K: A Rewriting-Based Framework for Computations

K is a definitional framework based on term rewriting, in which programming languages, calculi, as well as type systems or formal analysis tools can be defined making use of special list and/or set structures, called cells, which can be potentially nested. In addition to cells, K definitions contain equations capturing structural equivalences that do not count as computational steps, and rewrite rules capturing computational steps or irreversible transitions. Rewrite rules in K are unconditional, i.e., they need no computational premises (they are rule schemata and may have ordinary side conditions, though), and they are context-insensitive, so in K rewrite rules apply concurrently as soon as they match, without any contextual delay or restrictions. The distinctive feature of K compared to other term rewriting approaches in general and to rewriting logic in particular, is that K allows rewrite rules to apply concurrently even in cases when they overlap, provided that they do not change the overlapped portion of the term. This allows for truly concurrent semantics to programming languages and calculi. For example, two threads that read the same location of memory can do that concurrently, even though the corresponding rules overlap on the store location being read. The distinctive feature of K compared to other frameworks for true concurrency, like chemical abstract machines (Chams) or membrane systems (P-systems), is that equations and rewrite rules can match across multiple cells and thus perform changes many places at the same time, in one step. K provides special support for list cells that carry “computational meaning”, called computations. Computations are special “y”-separated lists “T1 y T2 y · · · y Tn” comprising computational tasks, thought of as having to be “processed” sequentially. Computation (structural) equations or heating/cooling equations, which technically are ordinary equations but which practically tend to have a