Programs with Continuations and Linear Logic

A programming language with continuations is studied in the framework of Girard's linear logic. The execution of a program with continuations is in general non-deterministic: the result of computation depends on the evaluation strategy, e.g. call-by-value evaluation, call-by-name evaluation, ..., etc. In this paper, we first introduce λ c → , a programming language with continuations, and then define the translation from λ c → to linear logic, which eliminates the non-determinism of λ c → . The relation between computation of λ c → and normalization of linear logic is also shown.