Equational axiomatization of call-by-name delimited control

Yukiyoshi Kameyama, Asami Tanaka
2010 Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming - PPDP '10  
Control operators for delimited continuations are useful in various fields such as partial evaluation, CPS translation, and representation of monadic effects. While many works in the literature study them in call-by-value, several recent works have shown call-by-name delimited control operators are also worth studying. In this paper, we study semantic foundation of the call-by-name variant of the delimited-control operators "shift" and "reset". In particular, we give a set of direct-style
more » ... ons as axioms for them, and prove that it is sound and complete with respect to the CPS translation by Biernacka and Biernacki. The key observations in our proof are (1) we need to use the linearity of certain variables in the CPS terms, and (2) we must distinguish continuation variables from ordinary variables in the source terms. We also show that our axiomatization holds for the typed calculus. • The semantics of the target calculus after the CPS translation: the standard CPS translation for delimited-control operators translates source terms into non-CPS terms, namely, arguments
doi:10.1145/1836089.1836100 dblp:conf/ppdp/KameyamaT10 fatcat:nxoi2vib2fgcvlc3g6hmhabkhe