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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-styledoi:10.1145/1836089.1836100 dblp:conf/ppdp/KameyamaT10 fatcat:nxoi2vib2fgcvlc3g6hmhabkhe