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135
Termination and confluence of higherorder rewrite systems
 In Proc. RTA ’00, volume 1833 of LNCS
, 2000
"... Abstract: In the last twenty years, several approaches to higherorder rewriting have been proposed, among which Klop’s Combinatory Rewrite Systems (CRSs), Nipkow’s Higherorder Rewrite Systems (HRSs) and Jouannaud and Okada’s higherorder algebraic specification languages, of which only the last on ..."
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Abstract: In the last twenty years, several approaches to higherorder rewriting have been proposed, among which Klop’s Combinatory Rewrite Systems (CRSs), Nipkow’s Higherorder Rewrite Systems (HRSs) and Jouannaud and Okada’s higherorder algebraic specification languages, of which only the last one considers typed terms. The later approach has been extended by Jouannaud, Okada and the present author into Inductive Data Type Systems (IDTSs). In this paper, we extend IDTSs with the CRS higherorder patternmatching mechanism, resulting in simplytyped CRSs. Then, we show how the termination criterion developed for IDTSs with firstorder patternmatching, called the General Schema, can be extended so as to prove the strong normalization of IDTSs with higherorder patternmatching. Next, we compare the unified approach with HRSs. We first prove that the extended General Schema can also be applied to HRSs. Second, we show how Nipkow’s higherorder critical pair analysis technique for proving local confluence can be applied to IDTSs. 1
An Illative Theory of Relations
, 1990
"... this paper we present a nonstandard logic for our structures. It is a typefree intensional logic, and is also in the tradition of Curry's illative logic [HS86]; see also [AczN, FM87, Smi84, MA88]. The logic has two judgments: that an object is a fact and that an object is a stateofa#airs (c ..."
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Cited by 16 (2 self)
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this paper we present a nonstandard logic for our structures. It is a typefree intensional logic, and is also in the tradition of Curry's illative logic [HS86]; see also [AczN, FM87, Smi84, MA88]. The logic has two judgments: that an object is a fact and that an object is a stateofa#airs (cf. truth and proposition). Objects are given using a variant of the traditional situation theory notation which is more standard, logically speaking, with explicit negation and quantification (see also [Bar87]). No metalinguistic apparatus is employed
Managing inconsistent repositories via prioritized repairs
 IN PROC. OF THE 2004 ACM SYMP. ON DOCUMENT ENGINEERING
, 2004
"... Whenever a group of authors collaboratively edits interrelated documents, semantic consistency is a major goal. Current document management systems (DMS) lack adequate consistency management facilities. We propose liberal use of formal consistency rules, which permits inconsistencies. In this paper ..."
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Cited by 14 (5 self)
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Whenever a group of authors collaboratively edits interrelated documents, semantic consistency is a major goal. Current document management systems (DMS) lack adequate consistency management facilities. We propose liberal use of formal consistency rules, which permits inconsistencies. In this paper we focus on deriving repairs for inconsistencies. Our major contributions are: (1) deriving (common) repairs for multiple rules, (2) resolving conflicts between repairs, (3) prioritizing repairs, and (4) support for partial inconsistency resolution, which resolves the most troubling inconsistencies and leaves less important inconsistencies for a later handling. The novel aspect of our approach is that we derive repairs from DAGs (directed acyclic graphs) and not from documents directly. That way the repository is locked during DAG generation only, which is performed incrementally.
Theories With SelfApplication and Computational Complexity
 Information and Computation
, 2002
"... Applicative theories form the basis of Feferman's systems of explicit mathematics, which have been introduced in the early seventies. In an applicative universe, all individuals may be thought of as operations, which can freely be applied to each other: selfapplication is meaningful, but n ..."
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Cited by 14 (9 self)
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Applicative theories form the basis of Feferman's systems of explicit mathematics, which have been introduced in the early seventies. In an applicative universe, all individuals may be thought of as operations, which can freely be applied to each other: selfapplication is meaningful, but not necessarily total. It has turned out that theories with selfapplication provide a natural setting for studying notions of abstract computability, especially from a prooftheoretic perspective.
A Complete Characterization of Complete IntersectionType Theories (Extended Abstract)
 ACM TOCL
, 2000
"... M. DEZANICIANCAGLINI Universita di Torino, Italy F. HONSELL Universita di Udine, Italy F. ALESSI Universita di Udine, Italy Abstract We characterize those intersectiontype theories which yield complete intersectiontype assignment systems for lcalculi, with respect to the three canonical ..."
