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3rd workshop on mathematically structured functional programming

作者： Escardo, Martin Oliva, Paulo Univ Birmingham Birmingham B15 2TT W Midlands England

ISBN: (纸本)9781450302555

This is a tutorial for mathematically inclined functional programmers, based on previously published, peered reviewed theoretical work. We discuss a higher-type functional, written here in the functional programming language Haskell, which (1) optimally plays sequential games, (2) implements a computational version of the Tychonoff Theorem from topology, and (3) realizes the Double-Negation Shift from logic and proof theory. The functional makes sense for finite and infinite (lazy) lists, and in the binary case it amounts to an operation that is available in any (strong) monad. In fact, once we define this monad in Haskell, it turns out that this amazingly versatile functional is already available in Haskell, in the standard prelude, called sequence, which iterates this binary operation. Therefore Haskell proves that this functional is even more versatile than anticipated, as the function sequence was introduced for other purposes by the language designers, in particular the iteration of a list of monadic effects (but effects are not what we discuss here).

关键词： functional programming Haskell monad search game theory optimal strategy exhaustible set axiom of choice infinite data dependent type Agda topology logic foundations

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Hereditarily Finite Representations of Natural Numbers and Self-Delimiting Codes

Hereditarily Finite Representations of Natural Numbers and S...

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3rd workshop on mathematically structured functional programming

作者： Tarau, Paul Univ N Texas Dept Comp Sci & Engn Denton TX 76203 USA

ISBN: (纸本)9781450302555

Using a bijection between natural numbers and hereditarily finite functions we derive a new reversible variable length self-delimiting code through a bitstring representation in a balanced parenthesis language. The code features the ability to encode arbitrarily nested data types, can represent huge (low "complexity") numbers, and is decodable from its beginning or its end. Besides its possible practical applications to media stream encodings, a comparison with the well-known Elias omega code and a conjecture about its asymptotic: behavior under the Kraft inequality suggest it as an interesting object of study for experimental mathematicians. The paper is organized as a self-contained literate Haskell program inviting the reader to explore its content independently. Its code is available at http://***/tarau/research/2010/***.

关键词： computational mathematics and functional programming hereditarily finite data types self-delimiting codes reversible variable length codes ranking/unranking bijections

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MSFP'10 - Proceedings of the 2010 ACM SIGPLAN workshop on mathematically structured functional programming, Co-located with ICFP'10

MSFP'10 - Proceedings of the 2010 ACM SIGPLAN Workshop on Ma...

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3rd workshop on mathematically structured functional programming, MSFP 2010

ISBN: (纸本)9781450302555

The proceedings contain 5 papers. The topics discussed include: hereditary substitutions for simple types, formalized;hereditarily finite representations of natural numbers and self-delimiting codes;foundational program verification in Coq with automated proofs;type inference in context;and arrows are strong monads.

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A multistrategy approach to relational knowledge discovery in databases

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MACHINE LEARNING 1997年第3期27卷 287-312页

作者： Morik, K Brockhausen, P Computer Science Department LS VIII Univ. Dortmund Dortmund

When learning from very large databases, the reduction of complexity is extremely important. Two extremes of making knowledge discovery in databases (KDD) feasible have been put forward. One extreme is to choose a very simple hypothesis language, thereby being capable of very fast learning on real-world databases. The opposite extreme is to select a small data set, thereby being able to learn very expressive (first-order logic) hypotheses. A multistrategy approach allows one to include most of these advantages and exclude most of the disadvantages. Simpler learning algorithms detect hierarchies which are used to structure the hypothesis space for a more complex learning algorithm. The better structured the hypothesis space is, the better learning can prune away uninteresting or losing hypotheses and the faster it becomes. We have combined inductive logic programming (ILP) directly with a relational database management system. The ILP algorithm is controlled in a model-driven way by the user and in a data-driven way by structures that are induced by three simple learning algorithms.

