diff --git a/SciLean/Core/Notation/Gradient.lean b/SciLean/Core/Notation/Gradient.lean
index 9968f087..f9d1ece4 100644
--- a/SciLean/Core/Notation/Gradient.lean
+++ b/SciLean/Core/Notation/Gradient.lean
@@ -1,14 +1,20 @@
 import SciLean.Core.FunctionTransformations.RevCDeriv
+import SciLean.Core.Notation.Autodiff
 import SciLean.Core.Notation.CDeriv
 
+
 namespace SciLean.NotationOverField
 
-scoped syntax "∇ " term:66 : term
+scoped syntax (name:=gradNotation1) "∇ " term:66 : term
 scoped syntax "∇ " diffBinder ", " term:66 : term
 scoped syntax "∇ " "(" diffBinder ")" ", " term:66 : term
+scoped syntax "∇! " term:66 : term
+scoped syntax "∇! " diffBinder ", " term:66 : term
+scoped syntax "∇! " "(" diffBinder ")" ", " term:66 : term
+
 
 open Lean Elab Term Meta in
-elab_rules : term
+elab_rules (kind:=gradNotation1) : term
 | `(∇ $f) => do
   let K := mkIdent (← currentFieldName.get)
   let KExpr ← elabTerm (← `($K)) none
@@ -21,16 +27,23 @@ elab_rules : term
   else
     throwUnsupportedSyntax
 
--- in this case we do not want to call scalarGradient
-| `(∇ $x:ident := $val:term; $codir:term, $b) => do
-  let K := mkIdent (← currentFieldName.get)
-  elabTerm (← `(gradient $K (fun $x => $b) $val $codir)) none false
+-- open Lean Elab Term Meta in
+-- elab_rules (kind:=gradNotation1) : term
+-- | `(∇ $x:ident := $val:term; $codir:term, $b) => do
+--   let K := mkIdent (← currentFieldName.get)
+--   elabTerm (← `(gradient $K (fun $x => $b) $val $codir)) none false
 
 macro_rules
 | `(∇ $x:ident, $f)              => `(∇ fun $x => $f)
 | `(∇ $x:ident : $type:term, $f) => `(∇ fun $x : $type => $f)
 | `(∇ $x:ident := $val:term, $f) => `((∇ fun $x => $f) $val)
 | `(∇ ($b:diffBinder), $f)       => `(∇ $b, $f)
+| `(∇! $f)                        => `((∇ $f) rewrite_by autodiff)
+| `(∇! $x:ident, $f)              => `(∇! fun $x => $f)
+| `(∇! $x:ident : $type:term, $f) => `(∇! fun $x : $type => $f)
+| `(∇! $x:ident := $val:term, $f) => `((∇! fun $x => $f) $val)
+| `(∇! ($b:diffBinder), $f)       => `(∇! $b, $f)
+
 
 @[app_unexpander gradient] def unexpandGradient : Lean.PrettyPrinter.Unexpander