The techniques presented in the paper allow for the derivation of various static and dynamic properties of Call-by-Name (CBN) and Call-by-Value (CBV) calculi from their counterparts in the Distant Bang Calculus (dBANG). Some of the properties that could potentially be derived include:
Type Systems: The type systems of CBN and CBV calculi could be analyzed and compared with the type system of dBANG to derive insights into type safety, type inference, and other type-related properties.
Operational Semantics: By studying the operational semantics of CBN and CBV in the context of dBANG, one could explore properties related to reduction strategies, evaluation orders, and the behavior of programs under different evaluation contexts.
Equational Reasoning: Properties related to equational reasoning, such as confluence, normalization, and preservation of properties under reduction, could be investigated by leveraging the embeddings and simulations between the calculi.
Denotational Semantics: The denotational semantics of CBN and CBV could be compared with the denotational semantics of dBANG to derive insights into the meaning and interpretation of programs in different evaluation models.
Proof Theory: Techniques from proof theory, such as soundness, completeness, and decidability, could be explored by relating the proof systems of CBN and CBV to that of dBANG.