Full abstraction for probabilistic PCF

We present a probabilistic version of PCF, a well-known simply typed universal functional language. The type hierarchy is based on a single ground type of natural numbers. Even if the language is globally call-by-name, we allow a call-by-value evaluation for ground type arguments in order to provide the language with a suitable algorithmic expressiveness. We describe a denotational semantics based on probabilistic coherence spaces, a model of classical Linear Logic developed in previous works. We prove an adequacy and an equational full abstraction theorem showing that equality in the model coincides with a natural notion of observational equivalence

Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality

We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts published in a same volume. Part II is dedicated to the relation between logic and information system, within the scope of Kolmogorov algorithmic information theory. We present a recent application of Kolmogorov complexity: classification using compression, an idea with provocative implementation by authors such as Bennett, Vitanyi and Cilibrasi. This stresses how Kolmogorov complexity, besides being a foundation to randomness, is also related to classification. Another approach to classification is also considered: the so-called "Google classification". It uses another original and attractive idea which is connected to the classification using compression and to Kolmogorov complexity from a conceptual point of view. We present and unify these different approaches to classification in terms of Bottom-Up versus Top-Down operational modes, of which we point the fundamental principles and the underlying duality. We look at the way these two dual modes are used in different approaches to information system, particularly the relational model for database introduced by Codd in the 70's. This allows to point out diverse forms of a fundamental duality. These operational modes are also reinterpreted in the context of the comprehension schema of axiomatic set theory ZF. This leads us to develop how Kolmogorov's complexity is linked to intensionality, abstraction, classification and information system.Comment: 43 page

A dependent nominal type theory

Nominal abstract syntax is an approach to representing names and binding pioneered by Gabbay and Pitts. So far nominal techniques have mostly been studied using classical logic or model theory, not type theory. Nominal extensions to simple, dependent and ML-like polymorphic languages have been studied, but decidability and normalization results have only been established for simple nominal type theories. We present a LF-style dependent type theory extended with name-abstraction types, prove soundness and decidability of beta-eta-equivalence checking, discuss adequacy and canonical forms via an example, and discuss extensions such as dependently-typed recursion and induction principles

Logic programming in the context of multiparadigm programming: the Oz experience

Oz is a multiparadigm language that supports logic programming as one of its major paradigms. A multiparadigm language is designed to support different programming paradigms (logic, functional, constraint, object-oriented, sequential, concurrent, etc.) with equal ease. This article has two goals: to give a tutorial of logic programming in Oz and to show how logic programming fits naturally into the wider context of multiparadigm programming. Our experience shows that there are two classes of problems, which we call algorithmic and search problems, for which logic programming can help formulate practical solutions. Algorithmic problems have known efficient algorithms. Search problems do not have known efficient algorithms but can be solved with search. The Oz support for logic programming targets these two problem classes specifically, using the concepts needed for each. This is in contrast to the Prolog approach, which targets both classes with one set of concepts, which results in less than optimal support for each class. To explain the essential difference between algorithmic and search programs, we define the Oz execution model. This model subsumes both concurrent logic programming (committed-choice-style) and search-based logic programming (Prolog-style). Instead of Horn clause syntax, Oz has a simple, fully compositional, higher-order syntax that accommodates the abilities of the language. We conclude with lessons learned from this work, a brief history of Oz, and many entry points into the Oz literature.Comment: 48 pages, to appear in the journal "Theory and Practice of Logic Programming

A knowledge-based approach to VLSI-design in an open CAD-environment

A knowledge-based approach is suggested to assist a designer in the increasingly complex task of generating VLSI-chips from abstract, high-level specifications of the system. The complexity of designing VLSI-circuits has reached a level where computer-based assistance has become indispensable. Not all of the design tasks allow for algorithmic solutions. AI technique can be used, in order to support the designer with computer-aided tools for tasks not suited for algorithmic approaches. The approach described in this paper is based upon the underlying characteristics of VLSI design processes in general, comprising all stages of the design. A universal model is presented, accompanied with a recording method for the acquisition of design knowledge - strategic and task-specific - in terms of the design actions involved and their effects on the design itself. This method is illustrated by a simple design example: the implementation of the logical EXOR-component. Finally suggestions are made for obtaining a universally usable architecture of a knowledge-based system for VLSI-design

On Equivalence and Canonical Forms in the LF Type Theory

Decidability of definitional equality and conversion of terms into canonical form play a central role in the meta-theory of a type-theoretic logical framework. Most studies of definitional equality are based on a confluent, strongly-normalizing notion of reduction. Coquand has considered a different approach, directly proving the correctness of a practical equivalance algorithm based on the shape of terms. Neither approach appears to scale well to richer languages with unit types or subtyping, and neither directly addresses the problem of conversion to canonical. In this paper we present a new, type-directed equivalence algorithm for the LF type theory that overcomes the weaknesses of previous approaches. The algorithm is practical, scales to richer languages, and yields a new notion of canonical form sufficient for adequate encodings of logical systems. The algorithm is proved complete by a Kripke-style logical relations argument similar to that suggested by Coquand. Crucially, both the algorithm itself and the logical relations rely only on the shapes of types, ignoring dependencies on terms.Comment: 41 page

GoFFish: A Sub-Graph Centric Framework for Large-Scale Graph Analytics

Large scale graph processing is a major research area for Big Data exploration. Vertex centric programming models like Pregel are gaining traction due to their simple abstraction that allows for scalable execution on distributed systems naturally. However, there are limitations to this approach which cause vertex centric algorithms to under-perform due to poor compute to communication overhead ratio and slow convergence of iterative superstep. In this paper we introduce GoFFish a scalable sub-graph centric framework co-designed with a distributed persistent graph storage for large scale graph analytics on commodity clusters. We introduce a sub-graph centric programming abstraction that combines the scalability of a vertex centric approach with the flexibility of shared memory sub-graph computation. We map Connected Components, SSSP and PageRank algorithms to this model to illustrate its flexibility. Further, we empirically analyze GoFFish using several real world graphs and demonstrate its significant performance improvement, orders of magnitude in some cases, compared to Apache Giraph, the leading open source vertex centric implementation.Comment: Under review by a conference, 201