Nested Term Graphs (Work In Progress)

We report on work in progress on 'nested term graphs' for formalizing higher-order terms (e.g. finite or infinite lambda-terms), including those expressing recursion (e.g. terms in the lambda-calculus with letrec). The idea is to represent the nested scope structure of a higher-order term by a nested structure of term graphs. Based on a signature that is partitioned into atomic and nested function symbols, we define nested term graphs both in a functional representation, as tree-like recursive graph specifications that associate nested symbols with usual term graphs, and in a structural representation, as enriched term graph structures. These definitions induce corresponding notions of bisimulation between nested term graphs. Our main result states that nested term graphs can be implemented faithfully by first-order term graphs. keywords: higher-order term graphs, context-free grammars, cyclic lambda-terms, higher-order rewrite systemsComment: In Proceedings TERMGRAPH 2014, arXiv:1505.0681

Layer Systems for Proving Confluence

We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that imply confluence. Our abstract framework covers known results like modularity, many-sorted persistence, layer-preservation and currying. We present a counterexample to an extension of persistence to order-sorted rewriting and derive new sufficient conditions for the extension to hold. All our proofs are constructive

Realising Optimal Sharing

Realising Optimal Sharin

Family Matters: Adjustment to genetic cancer susceptibility testing

Cancer is generally feared because it is associated with death and severe physical suffering. It is one of the most common causes of death in the Netherlands. Breast and colon cancer are the most prevalent types of cancer among women. Frequently occurring types in men are cancer of colon, lung and prostate. About 5% of colorectal and breast cancer arises as a result of a mutation in an inherited cancer susceptibility gene. Knowledge about these cancer susceptibility genes has been accumulating in an impressive manner over the last decades, resulting in the clinical availability of genetic testing from the mid-nineties onward. Through genetic testing, an individual’s risk to develop cancer can be determined more precisely. This can reduce feelings of uncertainty about the r