A new abstract model of interaction between agents and environments considered as objects of diierent types is introduced. Agents are represented by means of labelled transition systems considered up to bisimilarity. The equivalence of agents is characterised in terms of an algebra of behaviours which is a continuous algebra with approximation and two operations: nondeterministic choice and preexing. Environments are introduced as agents supplied with an insertion function which takes the behaviour of an agent and the behaviour of an environment as arguments and returns the new behaviour of an environment. Arbitrary continuous functions can be used as insertion functions, and we use functions deened by means of rewriting logic as computable ones. The transformation of environment behaviours deened by the insertion function also deenes a new type of agent equivalence | insertion equivalence. Two behaviours are insertion equivalent if they deene the same transformation of an environment. The properties of this equivalence are studied. Three main types of insertion functions are used to develop interesting applications: one-step insertion, head insertion, and look-ahead insertion functions.
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