Results

**11 - 20**of**20**### Programming With Functional Nets

- IN THE SCHOOL OF NIKLAUS WIRTH { THE ART OF SIMPLICITY
, 2000

"... ..."

### Notes on Discrete Mathematics for Computer Scientists

, 2003

"... 1.2 Formal Languages.......................... 2 ..."

### Naïve Type Theory

, 2002

"... This article follows the spirit of Halmos' book and introduces type theory without recourse to precise axioms and inference rules, and with a minimum of formalism. I start by paraphrasing the preface to Halmos' book. The sections of this article follow his chapters closely. Every computer scientist ..."

Abstract
- Add to MetaCart

This article follows the spirit of Halmos' book and introduces type theory without recourse to precise axioms and inference rules, and with a minimum of formalism. I start by paraphrasing the preface to Halmos' book. The sections of this article follow his chapters closely. Every computer scientist agrees that every computer scientist must know some type theory; the disagreement begins in trying to decide how much is some. This article contains my partial answer to that question. The purpose of the article is to tell the beginning student of advanced computer science the basic type theoretic facts of life, and to do so with a minimum of philosophical discourse and logical formalism. The point throughout is that of a prospective computer scientist eager to study programming languages, or database systems, or computational complexity theory, or distributed systems or information discovery

### Functions, Frames, and Interactions -- completing a λ-calculus-based purely functional language with respect to programming-in-the-large and interactions with runtime environments

, 1998

"... The original aim of the work that led to this dissertation was to extend an existing, purely functional language with facilities for input/output and modular programming. The language is based on an untyped -calculus, i.e., program execution is defined as program transformation according to a fixed ..."

Abstract
- Add to MetaCart

The original aim of the work that led to this dissertation was to extend an existing, purely functional language with facilities for input/output and modular programming. The language is based on an untyped -calculus, i.e., program execution is defined as program transformation according to a fixed set of reduction rules including fi-reduction. Consistently, the implementation comprises an interactive reduction system which is integrated with a syntax-oriented editor: any sub-expression or program result can be submitted for (stepwise) reduction. There is no distinguished main program, no `global' environment and no explicit static part of the language -- in particular, there is no static type system. It is therefore not clear how to add one of the known solutions for input/output or modular programming to such a programming environment. Furthermore, simply adding features to the language would lead to a complex language design with weakly integrated parts, thus losing much of the appe...

### The Triumph of Types: Principia Mathematica’s Impact on Computer Science

"... Types now play an essential role in computer science; their ascent originates from Principia Mathematica. Type checking and type inference algorithms are used to prevent semantic errors in programs, and type theories are the native language of several major interactive theorem provers. Some of these ..."

Abstract
- Add to MetaCart

Types now play an essential role in computer science; their ascent originates from Principia Mathematica. Type checking and type inference algorithms are used to prevent semantic errors in programs, and type theories are the native language of several major interactive theorem provers. Some of these trace key features back to Principia. This lecture examines the influence of Principia Mathematica on modern type theories implemented in software systems known as interactive proof assistants. These proof assistants advance daily the goal for which Principia was designed: to provide a comprehensive formalization of mathematics. For instance, the definitive formal proof of the Four Color Theorem was done in type theory. Type theory is considered seriously now more than ever as an adequate foundation for both classical and constructive mathematics as well as for computer science. Moreover, the seminal work in the history of formalized mathematics is the Automath project of N.G. de Bruijn whose formalism is type theory. In addition we explain how type theories have enabled the use of formalized mathematics as a practical programming language, a connection entirely unanticipated at the time of Principia Mathematica’s creation.

### Array Form Transformations: Proofs of Correctness

, 1995

"... A number of program transformations are proved to preserve the meaning of programs. The transformations convert array operations expressed using a small number of general-purpose functions into applications of a large number of functions suited to efficient implementation on an array processor. ..."

Abstract
- Add to MetaCart

A number of program transformations are proved to preserve the meaning of programs. The transformations convert array operations expressed using a small number of general-purpose functions into applications of a large number of functions suited to efficient implementation on an array processor.

