Pattern Calculus

Abstract

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: KünkelLopka, GmbH Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) To my parents VII VIII ForewordIntegrating the new technology in established settings in order to enhance their expressive power may well have a significant practical impact. People are much more prepared to accept new functionality in their known settings than totally changing paradigm. Another approach would be to use the pattern calculus as an "embedded technology" for dealing with matching and adaptation. Promising application scenarios for such an enterprise include Web Service discovery and mediation.The described multiple dimensions of impact of the pattern calculus indicate the potential audience. It may range from students who want to get a deeper insight into the basic principles, to language designers interested in enhancing the power of their languages, to tool and service designers in need of new, powerful technologies. The "How to Read This Book" chapter shows that the author wants to address all these communities, and he stands a good chance of being successful.It should not be forgotten, however, that the book focuses on foundations, and that it assumes a good theoretical background. Therefore interpreters will be needed so that the technology reaches the places where it will eventually have the largest impact, and I hope that the book will inspire this kind of technology transfer, whose value cannot be overestimated. Dortmund,Bernhard Steffen March, 2009 I am particularly indebted to Microsoft Research (Cambridge) for their support while writing this book, and to the University of Technology, Sydney for giving me the freedom to pursue my thoughts.

Semantics of Typed Lambda-Calculus with Constructors

“…Related works. The first presentation of the pattern calculus [13] comes with a ML-style type system. This type system is less expressive than ours and does not prevent match failure during reduction, but it is decidable.…”

“…In[19] the proof fails at Lemma 10. There is a counterexample to the converse of equivalence(13), surprisingly due to the notion of modified substitution used there.…”

Typed self-interpretation by pattern matching

“…This style of pattern matching, also known as path polymorphism [16,18,19], cannot be expressed in pure λ-calculus or even in a combinator calculus with the operators Y , S, K, B. So, our calculus has the operator F and the novel operator E, and we make them play key roles when we de-sugar pattern matching.…”

“…Berarducci and Bohm achieved this by considering how to solve equations inside lambda calculus but now there is a more direct and powerful method, in the pattern calculus of Jay and Kesner [16,18,19]. Although it may be possible to achieve our main goals in pure pattern calculus (or even static pattern calculus), this paper adopts a simpler and more direct approach.…”

Focusing on pattern matching

“…This ensures the correctness of the compilation, but he does not consider the question of coverage checking. Jay (2004) has also introduced a pattern calculus. Roughly, he takes the view that datatypes are just subsets of the universe of program terms (like Prolog's Herbrand universe), and then allows defining programs to match on the underlying tree representations of arbitrary data.…”