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Why am I getting Mapping Exception?

I am getting :

org.hibernate.MappingException: Foreign key (FKBB979BF4266AA123:address [a_id]))
must have same number of columns as the referenced 
primary key (address [p_id,a_id])

as I try to run the following (though incomplete) snippet :

    public static void main(String args[]) {
        Configuration config = new Configuration().configure();
        SessionFactory sessFact = config.buildSessionFactory();
        Session sess = sessFact.openSession();
        Transaction trans = sess.beginTransaction();    
    }

The hibernate mapping xml is shown below :

<class name="pojo.Person" table="person">
      <id column="p_id" name="personID">
          <generator class="increment" />
      </id>
      <property name="personName" column="p_name" />
      <set name="addressSet" table="address" cascade="all">
          <key column="p_id" />
          <many-to-many class="pojo.Address" column="a_id" />
      </set>
</class>

<class name="pojo.Address" table="address">
      <id column="a_id" name="addressID">
          <generator class="foreign" />
      </id>
      <property name="address" column="address" />
</class>

I am trying a many to many association between Person and Address class.

What is the reason for this exception ?

I have created two tables person and address using these sql commands :

CREATE TABLE person(p_id INTEGER,p_name TEXT,PRIMARY KEY(p_id));
CREATE TABLE address(a_id INTEGER,address TEXT);

POJO

Person

public class Person {
    private int personID;
    private String personName;
    private Set addressSet;

    public int getPersonID() {
        return personID;
    }

    public void setPersonID(int personID) {
        this.personID = personID;
    }

    public String getPersonName() {
        return personName;
    }

    public void setPersonName(String personName) {
        this.personName = personName;
    }

    public Set getAddressSet() {
        return addressSet;
    }

    public void setAddressSet(Set addressSet) {
        this.addressSet = addressSet;
    }

Address

public class Address {
    private int addressID;
    private String address;
    private Set personSet;

    public int getAddressID() {
        return addressID;
    }

    public void setAddressID(int addressID) {
        this.addressID = addressID;
    }

    public String getAddress() {
        return address;
    }

    public void setAddress(String address) {
        this.address = address;
    }

    public Set getPersonSet() {
        return personSet;
    }

    public void setPersonSet(Set personSet) {
        this.personSet = personSet;
    }

}

For a ManyToMany Relationshhip you need a dedicated mapping table

6.2.4. Collections of values and many-to-many associations

ie You need something like a PersonAddress Table

CREATE TABLE personaddress (p_id integer, a_id integer)

Where p_id is a FK Reference to the Person Table and a_id a FK Reference to the Address Table

You need to specify different table name for many-to-many association as it's handled by a separate table:

<class name="pojo.Person" table="person">
      <id column="p_id" name="personID">
          <generator class="increment" />
      </id>
      <property name="personName" column="p_name" />
      <set name="addressSet" table="person_address" cascade="all">
          <key column="p_id" />
          <many-to-many class="pojo.Address" column="a_id" />
      </set>
</class>

Note that <set> now references to person_addresses table. With default configuration, Hibernate is able to create it automatically.

There's another mistake that I see: ID generator for Address entity should not be foreign, it's usually used in 1-to-1 relationships (uses ID of another associated object). You can use the same 'increment' use used for Person entity:

<class name="Address" table="address">
    <id column="a_id" name="addressID">
        <generator class="increment" />
    </id>
    <property name="address" column="address" />
</class>

You need to create a reference table:

    CREATE TABLE PersonsAddresses (personId BIGINT, addressId BIGINT)

and change the mapping of the set to this:

    <set name="addressSet" table="PersonsAddresses" order-by="personId">
        <key column="personId" foreign-key="p_id"/>
        <many-to-many column="addressId" node="a_id" class="pojo.Address" />
    </set>

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