Paper detail

Strong Bisimulation for Control Operators

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 $\simeq$, defined over a revised presentation of Parigot's $λμ$-calculus we dub $ΛM$. Our result builds on two fundamental ingredients: (1) factorization of $λμ$-reduction into multiplicative and exponential steps by means of explicit term operators of $ΛM$, and (2) translation of $ΛM$-terms into Laurent's polarized proof-nets (PPN) such that cut-elimination in PPN simulates our calculus. Our proposed relation $\simeq$ is shown to characterize structural equivalence in PPN. Most notably, $\simeq$ is shown to be a strong bisimulation with respect to reduction in $ΛM$, i.e. two $\simeq$-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 $λμ$.