### The experimental effectiveness of mathematical proof

"... The aim of this paper is twofold. First, it is an attempt to give an answer to the famous essay of Eugene Wigner about the unreasonable effectiveness of mathematics in the natural sciences [25]. We will argue that mathematics are not only reasonably effective, but that they are also objectively effe ..."

Abstract
- Add to MetaCart

The aim of this paper is twofold. First, it is an attempt to give an answer to the famous essay of Eugene Wigner about the unreasonable effectiveness of mathematics in the natural sciences [25]. We will argue that mathematics are not only reasonably effective, but that they are also objectively effective in a sense

### λ-Types on the λ-Calculus with Abbreviations

, 2007

"... In this paper the author presents λδ, a λ-typed λ-calculus with a single λ binder and abbreviations. This calculus pursues the reuse of the term constructions both at the level of types and at the level of contexts as the main goal. Up to conversion λδ shares with Church λ → the subset of typable te ..."

Abstract
- Add to MetaCart

In this paper the author presents λδ, a λ-typed λ-calculus with a single λ binder and abbreviations. This calculus pursues the reuse of the term constructions both at the level of types and at the level of contexts as the main goal. Up to conversion λδ shares with Church λ → the subset of typable terms but in the “propositions as types ” perspective it can encode the implicative fragment of predicative logic without quantifiers because dependent types are allowed. λδ enjoys the properties of Church λ → (mainly subject conversion, strong normalization and decidability of type inference) and, in addition, it satisfies the correctness of types and the uniqueness of types up to conversion. We stress that λδ differs from the Automath-related λ-calculi in that they do not provide for an abbreviation construction at the level of terms. Moreover, unlike many λ-calculi, λδ features a type hierarchy with an infinite number of levels both above and below any reference point.

### SPECIFYING PEIRCE’S LAW IN CLASSICAL REALIZABILITY

"... Abstract. This paper deals with the specification problem in classical realizability (such as introduced by Krivine [17]), which is to characterize the universal realizers of a given formula by their computational behavior. After recalling the framework of classical realizability, we present the pro ..."

Abstract
- Add to MetaCart

Abstract. This paper deals with the specification problem in classical realizability (such as introduced by Krivine [17]), which is to characterize the universal realizers of a given formula by their computational behavior. After recalling the framework of classical realizability, we present the problem in the general case and illustrate it with some examples. In the rest of the paper, we focus on Peirce’s law, and present two game-theoretic characterizations of its universal realizers. First we consider the particular case where the language of realizers contains no extra instruction such as ‘quote ’ [16]. We present a first game G0 and show that the universal realizers of Peirce’s law can be characterized as the uniform winning strategies for G0, using the technique of interaction constants. Then we show that in presence of extra instructions such as ‘quote’, winning strategies for the game G0 are still adequate but no more complete. For that, we exhibit an example of a wild realizer of Peirce’s law, that introduces a purely game-theoretic form of backtrack that is not captured by G0. We finally propose a more sophisticated game G1, and show that winning strategies for the game G1 are both adequate and complete in the general case, without any further assumption about the instruction set used by the language of classical realizers. 1.

### Actors in an Ad-Hoc Wireless Network Environment

"... Abstract. Today mobile devices can interact with their environment, because of the introduction of wireless communication. Wireless networks have two properties that distinguishes itself from the wired networks: First, wireless communication is less reliable than their wired variants because they ha ..."

Abstract
- Add to MetaCart

Abstract. Today mobile devices can interact with their environment, because of the introduction of wireless communication. Wireless networks have two properties that distinguishes itself from the wired networks: First, wireless communication is less reliable than their wired variants because they have a limited communication range. Second, wireless communication is more dynamic as communication partners enter and leave frequently the communication range of the wireless network. These two distinct properties make the development of mobile software difficult. The actor model is a programming model that allows development of concurrent distributed software in open distributed environments. Actor models fail to handle these two distinct properties of wireless networks well. In this paper we extend the operational semantics of the actor model to capture these two properties in the actor model. We do this by adding a single new concept to the model: the mailbox. This paper provides a foundation for new implementations of the actor language and frameworks that are usable in the context of wireless network environments. 1