HOR 2012 6th International Workshop on Higher-Order Rewriting

The aim of HOR is to provide an informal forum to discuss all aspects of higher-order rewriting. The topics of the workshop include applications, foundations, frameworks, implementations , and semantics. HOR is a biannual meeting. The present volume provides final versions of six accepted contributed extended abstracts of talks selected for the workshop. HOR 2012 had also a tool session. The following termination checkers for higher-order rewriting systems was presented: • Carsten Fuhs: Haskell termination tool • Rene Thiemann: Isabelle termination tool • Takahito Aoto and Toshiyuki Yamada: Simply-typed TRS termination tool • Cynthia Kop: WANDA, termination tool for Algebraic Functional Systems We are grateful to these authors for accepting to present thier tools at HOR. We are also very grateful to Zhenjiang Hu (National Institute of Informatics, Japan) for kindly accepting to give an invited talk at HOR 2012. Many thanks to the program committee that I had the pleasure to chair, consisting of de Vries. The tasks were the decisions on the invited speakers, a timely refereeing of the submitted abstracts and the final decisions on the program. A heartfelt thank you to the HOR workshop series steering committee , Delia Kesner and Femke van Raamsdonk, who offered me to take this responsibility for the higher-order rewriting community and gave valuable advice throughout. Finally, we would like to thank the organizing committee of RTA 2012, and in particular Naoki Nishida, for all help in the preparation of the workshop. Bidirectional transformations provide a novel mechanism for synchronizing and maintaining the consistency of information between input and output. Despite many promising results on bidirectional transformations, these have been limited to lists and trees. We challenge the problem of bidirectional transformations on graphs, by proposing a formal definition of a well-behaved bidirectional semantics for UnCAL, a graph algebra. Our key idea is to treat graphs as compactable infinite trees and to manipulate trees by structural recursion. Specifically, we carefully refine the existing forward evaluation of structural recursion so that it can produce sufficient trace information for later backward evaluation, and we use the trace information for backward evaluation to reflect updates on the view to the source. We prove our bidirectional evaluation is well-behaved. We extend a framework of program transformation by templates based on first order term rewriting (Chiba et al., 2005) to simply typed term rewriting (Yamada, 2001), which is a framework of higher order term rewriting. A …