关键词： knowledge discovery in databases inductive logic programming functional dependencies numerical intervals background knowledge

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McFSM: Globally Taming Complex Systems 3

McFSM: Globally Taming Complex Systems

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IEEE/ACM 3rd International workshop on Software Engineering for Smart Cyber-Physical Systems (SEsCPS)

作者： Murr, Florian Mauerer, Wolfgang Siemens AG Corp Res Otto Hahn Ring 6 D-81739 Munich Germany Tech Univ Appl Sci Regensburg Siemens AG Corp Res Regensburg Germany Tech Univ Appl Sci Regensburg Siemens AG Corp Res Munich Germany

ISBN: (纸本)9781538640432

Industrial computing devices, in particular cyber-physical, real-time and safety-critical systems, focus on reacting to external events and the need to cooperate with other devices to create a functional system. They are often implemented with languages that focus on a simple, local description of how a component reacts to external input data and stimuli. Despite the trend in modern software architectures to structure systems into largely independent components, the remaining interdependencies still create rich behavioural dynamics even for small systems. Standard and industrial programming approaches do usually not model or extensively describe the global properties of an entire system. Although a large number of approaches to solve this dilemma have been suggested, it remains a hard and error-prone task to implement systems with complex interdependencies correctly. We introduce multiple coupled finite state machines (McFSMs), a novel mechanism that allows us to model and manage such interdependencies. It is based on a consistent, well-structured and simple global description. A sound theoretical foundation is provided, and associated tools allow us to generate efficient low-level code in various programming languages using model-driven techniques. We also present a domain specific language to express McFSMs and their connections to other systems, to model their dynamic behaviour, and to investigate their efficiency and correctness at compile-time.

关键词： Observers Unified modeling language programming DSL Object oriented modeling Software engineering

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Tools for the implementation of argumentation models

Tools for the implementation of argumentation models

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3rd Imperial College Computing Student workshop, ICCSW 2013

作者： Van Gijzel, Bas Functional Programming Laboratory School of Computer Science University of Nottingham United Kingdom

ISBN: (纸本)9783939897637

The structured approach to argumentation has seen a surge of models, introducing a multitude of ways to deal with the formalisation of arguments. However, while the development of the mathematical models have flourished, the actual implementations and development of methods for implementation of these models have been lagging behind. This paper attempts to alleviate this problem by providing methods that simplify implementation, i.e. we demonstrate how the functional programming language Haskell can naturally express mathematical definitions and sketch how a theorem prover can verify this implementation. Furthermore, we provide methods to streamline the documenting of code, showing how literate programming allows the implementer to write formal definition, implementation and documentation in one file. All code has been made publicly available and reusable.

关键词： functional programming

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Proceedings of the ACM SIGPLAN International Conference on functional programming, ICFP: Foreword

Proceedings of the ACM SIGPLAN International Conference on F...

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Proceedings of the ACM SIGPLAN International Conference on functional programming, ICFP 2010年 iii页

作者： Capretta, Venanzio Chapman, James University of Nottingham United Kingdom Institute of Cybernetics Tallinn Estonia

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Semantics of block structured languages with pointers 3rd

Semantics of block structured languages with pointers

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3rd workshop on the Mathematical Foundations of programming Language Semantics, 1987

作者： Wagner, Eric G. Mathematical Sciences Department IBM T.J. Watson Research Center Yorktown HeightsNY10598 United States

ISBN: (纸本)9783540190202

This paper presents an algebraic and categorical approach to the mathematical modeling of imperative programming languages. In particular we model languages with block structure, records and variants, user definable recursive types, and pointers, etc., and with "control constructs" such as primitive recursion (generalized to recursive types), while-do, if-then-else, and assignment. In our earlier papers on this subject ([4], [5], [6]) we showed how data types and operations can be defined in an algebraic framework. In this paper we present a more mathematically sophisticated version of that framework, and we show how it can be used to provide a new approach to languages that have block structure together with objects, such as pointers, which are dynamically declared and may persist outside the block in which they are declared. The main new mathematical concept, and the key to the development, is the concept of an EDHT-category which is an extension of the DHT-symmetric categories introduced by Hoehnke [13] as a categorical framework for partial algebras. © 1988, Springer-Verlag.

关键词： Semantics

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