An algebraic approach to computations with progress

The notion of progress appears in various computation models, for example, in the form of traces getting longer, passing of real time, incrementing a counter, going from termination to non-termination. We introduce a model of sequential computations that generalises and abstracts these examples. We generalise existing algebras for non-terminating executions and instantiate these with our model. Using these algebras we derive an approximation order for computations with time and for trace-based computations. We introduce a generalisation of omega algebras to express iteration in the new model.