New Notions of Reduction and Non-Semantic Proofs of β-Strong Normalization in Typed λ-Calculi

Two new notions of reduction for terms of the λ-calculus are introduced and the question of whether a λ-term is beta-strongly normalizing is reduced to the question of whether a λ-term is merely normalizing under one of the new notions of reduction. This leads to a new way to prove beta-strong normalization for typed λ-calculi. Instead of the usual semantic proof style based on Girard's "candidats de réductibilité'', termination can be proved using a decreasing metric over a well-founded ordering in a style more common in the field of term rewriting. This new proof method is applied to the simply-typed λ-calculus and the system of intersection types.

Addendum to "New Notions of Reduction and Non-Semantic Proofs of β-Strong Normalization in Typed λ-Calculi"

This is an addendum to our technical report BUCS TR-94-014 of December 19, 1994. It clarifies some statements, adds information on some related research, includes a comparison with research be de Groote, and fixes two minor mistakes in a proof.

Measuring Bottleneck Link Speed in Package-Switched Networks

The quality of available network connections can often have a large impact on the performance of distributed applications. For example, document transfer applications such as FTP, Gopher and the World Wide Web suffer increased response times as a result of network congestion. For these applications, the document transfer time is directly related to the available bandwidth of the connection. Available bandwidth depends on two things: 1) the underlying capacity of the path from client to server, which is limited by the bottleneck link; and 2) the amount of other traffic competing for links on the path. If measurements of these quantities were available to the application, the current utilization of connections could be calculated. Network utilization could then be used as a basis for selection from a set of alternative connections or servers, thus providing reduced response time. Such a dynamic server selection scheme would be especially important in a mobile computing environment in which the set of available servers is frequently changing. In order to provide these measurements at the application level, we introduce two tools: bprobe, which provides an estimate of the uncongested bandwidth of a path; and cprobe, which gives an estimate of the current congestion along a path. These two measures may be used in combination to provide the application with an estimate of available bandwidth between server and client thereby enabling application-level congestion avoidance. In this paper we discuss the design and implementation of our probe tools, specifically illustrating the techniques used to achieve accuracy and robustness. We present validation studies for both tools which demonstrate their reliability in the face of actual Internet conditions; and we give results of a survey of available bandwidth to a random set of WWW servers as a sample application of our probe technique. We conclude with descriptions of other applications of our measurement tools, several of which are currently under development.