diff --git a/SciLean/Core/Meta/GenerateRevCDeriv.lean b/SciLean/Core/Meta/GenerateRevCDeriv.lean
new file mode 100644
index 00000000..b1b1a9e1
--- /dev/null
+++ b/SciLean/Core/Meta/GenerateRevCDeriv.lean
@@ -0,0 +1,294 @@
+import SciLean.Core.Objects.FinVec
+import SciLean.Core.FunctionTransformations
+import SciLean.Core.Notation
+
+namespace SciLean.Meta
+
+open Lean Meta Qq
+
+def isTypeQ (e : Expr) : MetaM (Option ((u : Level) × Q(Type $u))) := do
+  let u ← mkFreshLevelMVar
+  let .some e ← checkTypeQ e q(Type $u)
+    | return none
+  return .some ⟨u, e⟩
+
+/-- Returns `(id, u, K)` where `K` is infered field type with universe level `u`
+
+The index `id` tells that arguments `args[id:]` have already `K` in its local context with valid `IsROrC K` instances. -/
+def getFieldOutOfContextQ (args : Array Expr) : MetaM (Option ((u : Level) × Q(Type $u))) := do
+
+  for arg in args do
+    let type ← inferType arg
+
+    if type.isAppOf ``IsROrC then
+      return ← isTypeQ (type.getArg! 0)
+
+    if type.isAppOf ``Scalar then
+      return ← isTypeQ (type.getArg! 1)
+
+    if type.isAppOf ``RealScalar then
+      return ← isTypeQ (type.getArg! 0)
+
+    if type.isAppOf ``Vec then
+      return ← isTypeQ (type.getArg! 0)
+
+    if type.isAppOf ``SemiInnerProductSpace then
+      return ← isTypeQ (type.getArg! 0)
+
+    if type.isAppOf ``SemiHilbert then
+      return ← isTypeQ (type.getArg! 0)
+
+    if type.isAppOf ``FinVec then
+      return ← isTypeQ (type.getArg! 1)
+
+  return none
+
+def firstExplicitNonTypeIdx (xs : Array Expr) : MetaM Nat := do
+  let mut i := 0
+  for x in xs do
+    let X ← inferType x
+    if (← x.fvarId!.getBinderInfo) == .default && 
+       ¬X.bindingBodyRec.isType then
+      return i
+    i := i + 1
+  return i
+
+
+/-- 
+Replaces `<∂ fᵢ x` with `Tfᵢ` in `e`
+- `argFuns = #[f₁, ..., fₙ]`
+- `transArgFuns = #[<∂ f₁ x, ..., <∂ fₙ x]`
+- `transArgFunVars  = #[Tf₁, ..., Tfₙ]`
+
+Throws an error if all `fᵢ` has not been liminated from `e`
+-/
+def eliminateTransArgFun (e : Expr) (argFuns transArgFuns transArgFunVars : Array Expr) : MetaM Expr := do
+  let e' ←
+    e.replaceM (fun x => do
+      if x.hasLooseBVars then
+        pure .noMatch
+      else
+        if let .some i ← transArgFuns.findIdxM? (isDefEq · x) then
+          IO.println s!"replacing {← ppExpr x} with {← ppExpr transArgFunVars[i]!}"
+          pure (.yield transArgFunVars[i]!)
+        else 
+          pure .noMatch)
+
+  IO.println s!"transformed function with arguments eliminated succesfully \n{← ppExpr e'}"
+
+  if let .some i := argFuns.findIdx? (fun argFun => e'.containsFVar argFun.fvarId!) then
+    throwError "Failed to elimate {← ppExpr argFuns[i]!} out of transformed function{←ppExpr e}\n it is expected that {← ppExpr argFuns[i]!} appears only in {← ppExpr transArgFuns[i]!}"
+
+  return e'
+
+
+def generateRevCDeriv (constName : Name) (argIds : ArraySet Nat) : MetaM Unit := do
+  let info ← getConstInfoDefn constName
+
+  forallTelescope info.type fun xs type => do
+
+    let (args, otherArgs, splitIds) := xs.splitIdx (fun i _ => i.1 ∈ argIds)
+
+    IO.println s!"arguments {← args.mapM fun arg => do pure s!"({←ppExpr arg} : {← ppExpr (← inferType arg)})"}"
+
+    let .some ⟨u,K⟩ ← getFieldOutOfContextQ xs
+      | throwError "unable to figure out what is the field"
+
+    IO.println s!"detected field {← ppExpr K}"
+
+    let _isROrC ← synthInstanceQ q(IsROrC $K)
+
+    -- check that return type form SemiInnerProductSpace
+    let .some _semiInnerProductSpace ← synthInstance? (← mkAppM ``SemiInnerProductSpace #[K, type])
+      | throwError "unable to synthesize `SemiInnerProductSpace` for the return type {← ppExpr type}"
+
+    -- check that all arguments form SemiInnerProductSpace
+    for arg in args do
+      let argType ← inferType arg
+      let .some _semiInnerProductSpace ← synthInstance? (← mkAppM ``SemiInnerProductSpace #[K, argType])
+        | throwError "unable to synthesize `SemiInnerProductSpace {← ppExpr K} {← ppExpr argType}` for the argument {← ppExpr arg}"
+      
+    IO.println "all necessary types form SemiInnerProductSpace!"
