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MultiStage Programming: Its Theory and Applications
, 1999
"... MetaML is a statically typed functional programming language with special support for program generation. In addition to providing the standard features of contemporary programming languages such as Standard ML, MetaML provides three staging annotations. These staging annotations allow the construct ..."
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Cited by 86 (18 self)
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MetaML is a statically typed functional programming language with special support for program generation. In addition to providing the standard features of contemporary programming languages such as Standard ML, MetaML provides three staging annotations. These staging annotations allow the construction, combination, and execution of objectprograms. Our thesis is that MetaML's three staging annotations provide a useful, theoretically sound basis for building program generators. This dissertation reports on our study of MetaML's staging constructs, their use, their implementation, and their formal semantics. Our results include an extended example of where MetaML allows us to produce efficient programs, an explanation of why implementing these constructs in traditional ways can be challenging, two formulations of MetaML's semantics, a type system for MetaML, and a proposal for extending ...
The Evolution of the Soar Cognitive Architecture
 In
, 1994
"... The origins of the Soar architecture can be traced back to the seminal research of Allen Newell and Herbert Simon on symbol systems, heuristic search, goals, problem spaces, and production systems. Since its official inception in 1982, Soar has evolved through six major releases, as both an AI archi ..."
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Cited by 63 (14 self)
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The origins of the Soar architecture can be traced back to the seminal research of Allen Newell and Herbert Simon on symbol systems, heuristic search, goals, problem spaces, and production systems. Since its official inception in 1982, Soar has evolved through six major releases, as both an AI architecture and as the basis for a unified theory of cognition. This paper traces this evolutionary path, starting with Soar's intellectual roots, and then proceeding through the stages defined by the six major system releases. Each stage is characterized with respect to a hierarchy of four levels of analysis: the knowledge level, the problem space level, the symbolic architecture level, and the implementation level.
The Second Calculus of Binary Relations
 In Proceedings of MFCS'93
, 1993
"... We view the Chu space interpretation of linear logic as an alternative interpretation of the language of the Peirce calculus of binary relations. Chu spaces amount to Kvalued binary relations, which for K = 2 n we show generalize nary relational structures. We also exhibit a fourstage unique fa ..."
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Cited by 55 (18 self)
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We view the Chu space interpretation of linear logic as an alternative interpretation of the language of the Peirce calculus of binary relations. Chu spaces amount to Kvalued binary relations, which for K = 2 n we show generalize nary relational structures. We also exhibit a fourstage unique factorization system for Chu transforms that illuminates their operation. 1 Introduction In 1860 A. De Morgan [DM60] introduced a calculus of binary relations equivalent in expressive power to one whose formulas, written in today's notation, are inequalities a b between terms a; b; . . . built up from variables with the operations of composition a; b, converse a, and complement a \Gamma . In 1870 C.S. Peirce [Pei33] extended De Morgan's calculus with Boolean connectives a + b and ab, Boolean constants 0 and 1, and an identity 1 0 for composition. In 1895 E. Schroder devoted a book [Sch95] to the calculus, and further extended it with the operations of reflexive transitive closure, a ...
Modular Reasoning in Isabelle
, 1999
"... The concept of locales for Isabelle enables local definition and assumption for interactive mechanical proofs. Furthermore, dependent types are constructed in Isabelle/HOL for first class representation of structure. These two concepts are introduced briefly. Although each of them has proved use ..."
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Cited by 13 (2 self)
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The concept of locales for Isabelle enables local definition and assumption for interactive mechanical proofs. Furthermore, dependent types are constructed in Isabelle/HOL for first class representation of structure. These two concepts are introduced briefly. Although each of them has proved useful in itself, their real power lies in combination. This paper illustrates by examples from abstract algebra how this combination works and argues that it enables modular reasoning.
Knowledge Management
 Journal of Management Information Systems
, 2001
"... Abstract. In [9], various observations on the handling of (physical) units in OpenMath were made. In this paper, we update those observations, and make some comments based on a working unit converter [21] that, because of its OpenMathbased design, is modular, extensible and reflective. We also note ..."
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Cited by 11 (0 self)
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Abstract. In [9], various observations on the handling of (physical) units in OpenMath were made. In this paper, we update those observations, and make some comments based on a working unit converter [21] that, because of its OpenMathbased design, is modular, extensible and reflective. We also note that some of the issues in an effective converter, such as the rules governing abbreviations, being more linguistic than mathematical, do not lend themselves to easy expression in OpenMath. 1
An Incompleteness Theorem via Abstraction
, 1996
"... ion Alan Bundy 1 , Fausto Giunchiglia 2;3 , Adolfo Villafiorita 4;5 and Toby Walsh 2;5 1. Mathematical Reasoning Group, Dept of AI, University of Edinburgh 2. Mechanized Reasoning Group, IRST 3. DISA, University of Trento 4. Istituto di Informatica, University of Ancona 5. Mechanized Re ..."
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Cited by 6 (4 self)
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ion Alan Bundy 1 , Fausto Giunchiglia 2;3 , Adolfo Villafiorita 4;5 and Toby Walsh 2;5 1. Mathematical Reasoning Group, Dept of AI, University of Edinburgh 2. Mechanized Reasoning Group, IRST 3. DISA, University of Trento 4. Istituto di Informatica, University of Ancona 5. Mechanized Reasoning Group, DIST, University of Genoa April 13, 1996 Abstract We demonstrate the use of abstraction in aiding the construction of an interesting and difficult example in a proof checking system. This experiment demonstrates that abstraction can make proofs easier to comprehend and to verify mechanically. To support such proof checking, we have developed a formal theory of abstraction and added facilities for using abstraction to the GETFOL proof checking system. 1 Introduction This paper describes an experiment in which we use abstraction to aid the construction of a simplified proof of Godel's first incompleteness theorem. We show that this use of abstraction makes the proof more ac...
Map calculus: Initial application scenarios and experiments based on Otter
, 1998
"... Properties of a few familiar structures (natural numbers, nested lists, lattices) are formally specified in TarskiGivant's map calculus, with the aim of bringing to light new translation techniques that may bridge the gap between firstorder predicate calculus and the map calculus. It is also highl ..."
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Cited by 6 (6 self)
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Properties of a few familiar structures (natural numbers, nested lists, lattices) are formally specified in TarskiGivant's map calculus, with the aim of bringing to light new translation techniques that may bridge the gap between firstorder predicate calculus and the map calculus. It is also highlighted to what extent a stateoftheart theoremprover for firstorder logic, namely Otter, can be exploited not only to emulate, but also to reason about, map calculus. 3 1 Introduction Everybody remembers that Boole's Laws of thought (1854), Frege's Begriffsschrift (1879), and the WhiteheadRussell's Principia Mathematica (1910) have been three major milestones in the development of contemporary logic (cf. [3, 8, 15, 4]). Only a few people are aware that very important prePrincipia milestones were laid down by C.S. Peirce and E. Schroder and culminated in the monumental work [11, 12] on the Algebra der Logik . The "rather capricious line of historical development" of the algebraic for...