We present a model and a core programming language appropriate for modeling and programming interactive computing systems. The model consists of rv-systems (interactive systems with registers and voices); it includes register machines, is space-time invariant, is compositional, may describe computations extending in both time and space, and is applicable to open, interactive systems. To achieve modularity in space the model uses voices (a voice is the time dual of a register) they provide a high level organization of temporal data and are used to describe interaction interfaces of processes. The programming language uses novel techniques for syntax and semantics to support computation in space paradigm. We describe rv-programs and base their syntax and operational semantics on FISes (finite interactive systems) and their grid languages (a FIS is a kind of 2-dimensional automaton specifying both control and interaction used in rv-programs). We also present specification techniques for rv-systems, using relations between input registers and voices and their output counterparts. The paper includes simple specifications for an OO-system and for an interactive game.