diff --git a/flap/src/hopix/hopixTypechecker.ml b/flap/src/hopix/hopixTypechecker.ml
index 036af21..ee89423 100644
--- a/flap/src/hopix/hopixTypechecker.ml
+++ b/flap/src/hopix/hopixTypechecker.ml
@@ -48,7 +48,42 @@ let check_type_scheme
   HopixTypes.Scheme (ts, HopixTypes.internalize_ty env ty), env
 ;;
 
-let synth_literal : HopixAST.literal -> HopixTypes.aty =
+
+
+let rec check_pattern
+  :  HopixTypes.typing_environment -> HopixAST.pattern Position.located -> HopixTypes.aty
+  -> HopixTypes.typing_environment
+  =
+  fun env Position.({ value = p; position = pos } as pat) expected ->
+  failwith "Students! This is your job! (check_pattern)"
+;;
+
+let rec synth_expression
+  :  HopixTypes.typing_environment -> HopixAST.expression Position.located
+  -> HopixTypes.aty
+  =
+  fun env Position.{ value = e; position = _ } ->
+  match e with
+  | Literal l -> synth_literal l.value
+  | Variable (id, tlist) -> synth_variable env id tlist
+  | Tagged (cons, tlist, elist) -> synth_tagged env cons tlist elist
+  | Apply (elist1, elist2) -> synth_apply env elist1 elist2
+  | Record (field, tlist) -> synth_record env field tlist
+  | Fun (FunctionDefinition (def, expr)) -> synth_fun env def expr
+  | TypeAnnotation (expr, t) -> synth_tannot env expr t
+  | Field (expr, lbl, tlist) -> synth_field env expr lbl tlist
+  | Tuple elist -> synth_tuple env elist
+  | Sequence elist -> synth_sequence env elist
+  | Define (vdef, expr) -> synth_define env vdef expr
+  | Ref expr -> synth_ref env expr
+  | Assign (expr1, expr2) -> synth_assign env expr1 expr2
+  | Read expr -> synth_read env expr
+  | Case (expr, branches) -> synth_case env expr branches
+  | IfThenElse (ecase, eif, eelse) -> synth_ifthenelse env ecase eif eelse
+  | While (ecase, expr) -> synth_while env ecase expr
+  | For (id, ecase, expr1, expr2) -> synth_for env id ecase expr1 expr2
+
+and  synth_literal : HopixAST.literal -> HopixTypes.aty =
   fun l ->
   match l with
   | LInt _ -> HopixTypes.hint
@@ -78,7 +113,16 @@ and synth_apply
   :  HopixTypes.typing_environment -> expression Position.located
   -> expression Position.located -> HopixTypes.aty
   =
-  fun tenv f x -> failwith "Students! This is your job! (synth_apply)"
+  fun tenv f x -> (*failwith "Students! This is your job! (synth_apply)"*)
+  let f_type = synth_expression tenv f in
+  match f_type with 
+  | HopixTypes.ATyArrow (gauche,droit) -> (*  a' -> b' *)
+  (
+    let x_type = synth_expression tenv x in
+    check_equal_types x.position  gauche x_type; droit
+  )
+  | _ -> failwith ""
+    
 
 and synth_record
   :  HopixTypes.typing_environment
@@ -163,40 +207,7 @@ and synth_for
   -> expression Position.located -> HopixTypes.aty
   =
   fun tenv id estart eend expr -> failwith "Students! This is your job! (synth_for)"
-;;
 
-let rec check_pattern
-  :  HopixTypes.typing_environment -> HopixAST.pattern Position.located -> HopixTypes.aty
-  -> HopixTypes.typing_environment
-  =
-  fun env Position.({ value = p; position = pos } as pat) expected ->
-  failwith "Students! This is your job! (check_pattern)"
-;;
-
-let rec synth_expression
-  :  HopixTypes.typing_environment -> HopixAST.expression Position.located
-  -> HopixTypes.aty
-  =
-  fun env Position.{ value = e; position = _ } ->
-  match e with
-  | Literal l -> synth_literal l.value
-  | Variable (id, tlist) -> synth_variable env id tlist
-  | Tagged (cons, tlist, elist) -> synth_tagged env cons tlist elist
-  | Apply (elist1, elist2) -> synth_apply env elist1 elist2
-  | Record (field, tlist) -> synth_record env field tlist
-  | Fun (FunctionDefinition (def, expr)) -> synth_fun env def expr
-  | TypeAnnotation (expr, t) -> synth_tannot env expr t
-  | Field (expr, lbl, tlist) -> synth_field env expr lbl tlist
-  | Tuple elist -> synth_tuple env elist
-  | Sequence elist -> synth_sequence env elist
-  | Define (vdef, expr) -> synth_define env vdef expr
-  | Ref expr -> synth_ref env expr
-  | Assign (expr1, expr2) -> synth_assign env expr1 expr2
-  | Read expr -> synth_read env expr
-  | Case (expr, branches) -> synth_case env expr branches
-  | IfThenElse (ecase, eif, eelse) -> synth_ifthenelse env ecase eif eelse
-  | While (ecase, expr) -> synth_while env ecase expr
-  | For (id, ecase, expr1, expr2) -> synth_for env id ecase expr1 expr2
 
 and check_expression
   :  HopixTypes.typing_environment -> HopixAST.expression Position.located