Migrate Env to use Thinned.

1 files changed, 24 insertions, 44 deletions

diff --git a/src/Core/Environment.idr b/src/Core/Environment.idr
index ff484f4..a0a10f4 100644
--- a/src/Core/Environment.idr
+++ b/src/Core/Environment.idr
@@ -14,7 +14,7 @@ import Syntax.PreorderReasoning
 public export
 data Env : Context -> Type where
   Lin : Env [<]
-  Add : Env sx -> sy `Thins` sx -> Term sy -> Env (sx :< n)
+  Add : Env sx -> Thinned sx -> Env (sx :< n)
 
 %name Env env
 
@@ -22,66 +22,46 @@ data Env : Context -> Type where
 
 public export
 (:<) : Env sx -> Term sx -> Env (sx :< n)
-env :< t = Add env (id _) t
+env :< t = Add env (t `Over` id sx)
 
--- Operations ------------------------------------------------------------------
+-- Equality --------------------------------------------------------------------
 
-record IndexResult (sx : Context) where
-  constructor MkRes
-  {0 sy : Context}
-  val : Term sy
-  thin : sy `Thins` sx
+namespace Eq
+  public export
+  data EnvEq : Env sx -> Env sx -> Type where
+    Base : EnvEq env env
+    (:<) : EnvEq env1 env2 -> expand t = expand u -> EnvEq (Add env1 t) (Add env2 u)
 
-shift : IndexResult sx -> IndexResult (sx :< n)
-shift (MkRes val thin) = MkRes val (drop thin n)
+  %name EnvEq prf
 
-expand : IndexResult sx -> Term sx
-expand (MkRes val thin) = wkn val thin
+-- Indexing --------------------------------------------------------------------
 
-doIndex : Env sx -> {0 i : Var sx} -> View i -> IndexResult sx
-doIndex (Add env thin t) Here = shift $ MkRes t thin
-doIndex (Add env thin t) (There i) = shift $ doIndex env $ view i
+doIndex : Env sx -> {0 i : Var sx} -> View i -> Thinned sx
+doIndex (Add env t) Here = shift t (wkn1 _ _)
+doIndex (Add env t) (There i) = shift (doIndex env $ view i) (wkn1 _ _)
 
 export
 index : Env sx -> Var sx -> Term sx
 index env i = expand $ doIndex env $ view i
 
--- Equality --------------------------------------------------------------------
-
-namespace Eq
-  public export
-  data EnvEq : Env sx -> Env sx -> Type where
-    Lin : EnvEq [<] [<]
-    (:<) :
-      EnvEq env1 env2 ->
-      Term.wkn t thin1 = wkn u thin2 ->
-      EnvEq (Add env1 thin1 t) (Add env2 thin2 u)
-
-  %name EnvEq prf
-
-expandShift : (val : IndexResult sx) -> expand (shift val) = wkn (expand val) (drop (id sx) n)
-expandShift (MkRes val thin) = sym $ Calc $
-  |~ wkn (wkn val thin) (drop (id sx) n)
-  ~~ wkn val (drop (id sx) n . thin)     ...(wknHomo val thin $ drop (id sx) n)
-  ~~ wkn val (drop (id sx . thin) n)     ...(cong (wkn val) $ compLeftDrop (id sx) thin n)
-  ~~ wkn val (drop thin n)               ...(cong (\thin => wkn val (drop thin n)) $ compLeftIdentity thin)
+-- Respects Equality
 
 doIndexEqIsEq :
-  -- {env1, env2 : _} ->
   EnvEq env1 env2 ->
   {0 i : Var sx} ->
   (view : View i) ->
   expand (doIndex env1 view) = expand (doIndex env2 view)
-doIndexEqIsEq {sx = sx :< n} ((:<) {t, u, thin1, thin2} prf eq) Here = Calc $
-  |~ wkn t (drop thin1 n)
-  ~~ wkn (wkn t thin1) (drop (id sx) n) ...(expandShift (MkRes t thin1))
-  ~~ wkn (wkn u thin2) (drop (id sx) n) ...(cong (\t => wkn t (drop (id sx) n)) $ eq)
-  ~~ wkn u (drop thin2 n)               ...(sym $ expandShift (MkRes u thin2))
+doIndexEqIsEq Base view = Refl
+doIndexEqIsEq {sx = sx :< n} ((:<) {t, u} prf eq) Here = Calc $
+  |~ expand (shift t $ wkn1 sx n)
+  ~~ wkn (expand t) (wkn1 sx n)   ...(expandShift t (wkn1 sx n))
+  ~~ wkn (expand u) (wkn1 sx n)   ...(cong (\t => wkn t (wkn1 sx n)) $ eq)
+  ~~ expand (shift u $ wkn1 sx n) ...(sym $ expandShift u (wkn1 sx n))
 doIndexEqIsEq {sx = sx :< n} ((:<) {env1, env2} prf eq) (There i) = Calc $
-  |~ expand (shift $ doIndex env1 $ view i)
-  ~~ wkn (expand $ doIndex env1 $ view i) (drop (id sx) n) ...(expandShift $ doIndex env1 $ view i)
-  ~~ wkn (expand $ doIndex env2 $ view i) (drop (id sx) n) ...(cong (\t => wkn t (drop (id sx) n)) $ doIndexEqIsEq prf (view i))
-  ~~ expand (shift $ doIndex env2 $ view i)                ...(sym $ expandShift $ doIndex env2 $ view i)
+  |~ expand (shift (doIndex env1 $ view i) (wkn1 sx n))
+  ~~ wkn (expand (doIndex env1 $ view i)) (wkn1 sx n)   ...(expandShift (doIndex env1 $ view i) (wkn1 sx n))
+  ~~ wkn (expand (doIndex env2 $ view i)) (wkn1 sx n)   ...(cong (\t => wkn t (wkn1 sx n)) $ doIndexEqIsEq prf (view i))
+  ~~ expand (shift (doIndex env2 $ view i) (wkn1 sx n)) ...(sym $ expandShift (doIndex env2 $ view i) (wkn1 sx n))
 
 export
 indexEqIsEq : EnvEq env1 env2 -> (i : Var sx) -> index env1 i = index env2 i