diff --git a/: b/:
deleted file mode 100644
index b86e16f..0000000
--- a/:
+++ /dev/null
@@ -1,44 +0,0 @@
-%{
-open Expr
-%}
-
-%token PLUS TIMES
-%token TOP BOTTOM EXFALSO
-%token LPAREN RPAREN
-%token FUN ARR COLON
-%token <string> VARID
-%token <string> TYID
-
-%token EOL
-   
-
-%left ARR
-
-%start main
-%type <Expr.expr> main
-                                                         
-%%
-main:
-e=expression EOL { e }
-
-ty_annot:
-  | id=VARID COLON t=ty     { (id, t) }
-
-ty:
-  | id=TYID                 { id }
-  | LPAREN t=ty RPAREN      { ty }
-  | t1=ty ARR t2=ty         { 
-
-expression:
-  | FUN LPAREN annot=ty_annot RPAREN ARR e=expression 
-                            { Fun (annot, e) }
-  | e=app_expr              { e }
-
-app_expr:
-  | e=app_expr a=atomic     { App (e, a) }
-  | a=atomic                { a }
-
-atomic:
-  | id=VARID                { Var id }
-  | LPAREN e=expression RPAREN
-                            { e }
diff --git a/expr.ml b/expr.ml
index 0601ea1..31d611c 100644
--- a/expr.ml
+++ b/expr.ml
@@ -7,3 +7,37 @@ type expr =
   | App of expr * expr
   | Var of id
   | Exf of expr * string
+
+(** alpha renaming in a deterministic way *)
+let alpha_convert (e : expr) : expr =
+  let cpt_ty = ref 0 in (* id cpt for type variables *)
+  let cpt_var = ref 0 in (* id cpt for variables *)
+  let generator (cpt : int ref) : id = (* id generator *)
+    let v = string_of_int !cpt
+    in incr cpt; v
+
+  in let renamed = ref []
+  in let rename (cpt : int ref) (var : id) : id = (* checks if a variable already has a new id, or generates one *)
+    match List.assoc_opt var !renamed with
+      | Some var' -> var'
+      | None -> let var' = generator cpt in (
+          renamed := (var, var')::!renamed;
+          var')
+
+  in let rec alpha_ty (t : Types.ty) : Types.ty = match t with
+    Arr (t1, t2) -> Arr (alpha_ty t1, alpha_ty t2)
+    | TVar (v) -> TVar (rename cpt_ty v)
+    | Bot -> Bot
+
+  
+  in let rec alpha_aux (e : expr) : expr = match e with (* actual renaming *)
+    Fun ((v, t), e) -> Fun ((rename cpt_var v, alpha_ty t), alpha_aux e)
+    | App (e1, e2) -> App (alpha_aux e1, alpha_aux e2)
+    | Var v -> Var (rename cpt_var v)
+    | Exf (e, s) -> Exf (alpha_aux e, s)
+  in alpha_aux e
+
+
+(** alpha equivalence *)
+let (=~) (e1 : expr) (e2 : expr) : bool =
+  alpha_convert e1 = alpha_convert e2
\ No newline at end of file