+
+    -- check for dependent types
+    for x in xs do
+      let X ← inferType x
+      if let .some arg := args.find? (fun arg => X.containsFVar arg.fvarId!) then
+        throwError s!"argument ({← ppExpr x} : {← inferType x >>= ppExpr}) depends on the argument {← ppExpr arg}, dependent types like this are not supported"
+
+    -- let vLvlName := `v
+    -- let v ← mkFreshLevelMVar
+    -- let v := Level.param vLvlName
+    withLocalDeclQ `W .implicit q(Type) fun W => do
+    withLocalDeclQ `instW .instImplicit q(SemiInnerProductSpace $K $W) fun instW => do
+    withLocalDeclQ (u:=levelOne) `w .default W fun w => do
+
+      -- argFuns are selected arguments parametrized by `W`
+      let argFunDecls ← 
+        args.mapM (fun arg => do
+          let name ← arg.fvarId!.getUserName
+          let bi : BinderInfo := .default
+          let type ← mkArrow W (← inferType arg)
+          pure (name, bi, fun _ : Array Expr => pure (f:=MetaM) type))
+
+      withLocalDecls argFunDecls fun argFuns => do
+
+        let argFunApps := argFuns.map (fun argFun => argFun.app w)
+
+        let xs' := Array.mergeSplit splitIds argFunApps otherArgs
+
+        let f ← mkLambdaFVars #[w] (mkAppN (← mkConst' constName) xs')
+        let lhs ← mkAppM ``revCDeriv #[K,f]
+
+        let argFunPropDecls ← 
+          argFuns.mapM (fun argFun => do
+            let name := (← argFun.fvarId!.getUserName).appendBefore "h"
+            let bi : BinderInfo := .default
+            let type ← mkAppM ``HasAdjDiff #[K,argFun]
+            pure (name, bi, fun _ : Array Expr => pure (f:=MetaM) type))
+
+        withLocalDecls argFunPropDecls fun argFunProps => do
+
+          let constId := mkIdent constName
+          let (rhs, proof) ← rewriteByConv lhs (← `(conv| (unfold $constId; autodiff)))
+
+          IO.println s!"lhs: {← ppExpr lhs}"
+          IO.println s!"rhs: {← ppExpr rhs}"
+
+          if ¬(← isDefEq (← mkEq lhs rhs) (← inferType proof)) then
+            throwError "generated proof is not type correct, expected proof of\n{← ppExpr (← mkEq lhs rhs)}\nbut got proof of\n{← ppExpr (← inferType proof)}"
+
+          if let .lam _ _ b _ := rhs then
+            let b := b.instantiate1 w
+
+            let transArgFuns ← argFuns.mapM (fun argFun => mkAppM ``revCDeriv #[K, argFun, w])
+
+            let transArgFunDecls ←
+              argFuns.mapIdxM (fun i argFun => do
+                let name := (← argFun.fvarId!.getUserName)
+                let bi : BinderInfo := .default
+                let type ← inferType transArgFuns[i]!
