Abstract. The asynchronous-calculus is considered the basis of experimental programming languages (or proposal of programming languages) like Pict, Join, and Blue calculus. However, at a closer inspection, these languages are based on an even simpler calculus, called Local (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 bisimulation-based 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 delayed input; the correctness of an optimisation of the encoding of call-by-name-calculus; the validity of some laws for Join. 1
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