
Strong Bisimulation for Control Operators
The purpose of this paper is to identify programs with control operators...
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A Strong Bisimulation for Control Operators by Means of Multiplicative and Exponential Reduction
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 λμcalculus we dub Λ M. Our result builds on three main ingredients which guide our semantical development: (1) factorization of Parigot's λμreduction into multiplicative and exponential steps by means of explicit operators, (2) adaptation of Laurent's original ≃_σequivalence to Λ M, and (3) interpretation of Λ M into Laurent's polarized proofnets (PPN). More precisely, we first give a translation of Λ Mterms into PPN which simulates the reduction relation of our calculus via cut elimination of PPN. Second, we establish a precise correspondence between our relation ≃ and Laurent's ≃_σequivalence for λμterms. Moreover, ≃equivalent terms translate to structurally equivalent PPN. Most notably, ≃ is shown to be a strong bisimulation with respect to reduction in Λ M, i.e. two ≃equivalent terms have the exact same reduction semantics, a result which fails for Regnier's ≃_σequivalence in λcalculus as well as for Laurent's ≃_σequivalence in λμ.
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