ABSTRACT. Proof-relevant resolution is a new variant of resolution in Horn-clause logic and its extensions. We propose proof-relevant resolution as a systematic approach to elaboration in programming languages that is close to formal specification and hence allows for analysis of semantics of the language. We demonstrate the approach on two case studies; we describe a novel, proof-relevant approach to type inference and term synthesis in dependently types languages and we show how proof-relevant resolution allows for analysis of inductive and coinductive soundness of type class resolution. We conclude by a discussion of overall contributions of our current work.