Optimizing Abstract Abstract Machines

The technique of abstracting abstract machines (AAM) provides a systematic approach for deriving computable approximations of evaluators that are easily proved sound. This article contributes a complementary step-by-step process for subsequently going from a naive analyzer derived under the AAM approach, to an efficient and correct implementation. The end result of the process is a two to three order-of-magnitude improvement over the systematically derived analyzer, making it competitive with hand-optimized implementations that compute fundamentally less precise results.Comment: Proceedings of the International Conference on Functional Programming 2013 (ICFP 2013). Boston, Massachusetts. September, 201

Addressing Machines as models of lambda-calculus

Turing machines and register machines have been used for decades in theoretical computer science as abstract models of computation. Also the $\lambda$-calculus has played a central role in this domain as it allows to focus on the notion of functional computation, based on the substitution mechanism, while abstracting away from implementation details. The present article starts from the observation that the equivalence between these formalisms is based on the Church-Turing Thesis rather than an actual encoding of $\lambda$-terms into Turing (or register) machines. The reason is that these machines are not well-suited for modelling \lam-calculus programs. We study a class of abstract machines that we call \emph{addressing machine} since they are only able to manipulate memory addresses of other machines. The operations performed by these machines are very elementary: load an address in a register, apply a machine to another one via their addresses, and call the address of another machine. We endow addressing machines with an operational semantics based on leftmost reduction and study their behaviour. The set of addresses of these machines can be easily turned into a combinatory algebra. In order to obtain a model of the full untyped $\lambda$-calculus, we need to introduce a rule that bares similarities with the $\omega$-rule and the rule $\zeta_\beta$ from combinatory logic

Can Automatic Abstracting Improve on Current Extracting Techniques in Aiding Users to Judge the Relevance of Pages in Search Engine Results?

Current search engines use sentence extraction techniques to produce snippet result summaries, which users may find less than ideal for determining the relevance of pages. Unlike extracting, abstracting programs analyse the context of documents and rewrite them into informative summaries. Our project aims to produce abstracting summaries which are coherent and easy to read thereby lessening users’ time in judging the relevance of pages. However, automatic abstracting technique has its domain restriction. For solving this problem we propose to employ text classification techniques. We propose a new approach to initially classify whole web documents into sixteen top level ODP categories by using machine learning and a Bayesian classifier. We then manually create sixteen templates for each category. The summarisation techniques we use include a natural language processing techniques to weight words and analyse lexical chains to identify salient phrases and place them into relevant template slots to produce summaries

Instruction sequence processing operators

Instruction sequence is a key concept in practice, but it has as yet not come prominently into the picture in theoretical circles. This paper concerns instruction sequences, the behaviours produced by them under execution, the interaction between these behaviours and components of the execution environment, and two issues relating to computability theory. Positioning Turing's result regarding the undecidability of the halting problem as a result about programs rather than machines, and taking instruction sequences as programs, we analyse the autosolvability requirement that a program of a certain kind must solve the halting problem for all programs of that kind. We present novel results concerning this autosolvability requirement. The analysis is streamlined by using the notion of a functional unit, which is an abstract state-based model of a machine. In the case where the behaviours exhibited by a component of an execution environment can be viewed as the behaviours of a machine in its different states, the behaviours concerned are completely determined by a functional unit. The above-mentioned analysis involves functional units whose possible states represent the possible contents of the tapes of Turing machines with a particular tape alphabet. We also investigate functional units whose possible states are the natural numbers. This investigation yields a novel computability result, viz. the existence of a universal computable functional unit for natural numbers.Comment: 37 pages; missing equations in table 3 added; combined with arXiv:0911.1851 [cs.PL] and arXiv:0911.5018 [cs.LO]; introduction and concluding remarks rewritten; remarks and examples added; minor error in proof of theorem 4 correcte