An apparatus for handling string variables with open domains is provided. In some implementations, the apparatus performs operations including retrieving a first string variable having a first domain, the first domain comprising at least one undefined string value. The operations further include retrieving a second string variable having a second domain, the second domain comprising one or more string values each assigned an integer value in a second set of integer values. The operations further include applying a constraint relating the first string variable with the second string variable. The operations further include comparing the first set of integer values with the second set of integer values and filtering the first set of integer values in the first domain to a third set of integer values in the first domain. The operations further include displaying the third set of integer values for the first string variable.