Balancing Lists: A Proof Pearl

Proof Pearl: Defining Functions over Finite Sets

Structural recursion over sets is meaningful only if the result is independent of the order in which the set’s elements are enumerated. This paper outlines a theory of function definition for finite sets, based on the fold functionals often used with lists. The fold functional is introduced as a relation, which is then shown to denote a function under certain conditions. Applications include su...

Cycle Time Optimization of Processes Using an Entropy-Based Learning for Task Allocation

Cycle time optimization could be one of the great challenges in business process management. Although there is much research on this subject, task similarities have been paid little attention. In this paper, a new approach is proposed to optimize cycle time by minimizing entropy of work lists in resource allocation while keeping workloads balanced. The idea of the entropy of work lists comes fr...

Proof Pearl: The Termination Analysis of Terminator

Terminator is a static analysis tool developed by Microsoft Research for proving termination of Windows device drivers written in C. This proof pearl describes a formalization in higher order logic of the program analysis employed by Terminator, and verifies that if the analysis succeeds then program termination logically follows.

Proof Pearl: A New Foundation for Nominal Isabelle

Pitts et al introduced a beautiful theory about names and binding based on the notions of permutation and support. The engineering challenge is to smoothly adapt this theory to a theorem prover environment, in our case Isabelle/HOL. We present a formalisation of this work that differs from our earlier approach in two important respects: First, instead of representing permutations as lists of pa...

Proof Pearl : Dijkstra ' s Shortest Path