diff --git a/compiler/catala_utils/cli.ml b/compiler/catala_utils/cli.ml
index 086a028f..4b7dbe44 100644
--- a/compiler/catala_utils/cli.ml
+++ b/compiler/catala_utils/cli.ml
@@ -486,9 +486,15 @@ let debug_format (format : ('a, Format.formatter, unit) format) =
 let error_print (format : ('a, out_channel, unit) format) =
   Printf.eprintf ("%s" ^^ format ^^ "\n%!") (error_marker ())
 
+let error_format (format : ('a, Format.formatter, unit) format) =
+  Format.eprintf ("%s" ^^ format ^^ "\n%!") (error_marker ())
+
 let warning_print (format : ('a, out_channel, unit) format) =
   Printf.printf ("%s" ^^ format ^^ "\n%!") (warning_marker ())
 
+let warning_format (format : ('a, Format.formatter, unit) format) =
+  Format.printf ("%s" ^^ format ^^ "\n%!") (warning_marker ())
+
 let result_print (format : ('a, out_channel, unit) format) =
   Printf.printf ("%s" ^^ format ^^ "\n%!") (result_marker ())
 
diff --git a/compiler/catala_utils/cli.mli b/compiler/catala_utils/cli.mli
index 43702054..17a8d6cb 100644
--- a/compiler/catala_utils/cli.mli
+++ b/compiler/catala_utils/cli.mli
@@ -142,11 +142,13 @@ val concat_with_line_depending_prefix_and_suffix :
 val add_prefix_to_each_line : string -> (int -> string) -> string
 (** The int argument of the prefix corresponds to the line number, starting at 0 *)
 
-val debug_print : ('a, out_channel, unit) format -> 'a
 val debug_format : ('a, Format.formatter, unit) format -> 'a
+val debug_print : ('a, out_channel, unit) format -> 'a
+val error_format : ('a, Format.formatter, unit) format -> 'a
 val error_print : ('a, out_channel, unit) format -> 'a
-val warning_print : ('a, out_channel, unit) format -> 'a
-val result_print : ('a, out_channel, unit) format -> 'a
-val result_format : ('a, Format.formatter, unit) format -> 'a
-val log_print : ('a, out_channel, unit) format -> 'a
 val log_format : ('a, Format.formatter, unit) format -> 'a
+val log_print : ('a, out_channel, unit) format -> 'a
+val result_format : ('a, Format.formatter, unit) format -> 'a
+val result_print : ('a, out_channel, unit) format -> 'a
+val warning_format : ('a, Format.formatter, unit) format -> 'a
+val warning_print : ('a, out_channel, unit) format -> 'a
diff --git a/compiler/dcalc/from_scopelang.ml b/compiler/dcalc/from_scopelang.ml
index f473d8bf..78233321 100644
--- a/compiler/dcalc/from_scopelang.ml
+++ b/compiler/dcalc/from_scopelang.ml
@@ -580,16 +580,16 @@ let translate_rule
     let a_var = Var.make (Marked.unmark a_name) in
     let new_e = translate_expr ctx e in
     let a_expr = Expr.make_var a_var (pos_mark var_def_pos) in
+    let is_func =
+      match Marked.unmark tau with TArrow _ -> true | _ -> false
+    in
     let merged_expr =
       match Marked.unmark a_io.io_input with
       | OnlyInput -> failwith "should not happen"
       (* scopelang should not contain any definitions of input only variables *)
-      | Reentrant ->
-        merge_defaults
-          ~is_func:
-            (match Marked.unmark tau with TArrow _ -> true | _ -> false)
-          a_expr new_e
-      | NoInput -> Expr.eerroronempty new_e (pos_mark_as a_name)
+      | Reentrant -> merge_defaults ~is_func a_expr new_e
+      | NoInput ->
+        if is_func then new_e else Expr.eerroronempty new_e (pos_mark_as a_name)
     in
     let merged_expr =
       tag_with_log_entry merged_expr
diff --git a/compiler/dcalc/invariant.ml b/compiler/dcalc/invariant.ml
index bfe04e64..6d724dda 100644
--- a/compiler/dcalc/invariant.ml
+++ b/compiler/dcalc/invariant.ml
@@ -23,6 +23,9 @@ let invariant_no_partial_evaluation () : string * invariant_expr =
   ( __FUNCTION__,
     fun e ->
       match Marked.unmark e with
+      | EApp { f = EOp { op = Op.Log _; _ }, _; _ } ->
+        (* logs are differents. *)
+        Some true
       | EApp _ -> begin
         match Marked.unmark (Expr.ty e) with
         | TArrow _ -> Some false
@@ -57,9 +60,10 @@ let check_invariant (inv : string * invariant_expr) (p : typed program) =
             match inv e with
             | None -> true
             | Some false ->
-              Cli.error_print "%s Invariant failed %s."
+              Cli.error_format "%s failed in %s.\n\n %a" name
                 (Pos.to_string_short (Expr.pos e))
-                name;
+                (Print.expr ~debug:true p.decl_ctx)
+                e;
               incr total;
               false
             | Some true ->