A Type-Directed Operational Semantics For a Calculus with a Merge Operator (Artifact)

Our companion paper proposes a type-directed operational semantics (TDOS) for λ_i^{:}: a calculus with intersection types and a merge operator. The artifact contains the specification of λ_i^{:} and its TDOS, and related Coq code. λ_i^{:} is formalized using the locally nameless representation with cofinite quantification. The Coq definition and some infrastructure code are generated by Ott and LNgen. λ_i^{:} is inspired by two closely related calculi by Dunfield (2014) and Oliveira et al. (2016), and a simple variant of it is designed to demonstrate the possibility to match with them without any modification. To relate the two calculi with λ_i^{:}, a sound theorem on semantics and a completeness theorem on typing are proved for each variant. In addition, we extended the bidirectional typing of Oliveira et al.’s λ_i calculus, and designed an elaboration from it to λ_i^{:}, to show that many of λ_i^{:}’s explicit annotations can be inferred automatically.