The asynchronous #-calculus is considered the basis of experimental programming languages (or proposal of programming languages) like Pict, Join, and TyCO. However, at a closer inspection, these languages are based on an even simpler calculus, called Localised # (L#), where: (a) only the output capability of names may be transmitted; (b) there is no matching or similar constructs for testing equality between names. We study the basic operational and algebraic theory of L#. We focus on bisimulationbased behavioural equivalences, precisely on barbed congruence. We prove two coinductive characterisations of barbed congruence in L#, and some basic algebraic laws. We then show applications of this theory, including: the derivability of the delayed input; the correctness of an optimisation of the encoding of call-by-name #-calculus; the validity of some laws for Join;
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