A Bisimulation for Type Abstraction and Recursion
We present a sound, complete, and elementary proof method, based on bisimulation, for contextual equivalence in a λ-calculus with full universal, existential, and recursive types. Unlike logical relations (either semantic or syntactic), our development is elementary, using only sets and relations and avoiding advanced machinery such as domain theory, admissibility, and TT-closure. Unlike other bisimulations, ours is complete even for existential types. The key idea is to consider sets of relations—instead of just relations—as bisimulations.
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Postprint version. Copyright ACM, 2005. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages 2005, pages 63-74. Publisher URL: http://doi.acm.org/10.1145/1040305.1040311