1 files changed, 16 insertions, 0 deletions
diff --git a/src/CHAD/Types.hs b/src/CHAD/Types.hs
index 83f013d..8b3a8db 100644
--- a/src/CHAD/Types.hs
+++ b/src/CHAD/Types.hs
@@ -1,4 +1,5 @@
 {-# LANGUAGE DataKinds #-}
+{-# LANGUAGE LambdaCase #-}
 {-# LANGUAGE TypeFamilies #-}
 {-# LANGUAGE TypeOperators #-}
 module CHAD.Types where
@@ -124,3 +125,18 @@ lemZeroInfoScal STI64 = Refl
 lemZeroInfoScal STF32 = Refl
 lemZeroInfoScal STF64 = Refl
 lemZeroInfoScal STBool = Refl
+
+d1Identity :: STy t -> D1 t :~: t
+d1Identity = \case
+  STNil -> Refl
+  STPair a b | Refl <- d1Identity a, Refl <- d1Identity b -> Refl
+  STEither a b | Refl <- d1Identity a, Refl <- d1Identity b -> Refl
+  STLEither a b | Refl <- d1Identity a, Refl <- d1Identity b -> Refl
+  STMaybe t | Refl <- d1Identity t -> Refl
+  STArr _ t | Refl <- d1Identity t -> Refl
+  STScal _ -> Refl
+  STAccum{} -> error "Accumulators not allowed in input program"
+
+d1eIdentity :: SList STy env -> D1E env :~: env
+d1eIdentity SNil = Refl
+d1eIdentity (t `SCons` env) | Refl <- d1Identity t, Refl <- d1eIdentity env = Refl