@article{Støvring_Lassen_2007, title={A Complete, Co-Inductive Syntactic Theory of Sequential Control and State}, volume={14}, url={https://tidsskrift.dk/brics/article/view/21927}, DOI={10.7146/brics.v14i4.21927}, abstractNote={We present a new co-inductive syntactic theory, eager normal form bisimilarity, for the untyped call-by-value lambda calculus extended with continuations and mutable references.<br /> <br />We demonstrate that the associated bisimulation proof principle is easy to use and that it is a powerful tool for proving equivalences between recursive imperative higher-order programs.<br /> <br />The theory is modular in the sense that eager normal form bisimilarity for each of the calculi extended with continuations and/or mutable references is a fully abstract extension of eager normal form bisimilarity for its sub-calculi. For each calculus, we prove that eager normal form bisimilarity is a congruence and is sound with respect to contextual equivalence. Furthermore, for the calculus with both continuations and mutable references, we show that eager normal form bisimilarity is complete: it coincides with contextual equivalence.}, number={4}, journal={BRICS Report Series}, author={Støvring, Kristian and Lassen, Søren B.}, year={2007}, month={Feb.} }