Theorywhile

Theorywhile is a formal framework in theoretical computer science for the analysis and verification of while loops in imperative programming languages. It offers a calculus for deriving preconditions and postconditions for programs that feature while constructs, with particular emphasis on termination properties and the propagation of loop invariants across iterations.

The core idea of theorywhile is to model a loop as a state-transition system augmented with a progress metric. A program state encodes the values of variables, while a time or step index captures iteration progress. A loop invariant is a property that remains true before and after each iteration, and a well-founded termination measure that strictly decreases with each iteration guarantees termination under the loop’s guard.

Formal foundations of theorywhile integrate concepts from Hoare logic with notions of temporal or step-based semantics. The framework describes rules for the while construct that pair invariant maintenance with a ranking function, and it treats the loop as a least fixed point of a transition operator. This provides a basis for proving partial correctness together with termination.

Relations to existing work and applications: theorywhile relates to Hoare logic, temporal logic, and fixed-point theory. It is used primarily in academic discussions, pedagogy, and formal verification research to reason about iterative behavior. Tool support exists in prototype verifiers and educational simulators, though automation remains challenging for complex loops.

History and usage notes: The term theorywhile emerged in the mid-2010s in theoretical discussions about loop reasoning and has since appeared in textbooks and conference tutorials as a compact framework for presenting loop verification concepts.