Modeling Terms by Graphs with Structure Constraints (Two Illustrations)

In the talk at the workshop my aim was to demonstrate the usefulness of graph techniques for tackling problems that have been studied predominantly as problems on the term level: increasing sharing in functional programs, and addressing questions about Milner's process semantics for regular expressions. For both situations an approach that is based on modeling terms by graphs with structure constraints has turned out to be fruitful. In this extended abstract I describe the underlying problems, give references, provide examples, indicate the chosen approaches, and compare the initial situations as well as the results that have been obtained, and some results that are being developed at present.