Verifying Explicit Substitution Calculi in Binding Structures with Effect-Binding

Binding structures enrich traditional abstract syntax by providing support for representing binding mechanisms (based on deBruijn indices), term-schemata and a very clean algebraic theory of substitution. We provide a novel binding structure with the following main results: 1) The formalisation of a generic binding structure with the novel concept of effect-binding that enables the explicit representations of both contexts and terms inside one term meta-language, 2) The foundation of a formal (machine-assisted) substitution theory of effect-binding that is well-suited for mechanisation. This can be used for the systematic and correct development of new calculi with explicit substitutions. The substitution theory is formally proven in Isabelle/HOL; the implementation may serve as (untyped) framework for deep embeddings.