Technical Report, Department of Computer Science, the University of Hong Kong, Jan 2021. 1 TAMING THE MERGE OPERATOR A Type-directed Operational Semantics Approach XUEJING HUANG JINXU ZHAO BRUNO C. D. S. OLIVEIRA The University of Hong Kong (e-mail: fxjhuang, jxzhao,
[email protected]) Abstract Calculi with disjoint intersection types support a symmetric merge operator with subtyping. The merge operator generalizes record concatenation to any type, enabling expressive forms of object composition, and simple solutions to hard modularity problems. Unfortunately, recent calculi with disjoint intersection types and the merge operator lack a (direct) operational semantics with expected properties such as determinism and subject reduction, and only account for terminating programs. This paper proposes a type-directed operational semantics (TDOS) for calculi with intersection types and a merge operator. We study two variants of calculi in the literature. The first calculus, called li, is a variant of a calculus presented by Oliveira et al. (2016) and closely related to another calculus by Dunfield (2014). Although Dunfield proposes a direct small-step semantics for her calcu- lus, her semantics lacks both determinism and subject reduction. Using our TDOS we obtain a direct + semantics for li that has both properties. The second calculus, called li , employs the well-known + subtyping relation of Barendregt, Coppo and Dezani-Ciancaglini (BCD). Therefore, li extends the more basic subtyping relation of li, and also adds support for record types and nested composition (which enables recursive composition of merged components). To fully obtain determinism, both li + and li employ a disjointness restriction proposed in the original li calculus.