diff --git a/lib/inference.ml b/lib/inference.ml
index 2e8ec50..4a3ad5b 100644
--- a/lib/inference.ml
+++ b/lib/inference.ml
@@ -1,43 +1,47 @@
 (** Infer the type of a given term and, if exists, returns the type of the term *)
-let rec typeof = function
-  | Term.Var id ->
-    (match Unification.unify (Type.Var id) Type.Int with
-     | Some _ -> Some Type.Int
-     | None -> Some (Type.Var id))
-  | Term.IntConst _ -> Some Type.Int
-  | Term.Binop (t1, _, t2) ->
-    (* Both operands must have type Int *)
-    (match typeof t1, typeof t2 with
-     | Some ty1, Some ty2 ->
-       (match Unification.unify ty1 Type.Int, Unification.unify ty2 Type.Int with
-        | Some _, Some _ -> Some Type.Int
-        | _ -> None)
-     | _, _ -> None)
-  | Term.Pair (t1, t2) ->
-    (match typeof t1, typeof t2 with
-     | Some ty1, Some ty2 -> Some (Type.Product (ty1, ty2))
-     | _, _ -> None)
-  | Term.Proj (proj, t) ->
-    (* Check if the term is a pair *)
-    (match typeof t with
-     | Some (Type.Product (ty1, ty2)) ->
-       (match proj with
-        | Term.First -> Some ty1
-        | Term.Second -> Some ty2)
-     | _ -> None)
-  | Term.Fun (id, body) ->
-    (match typeof body with
-     | Some ty_body ->
-       (match typeof (Term.Var id) with
-        | Some tt -> Some (Type.Arrow (tt, ty_body))
-        | None -> Some (Type.Arrow (Type.Var id, ty_body)))
-     | _ -> None)
-  | Term.App (t1, t2) ->
-    (* Check if the function type matches the arguments *)
-    (match typeof t1, typeof t2 with
-     | Some (Type.Arrow (ty_param, ty_fn)), Some ty_args ->
-       (match Unification.unify ty_param ty_args with
-        | Some _ -> Some ty_fn
-        | None -> None)
-     | _, _ -> None)
+let typeof t =
+  let rec infer env = function
+    | Term.Var id ->
+      ( (match TypeSubstitution.find id env with
+         | Some ty -> Some ty
+         | None -> Some (Type.Var id))
+      , env )
+    | Term.IntConst _ -> Some Type.Int, env
+    | Term.Binop (t1, _, t2) ->
+      (* Both operands must have type Int *)
+      (match infer env t1, infer env t2 with
+       | (Some ty1, _), (Some ty2, _) ->
+         (match Unification.unify ty1 Type.Int, Unification.unify ty2 Type.Int with
+          | Some env1, Some env2 -> Some Type.Int, TypeSubstitution.compose env1 env2
+          | _ -> None, env)
+       | _, _ -> None, env)
+    | Term.Pair (t1, t2) ->
+      (match infer env t1, infer env t2 with
+       | (Some ty1, _), (Some ty2, _) -> Some (Type.Product (ty1, ty2)), env
+       | _, _ -> None, env)
+    | Term.Proj (proj, t) ->
+      (* Check if the term is a pair *)
+      (match infer env t with
+       | Some (Type.Product (ty1, ty2)), _ ->
+         (match proj with
+          | Term.First -> Some ty1, env
+          | Term.Second -> Some ty2, env)
+       | _ -> None, env)
+    | Term.Fun (id, body) ->
+      (match infer env body with
+       | Some ty_body, env' ->
+         (match infer env' (Term.Var id) with
+          | Some ty, _ -> Some (Type.Arrow (ty, ty_body)), env'
+          | None, _ -> Some (Type.Arrow (Type.Var id, ty_body)), env')
+       | _ -> None, env)
+    | Term.App (t1, t2) ->
+      (* Check if the function type matches the arguments *)
+      (match infer env t1, infer env t2 with
+       | (Some (Type.Arrow (ty_param, ty_fn)), _), (Some ty_args, _) ->
+         (match Unification.unify ty_param ty_args with
+          | Some _ -> Some ty_fn, env
+          | None -> None, env)
+       | _, _ -> None, env)
+  in
+  fst (infer TypeSubstitution.empty t)
 ;;
diff --git a/lib/typeSubstitution.ml b/lib/typeSubstitution.ml
index 007655f..6d07155 100644
--- a/lib/typeSubstitution.ml
+++ b/lib/typeSubstitution.ml
@@ -37,3 +37,5 @@ let compose s2 s1 =
     s1
     s2
 ;;
+
+let find = IdentifierMap.find_opt
diff --git a/lib/typeSubstitution.mli b/lib/typeSubstitution.mli
index 2053180..7a7154f 100644
--- a/lib/typeSubstitution.mli
+++ b/lib/typeSubstitution.mli
@@ -6,3 +6,4 @@ val apply : t -> Type.t -> Type.t
 val compose : t -> t -> t
 val empty : t
 val singleton : Identifier.t -> Type.t -> t
+val find : Identifier.t -> t -> Type.t option
diff --git a/test/test_projet_pfa_23_24.ml b/test/test_projet_pfa_23_24.ml
index c296e03..60af70a 100644
--- a/test/test_projet_pfa_23_24.ml
+++ b/test/test_projet_pfa_23_24.ml
@@ -11,7 +11,7 @@ let tests_typeof =
     , Term.(Fun (x, Fun (y, Binop (Var x, Plus, Var y))))
     , Some Type.(Arrow (Int, Arrow (Int, Int))) )
   ; (* Not typed variable *)
-    "x", Term.(Var "x"), None
+    "x", Term.(Var "x"), Some (Type.Var "x")
   ; (* Binary operation *)
     "1 + 2", Term.(Binop (IntConst 1, Plus, IntConst 2)), Some Type.Int
   ; (* Pair *)