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A Complete, Co-Inductive Syntactic Theory of Sequential Control and
State
Kristian Støvring
February 2007 |
Abstract:
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.
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. 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. Available as PostScript, PDF, DVI. |