A synthesis procedure acts as a compiler for declarative specifications. It accepts a formula describing a relation between inputs and outputs, and generates a function implementing this relation. This paper presents synthesis procedures for data structures. Our procedures are reductions that lift a synthesis procedure for the elements into synthesis procedures for containers storing these elements. We introduce a framework to describe synthesis procedures as systematic applications of inference rules. We show that, by interpreting both synthesis problems and programs as relations, we can derive and modularly prove transformation rules that are widely applicable, thus simplifying both the presentation and the correctness argument.