @@ parameters {auto _ : CanWhnf Term Interface.isRedexT}
   ||| `reduceTypeCase A i Q arms def _` reduces an expression
   ||| `type-case A ∷ ★ᵢ return Q of { arms; _ ⇒ def }`
   export covering
-  reduceTypeCase : (ty : Term d n) -> (u : Universe) -> (ret : Term d n) ->
-                   (arms : TypeCaseArms d n) -> (def : Term d n) ->
+  reduceTypeCase : (ty : Term q d n) -> (u : Universe) -> (ret : Term q d n) ->
+                   (arms : TypeCaseArms q d n) -> (def : Term q d n) ->
                    (0 _ : So (isTyCon ty)) => Loc ->
-                   Eff Whnf (Subset (Elim d n) (No . isRedexE defs ctx SZero))
+                   Eff Whnf (Subset (Elim q d n) (No . isRedexE defs ctx SZero))
   reduceTypeCase ty u ret arms def loc = case ty of
     -- (type-case ★ᵢ ∷ _ return Q of { ★ ⇒ s; ⋯ }) ⇝ s ∷ Q
     TYPE {} =>
@@ -120,9 +124,10 @@ parameters {auto _ : CanWhnf Term Interface.isRedexT}
     -- (type-case π.(x : A) → B ∷ ★ᵢ return Q of { (a → b) ⇒ s; ⋯ }) ⇝
     -- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ Q
     Pi {arg, res, loc = piLoc, _} =>
-      let arg' = Ann arg (TYPE u arg.loc) arg.loc
-          res' = Ann (Lam res res.loc)
-                     (Arr Zero arg (TYPE u arg.loc) arg.loc) res.loc
+      let Val q = ctx.qtyLen
+          arg'  = Ann arg (TYPE u arg.loc) arg.loc
+          res'  = Ann (Lam res res.loc)
+                      (Arr (zero loc) arg (TYPE u arg.loc) arg.loc) res.loc
       in
       whnf defs ctx SZero $
         Ann (subN (tycaseRhsDef def KPi arms) [< arg', res']) ret loc
@@ -130,9 +135,10 @@ parameters {auto _ : CanWhnf Term Interface.isRedexT}
     -- (type-case (x : A) × B ∷ ★ᵢ return Q of { (a × b) ⇒ s; ⋯ }) ⇝
     -- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ Q
     Sig {fst, snd, loc = sigLoc, _} =>
-      let fst' = Ann fst (TYPE u fst.loc) fst.loc
-          snd' = Ann (Lam snd snd.loc)
-                     (Arr Zero fst (TYPE u fst.loc) fst.loc) snd.loc
+      let Val q = ctx.qtyLen
+          fst'  = Ann fst (TYPE u fst.loc) fst.loc
+          snd'  = Ann (Lam snd snd.loc)
+                      (Arr (zero loc) fst (TYPE u fst.loc) fst.loc) snd.loc
       in
       whnf defs ctx SZero $
         Ann (subN (tycaseRhsDef def KSig arms) [< fst', snd']) ret loc
diff --git a/tests/Tests/Qty.idr b/tests/Tests/Qty.idr
new file mode 100644
index 0000000..73daccc
--- /dev/null
+++ b/tests/Tests/Qty.idr
@@ -0,0 +1,8 @@
+module Tests.Qty
+
+import TAP
+import Quox.Syntax.Qty
+import PrettyExtra
+
+
+
-- 
2.39.5