-- main.adb
with MyProc;

procedure test is
  type MyFloat is new Float with Default_Value => 10.0;
  package P is new MyProc (MyFloat);
  Var : P.Bla;
  Var2 : MyFloat := P.Stuff (Var);
begin
  null;
end test;

-- MyProc.ads
generic
  type MyTypeWithDefault is private;
package MyProc is
  type Bla is tagged private;
  function Stuff (Self : Bla) return MyTypeWithDefault;
private
  type Bla is tagged record
    Data : MyTypeWithDefault;
  end record;
end MyProc;

-- MyProc.adb
package body MyProc is
  function Stuff (Self : Bla) return MyTypeWithDefault is
  begin
    return Self.Data;
  end Stuff;
end MyProc;

generic
  type MyTypeWithDefault is private;
  Default_Value : in MyTypeWithDefault;
package MyProc is
  type Bla is tagged private;
  function Stuff (Self : Bla) return MyTypeWithDefault;
private
  type Bla is tagged record
    Data : MyTypeWithDefault:= Default_Value;
  end record;
end MyProc;