Relational grammar is a syntactic theory which was introduced in the 1970's. It has declined in popularity but is nonetheless an alternative framework to transformational grammar for analyzing grammatical relations in languages. Among the grammatical relations which it analyzes are passivization and dative shift.
In the sentence "William Shakespeare wrote Hamlet," the subject is "William Shakespeare" and the object is "Hamlet." However, in the sentence "Hamlet was written by William Shakespeare," the subject is "Hamlet" and "William Shakespeare" is the agent. Relational grammar explores the relationship between the subject and object and between the subject and agent.
According to relational grammar, the sentence "Hamlet was written by William Shakespeare" has a subject, a predicate and a chomeur. The chomeur in this case is "William Shakespeare" and this simply means that the constituent no longer has a grammatical relation.
In the sentence "Paul gave a gift to Lisa," the subject is "Paul," the direct object is "a gift" and the indirect object is "Lisa." In dative shift, the sentence is expressed as "Paul gave Lisa a gift." The dative is "Lisa" because this is the indirect object which now precedes the direct object "a gift."
In relational grammar, the constituents which serve as arguments to predicates are numbered. Thus, in the sentence "Paul gave Lisa a gift," the subject is (1), the direct object is (2) and the indirect object is (3). The sentence "Paul gave Lisa a gift," the structure is (1) P (3) (2). P stands for predicate. In the sentence "Paul gave a gift to Lisa," the structure is (1) P (2) (3).
Relational grammar is a theory of grammatical relations. It is more closely connected to semantics than is transformational grammar. The chomeur is an idea which is particular to relational grammar.