+                pure (name, bi, fun _ : Array Expr => pure (f:=MetaM) type))
+
+            withLocalDecls transArgFunDecls fun transArgFunVars => do
+
+              -- find all occurances of `<∂ (w':=w), argFunᵢ w` and replace it with recently introduced fvar
+              let b' ← eliminateTransArgFun b argFuns transArgFuns transArgFunVars
+              if b'.containsFVar w.fvarId! then
+                throwError s!"transformed function {← ppExpr b'} still contains {← ppExpr w}"
+
+              let idx ← firstExplicitNonTypeIdx xs
+
+              let xs' := Array.mergeSplit splitIds transArgFunVars otherArgs
+              let fvars := xs'[0:idx] ++ (#[W,instW] : Array Expr) ++ xs'[idx:]
+              let transFun ← instantiateMVars (← mkLambdaFVars fvars b')
+              let transFunName := constName.append "arg_" |>.append "revCDeriv"
+              IO.println s!"revCDeriv def fun\n{← ppExpr transFun}"
+
+              let transFunInfo : DefinitionVal := 
+              {
+                name  := transFunName
+                type  := (← inferType transFun)
+                value := transFun
+                hints := .regular 0
+                safety := .safe
+                levelParams := info.levelParams
+              }
+
+              addAndCompile (.defnDecl transFunInfo)
+
+
+              let xs' := Array.mergeSplit splitIds argFuns otherArgs
+              let fvars := xs'[0:idx] ++ (#[W, instW] : Array Expr) ++ xs'[idx:] ++ argFunProps
+              let ruleProof ← instantiateMVars (← mkLambdaFVars fvars proof)
+              let ruleName := constName.append "arg_" |>.append "revCDeriv_rule"
+              IO.println s!"revCDeriv rule\n{← ppExpr (← inferType ruleProof)}"
+
+              let ruleInfo : TheoremVal := 
+              {
+                name  := ruleName
+                type  := (← inferType ruleProof)
+                value := ruleProof
+                levelParams := info.levelParams
+              }
+
+              addDecl (.thmDecl ruleInfo)
+              
+              -- turn ftransArgFunVars to let bindings
+              let mut lctx ← getLCtx
+              for transArgFunVar in transArgFunVars, transArgFun in transArgFuns do
+                lctx := lctx.modifyLocalDecl transArgFunVar.fvarId!
+                  fun decl => 
+                    match decl with
+                    | .cdecl index fvarId userName type _ kind =>
+                      .ldecl index fvarId userName type transArgFun false kind
+                    | _ => unreachable!
+
+              withLCtx lctx (← getLocalInstances) do
+
+                let xs' := Array.mergeSplit splitIds transArgFunVars otherArgs
+                let fvars := xs'[0:idx] ++ (#[W,instW] : Array Expr) ++ xs'[idx:]
+                -- TODO: !!!replace transformedFun with new declaration!!!
+                let rhs ← mkLambdaFVars ((#[w] : Array Expr) ++ transArgFunVars) (← mkAppOptM transFunName (fvars.map .some))
+                  
+                let xs' := Array.mergeSplit splitIds argFuns otherArgs
+                let fvars := xs'[0:idx] ++ (#[W, instW] : Array Expr) ++ xs'[idx:] ++ argFunProps
+                let ruleDef ← instantiateMVars (← mkForallFVars fvars (← mkEq lhs rhs))
+                let ruleDefName := constName.append "arg_" |>.append "revCDeriv_rule_def"
+                IO.println s!"revCDeriv rule def\n{← ppExpr ruleDef}"
+
+                let ruleDefInfo : TheoremVal := 
+                {
+                  name  := ruleDefName
+                  type  := ruleDef
+                  value := ruleProof
+                  levelParams := info.levelParams
+                }
+
+                addDecl (.thmDecl ruleDefInfo)
+
+                pure ()
+
+            pure ()
+          else
+            throwError "transformed function should be in the form `fun w => ...` but got\n{← ppExpr rhs}"
+          pure ()
+
+
+def mymul {K : Type} [IsROrC K] (x y : K) := x * y
+
+
+variable {K : Type} [IsROrC K] {W : Type v} [SemiInnerProductSpace K W]
+
+set_default_scalar K
+
+
+set_option trace.Meta.Tactic.fprop.discharge true in
+set_option trace.Meta.Tactic.simp.discharge true in
+set_option trace.Meta.Tactic.simp.unify true in
+example (x y : W → K) (hx : HasAdjDiff K x) (hy : HasAdjDiff K y)
+  : (<∂ w, mymul (x w) (y w))
+    =
+    sorry :=
+by
+  unfold mymul
+  ftrans only
+#exit
+
+set_option pp.funBinderTypes true in
+-- set_option trace.Meta.Tactic.ftrans.step true in
+-- set_option trace.Meta.Tactic.simp.discharge true in
+set_option trace.Meta.Tactic.fprop.discharge true in
+set_option trace.Meta.Tactic.simp.discharge true in
+set_option trace.Meta.Tactic.simp.unify true in
+set_option trace.Meta.Tactic.ftrans.step true in
+#eval show MetaM Unit from do
+
+  -- generateRevCDeriv ``norm2 #[4].toArraySet
+  generateRevCDeriv ``mymul #[2,3].toArraySet
+
+
+
+#print mymul.arg_.revCDeriv
+#check mymul.arg_.revCDeriv_rule
+#check mymul.arg_.revCDeriv_rule_def