Formal metatheory of second-order abstract syntax

Despite extensive research both on the theoretical and practical fronts, formalising, reasoning about, implementing languages with variable binding is still a daunting endeavour – repetitive boilerplate overly complicated metatheory of capture-avoiding substitution often get in way progressing to actually interesting properties language. Existing developments offer some relief, however at expense inconvenient error-prone term encodings lack formal foundations. We present mathematically-inspired language-formalisation framework implemented Agda. The system translates description syntax signature variable-binding operators into an intrinsically-encoded, inductive data type equipped syntactic operations such as weakening substitution, along their correctness properties. generated further incorporates metavariables associated operation metasubstitution, which enables second-order equational/rewriting reasoning. underlying mathematical foundation initial algebra semantics derives compositional interpretations models satisfying semantic lemma by construction.