diff --git a/flap/src/fopix/hobixToFopix.ml b/flap/src/fopix/hobixToFopix.ml
index d49fe01..518ad41 100644
--- a/flap/src/fopix/hobixToFopix.ml
+++ b/flap/src/fopix/hobixToFopix.ml
@@ -120,16 +120,26 @@ let free_variables =
     | [ s ] -> f s
     | s :: xs -> M.union (f s) (unions f xs)
   in
+  (*Une variable libre est une variable qui peut être substitué*)
+  
+  (*TODO : rajouter des explications pour While Define et Fun*)
   let rec fvs = function
     | S.Literal _ -> M.empty
     | S.Variable x -> M.singleton x
-    | S.While (cond, e) -> failwith "Students! This is your job!"
-    | S.Define (vd, a) -> failwith "Students! This is your job!"
+    | S.While (cond, e) -> unions fvs [cond;e]
+    | S.Define (vd, a) ->
+      let liste_def_valeur =
+      match vd with
+      | S.SimpleValue (id,expr) -> [(id,expr)]
+      | S.RecFunctions (list) -> list 
+    in
+    let id, expr = List.split liste_def_valeur in 
+    M.diff (unions fvs (a::expr)) (M.of_list id)
     | S.ReadBlock (a, b) -> unions fvs [ a; b ]
     | S.Apply (a, b) -> unions fvs (a :: b)
     | S.WriteBlock (a, b, c) | S.IfThenElse (a, b, c) -> unions fvs [ a; b; c ]
     | S.AllocateBlock a -> fvs a
-    | S.Fun (xs, e) -> failwith "Students! This is your job!"
+    | S.Fun (xs, e) -> M.diff (fvs e) (M.of_list xs)
     | S.Switch (a, b, c) ->
       let c =
         match c with
@@ -139,7 +149,7 @@ let free_variables =
       unions fvs ((a :: ExtStd.Array.present_to_list b) @ c)
   in
   fun e -> M.elements (fvs e)
-;;
+
 
 (** A closure compilation environment relates an identifier to the way
     it is accessed in the compiled version of the function's