diff --git a/lambda.ml b/lambda.ml
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index 0000000..72a028b
--- /dev/null
+++ b/lambda.ml
@@ -0,0 +1,112 @@
+type term = 
+  | Var of string
+  | Lambda of string * term
+  | App of term * term
+
+
+let rec apply x sub = function
+  | Var (y) -> if y = x then sub else Var (y)
+  | Lambda (y,t) -> Lambda (y, apply x sub t)
+  | App (t1, t2) -> App (apply x sub t1, apply x sub t2)
+    
+let rec subst t sub_list =
+  List.fold_left (fun t (x, sub) -> apply x sub t) t sub_list
+  
+let rec beta = function
+  | App (Lambda (x, t), u) -> subst t [(x, u)]
+  | _ -> failwith  "This term is not a redex"
+
+(* ---------------------------------------
+   Exemples
+   --------------------------------------- *)
+
+let x = Var "x";;
+let y = Var "y";;
+let a = Var "a" ;;
+let b = Var "b" ;;
+let i = Lambda ("x", x);;
+
+(*(λx. x x) a — duplication*)
+let n1 = App (Lambda ("x", App (x, x)), a);;
+(*(λx. x x) (λa. a) — passage de fonction / ordre supérieur*)
+let n2 = App (Lambda ("x", App (x, x)), Lambda (("a"), a));;
+(*(λx. x (λx.x)) y — variable libres/liées*)
+let n3 = App (Lambda ("x", App (x, Lambda ("x", x) ) ), y) ;;
+(*(λx. x (λy. x y)) y — capture de variable*)
+let n4 = App (Lambda ("x", App(x, Lambda ("y", App (x, y)))), y);;
+(*(λxy. x) a b — fonction à deux entrées et effacement*)
+let n5 = App ( App ( Lambda ("x", ( Lambda ("y", x))), a), b);;
+(*(λxy. x) a — application partielle pour deux entrées*)
+let n6 = App ( Lambda ("x", ( Lambda ("y", x))), a);;
+(*(λxy. x) I a b — sur application pour deux entrées*)
+let n7 = App (App ( App (Lambda ("x", ( Lambda ("y", x))), i), a), b);;
+(*(λx. x x) (I I) — duplication inutile dans une stratégie*)
+let n8 = App ( Lambda ("x", App (x, x)), App ( i, i));;
+(*(λxy. y) (I I) I — différence de complexité selon la stratégie*)
+let n9 = App ( App (Lambda ("x", ( Lambda ("y", y))), App (i, i)), i);;
+
+(* ---------------------------------------
+   Display
+   --------------------------------------- *)
+
+let rec string_of_list printer sep = function
+  | [] -> ""
+  | [x] -> printer x
+  | h::t ->
+      (printer h) ^ sep ^ (string_of_list printer sep t)
+ 
+
+let rec string_of_term = function
+  | Var x -> x
+  | Lambda (x, Lambda (y, t)) -> "λ" ^ x ^ y ^ ". " ^ string_of_term t ^ ""
+  | Lambda (x, t) -> "λ" ^ x ^ ". " ^ string_of_term t ^ ""
+  | App (Var x, Var y) -> x ^ " " ^ y
+  | App (t, Var x) -> "(" ^ string_of_term t ^ ") " ^ x
+  | App ( App  ( t, u), v) -> "(" ^ string_of_term (App (t, u)) ^ ") " ^ string_of_term v 
+  | App ( u, App  ( t, v)) -> string_of_term u ^ " (" ^ string_of_term (App (t, v)) ^ ")"
+  | App ( Lambda (x, App (t, y)), v) -> "(" ^ string_of_term (Lambda (x, App (t, y))) ^ ") " ^ string_of_term v
+  | App ( Lambda (x, t), u) -> string_of_term (Lambda (x,t)) ^ " (" ^ string_of_term u ^")" 
+  | App (t, u) -> string_of_term t ^ " (" ^ string_of_term u ^ ")"
+
+
+(* ---------------------------------------
+  Réduction
+  --------------------------------------- *)
+
+exception Irreductible
+
+let is_value = function
+  | Lambda (_, _) -> true
+  | Var _ -> true
+  | _ -> false 
+
+let rec lo_reduction = function 
+  | App ( Lambda (x, t), u) as redex -> (beta redex)
+  | App (Var x, (_ as t)) -> App (Var x, lo_reduction t)
+  | App (App (_,_) as t, Var x) -> App (lo_reduction t, Var x)
+  | App (t, u) -> (App (lo_reduction t, lo_reduction u))
+  | Lambda (x, t) -> Lambda (x, lo_reduction t)
+  | _ -> raise Irreductible
+
+
+let rec lo_eval t = 
+  try let t' = lo_reduction t in
+    lo_eval t' with Irreductible -> t 
+      
+
+let (*cbv*) cbv = function
+  | App ( Lambda (x, t), v) as redex when is_value v -> (*cbv*) (beta redex)
+  | App (t, u) -> (App (t, (*cbv*) u))
+  | Lambda (x, t) as l -> l 
+  | Var x -> Var x
+
+let rec cbv_loop t = 
+  let t' = cbv t in 
+  if t' = t then t'
+  else cbv_loop t'
+
+let rec cbn = function
+  | App ( Lambda (x, t), v) as redex -> cbn (beta redex)
+  | App (t, u) -> cbn (App (cbn t, u))
+  | Lambda (x, t) -> Lambda (x, t)
+  | Var x -> Var x
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