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.

Basis Token Consistency: A Practical Mechanism for Strong Web Cache Consistency

With web caching and cache-related services like CDNs and edge services playing an increasingly significant role in the modern internet, the problem of the weak consistency and coherence provisions in current web protocols is becoming increasingly significant and drawing the attention of the standards community [LCD01]. Toward this end, we present definitions of consistency and coherence for web-like environments, that is, distributed client-server information systems where the semantics of interactions with resource are more general than the read/write operations found in memory hierarchies and distributed file systems. We then present a brief review of proposed mechanisms which strengthen the consistency of caches in the web, focusing upon their conceptual contributions and their weaknesses in real-world practice. These insights motivate a new mechanism, which we call "Basis Token Consistency" or BTC; when implemented at the server, this mechanism allows any client (independent of the presence and conformity of any intermediaries) to maintain a self-consistent view of the server's state. This is accomplished by annotating responses with additional per-resource application information which allows client caches to recognize the obsolescence of currently cached entities and identify responses from other caches which are already stale in light of what has already been seen. The mechanism requires no deviation from the existing client-server communication model, and does not require servers to maintain any additional per-client state. We discuss how our mechanism could be integrated into a fragment-assembling Content Management System (CMS), and present a simulation-driven performance comparison between the BTC algorithm and the use of the Time-To-Live (TTL) heuristic.

Safe Compositional Specification of Networking Systems: TRAFFIC The Language and Its Type Checking

This paper formally defines the operational semantic for TRAFFIC, a specification language for flow composition applications proposed in BUCS-TR-2005-014, and presents a type system based on desired safety assurance. We provide proofs on reduction (weak-confluence, strong-normalization and unique normal form), on soundness and completeness of type system with respect to reduction, and on equivalence classes of flow specifications. Finally, we provide a pseudo-code listing of a syntax-directed type checking algorithm implementing rules of the type system capable of inferring the type of a closed flow specification.

A Self-Organizing Neural Network Model for Redundant Sensory-Motor Control, Motor Equivalence, and Tool Use

A neural network is introduced which provides a solution of the classical motor equivalence problem, whereby many different joint configurations of a redundant manipulator can all be used to realize a desired trajectory in 3-D space. To do this, the network self-organizes a mapping from motion directions in 3-D space to velocity commands in joint space. Computer simulations demonstrate that, without any additional learning, the network can generate accurate movement commands that compensate for variable tool lengths, clamping of joints, distortions of visual input by a prism, and unexpected limb perturbations. Blind reaches have also been simulated.