The Benefits of Diligence

Abstract

AbstractThis paper studies the strength of embedding Call-by-Name () and Call-by-Value () into a unifying framework called the Bang Calculus (). These embeddings enable establishing (static and dynamic) properties of and through their respective counterparts in $$\texttt {dBANG} $$ dBANG . While some specific static properties have been already successfully studied in the literature, the dynamic ones are more challenging and have been left unexplored. We accomplish that by using a standard embedding for the (easy) case, while a novel one must be introduced for the (difficult) case. Moreover, a key point of our approach is the identification of diligent reduction sequences, which eases the preservation of dynamic properties from $$\texttt {dBANG} $$ dBANG to $$\texttt {dCBN}/\texttt {dCBV} $$ dCBN / dCBV . We illustrate our methodology through two concrete applications: confluence/factorization for both and are respectively derived from confluence/factorization for .