Strong Bisimulation for Control Operators

06/22/2019 ∙ by Eduardo Bonelli, et al. ∙ 0

The purpose of this paper is to identify programs with control operators whose reduction semantics are in exact correspondence. This is achieved by introducing a relation ≃, defined over a revised presentation of Parigot's λμ-calculus we dub Λ M. Our result builds on three main ingredients which guide our semantical development: (1) factorization of Parigot's λμ-reduction into multiplicative and exponential steps by means of explicit operators, (2) adaptation of Laurent's original σ-equivalence to Λ M, and (3) interpretation of Λ M into Laurent's polarized proof-nets (PPN). More precisely, we first give a translation of Λ M-terms into PPN which simulates the reduction relation of our calculus into cut elimination of PPN. Second, we establish a precise relation between our relation ≃ and Laurent's σ-equivalence for λμ-terms. Moreover, ≃ is shown to characterize structural equivalence in PPN. Most notably, ≃ is shown to be a strong bisimulation with respect to reduction in Λ M, two ≃-equivalent terms have the exact same reduction semantics, a result which fails for Regnier's σ-equivalence in λ-calculus as well as for Laurent's σ-equivalence in λμ.

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