Slotted-Circus: A UTP-Family of Reactive Theories

Abstract

We present a generic framework of UTP theories for describing systems whose behaviour is characterised by regular time-slots, compatible with the general structure of the Circus language [WC01a]. This ?slotted-Circus? framework is parameterised by the particular way in which event histories are observable within a time-slot, and specifies what laws a desired parameterisation must obey in order for a satisfactory theory to emerge. Two key results of this work are: the need to be very careful in formulating the healthiness conditions, particularly R2 ; and the demonstration that synchronous theories like SCSP [Bar93] do not fit well with the way reactive systems are currently formulated in UTP and Circus.