A Short Mechanized Proof of the Church-Rosser Theorem by the Z-property for the λβ-calculus in Nominal Isabelle

5th International Workshop on Confluence5th International Workshop on ConfluenceWe present a short proof of the Church-Rosser property for the lambda-calculus enjoying two distinguishing features: Firstly, it employs the Z-property, resulting in a short and elegant proof; and secondly, it is formalized in the nominal higher-order logic available for the proof assistant Isabelle/HOL

Critical Peaks Redefined - Φ⊔Ψ=⊤

6th International Workshop on Confluence6th International Workshop on ConfluenceLet a cluster be a term with a number of patterns occurring in it. We give two accounts of clusters, a geometric one as sets of (node and edge) positions, and an inductive one as pairs of terms with gaps (2nd order variables) and pattern-substitutions for the gaps. We show both notions of cluster and the corresponding refinement/coarsening orders on them, to be isomorphic. This equips clusters with a lattice structure which we lift to (parallel/multi) steps to yield an alternative account of the notion of critical peak

Consensus guidelines for the use and interpretation of angiogenesis assays

The formation of new blood vessels, or angiogenesis, is a complex process that plays important roles in growth and development, tissue and organ regeneration, as well as numerous pathological conditions. Angiogenesis undergoes multiple discrete steps that can be individually evaluated and quantified by a large number of bioassays. These independent assessments hold advantages but also have limitations. This article describes in vivo, ex vivo, and in vitro bioassays that are available for the evaluation of angiogenesis and highlights critical aspects that are relevant for their execution and proper interpretation. As such, this collaborative work is the first edition of consensus guidelines on angiogenesis bioassays to serve for current and future reference