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Cited by 13 (5 self)
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M. DEZANICIANCAGLINI Universita di Torino, Italy F. HONSELL Universita di Udine, Italy F. ALESSI Universita di Udine, Italy Abstract We characterize those intersectiontype theories which yield complete intersectiontype assignment systems for lcalculi, with respect to the three canonical settheoretical semantics for intersectiontypes: the inference semantics, the simple semantics and the Fsemantics. Keywords Lambda Calculus, Intersection Types, Semantic Completeness, Filter Structures. 1 Introduction Intersectiontypes disciplines originated in [6] to overcome the limitations of Curry 's type assignment system and to provide a characterization of strongly normalizing terms of the lcalculus. But very early on, the issue of completeness became crucial. Intersectiontype theories and filter lmodels have been introduced, in [5], precisely to achieve the completeness for the type assignment system l" BCD W , with respect to Scott's simple semantics. And this result, ...
2008, Demonstratives as individual concepts
 Linguistics and Philosophy
"... Abstract. Using a version of situation semantics, this article argues that bare and complex demonstratives are interpreted as individual concepts. ..."
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Abstract. Using a version of situation semantics, this article argues that bare and complex demonstratives are interpreted as individual concepts.
Efficient Interpretation by Transforming Data Types and Patterns to Functions
 In Trends in Functional Programming, volume 7. Intellect
, 2007
"... In this paper we present the stepwise construction of an efficient interpreter for lazy functional programming languages like Haskell and Clean. The interpreter is realized by first transforming the source language to the intermediate language SAPL (Simple Application Programming Language) consistin ..."
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Cited by 11 (4 self)
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In this paper we present the stepwise construction of an efficient interpreter for lazy functional programming languages like Haskell and Clean. The interpreter is realized by first transforming the source language to the intermediate language SAPL (Simple Application Programming Language) consisting of pure functions only. During this transformation algebraic data types and patternbased function definitions are mapped to functions. This eliminates the need for constructs for Algebraic Data Types and Pattern Matching in SAPL. For SAPL a simple and elegant interpreter is constructed using straightforward graph reduction techniques. This interpreter can be considered as a prototype implementation of lazy functional programming languages. Using abstract interpretation techniques the interpreter is optimised. The performance of the resulting interpreter turns out to be very competitive in a comparison with other interpreters like Hugs, Helium, GHCi and Amanda for a number benchmarks. For some benchmarks the interpreter even rivals the speed of the GHC compiler. Due to its simplicity and the stepwise construction this implementation is an ideal subject for introduction courses on implementation aspects of lazy functional programming languages. 1
A realizability interpretation for classical arithmetic
 In Buss, Hájek, and Pudlák eds., Logic colloquium ’98, AK Peters, 57–90
, 2000
"... Summary. A constructive realizablity interpretation for classical arithmetic is presented, enabling one to extract witnessing terms from proofs of Σ1 sentences. The interpretation is shown to coincide with modified realizability, under a novel translation of classical logic to intuitionistic logic, ..."
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Summary. A constructive realizablity interpretation for classical arithmetic is presented, enabling one to extract witnessing terms from proofs of Σ1 sentences. The interpretation is shown to coincide with modified realizability, under a novel translation of classical logic to intuitionistic logic, followed by the FriedmanDragalin translation. On the other hand, a natural set of reductions for classical arithmetic is shown to be compatible with the normalization of the realizing term, implying that certain strategies for eliminating cuts and extracting a witness from the proof of a Σ1 sentence are insensitive to the order in which reductions are applied. 1
Synthesis of programs in computational logic
 PROGRAM DEVELOPMENT IN COMPUTATIONAL LOGIC
, 2004
"... Since the early days of programming and automated reasoning, researchers have developed methods for systematically constructing programs from their specifications. Especially the last decade has seen a flurry of activities including the advent of specialized conferences, such as LOPSTR, covering the ..."
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Since the early days of programming and automated reasoning, researchers have developed methods for systematically constructing programs from their specifications. Especially the last decade has seen a flurry of activities including the advent of specialized conferences, such as LOPSTR, covering the synthesis of programs in computational logic. In this paper we analyze and compare three stateoftheart methods for synthesizing recursive programs in computational logic. The three approaches are constructive/deductive synthesis, schemaguided synthesis, and inductive synthesis. Our comparison is carried out in a systematic way where, for each approach, we describe the key ideas and synthesize a common running example. In doing so, we explore the synergies between the approaches, which we believe are necessary in order to achieve progress over the next decade in this field.
Formal structure of Sanskrit text: Requirements analysis for a mechanical Sanskrit processor
"... Abstract. We discuss the mathematical structure of various levels of representation of Sanskrit text in order to guide the design of computer aids aiming at useful processing of the digitalised Sanskrit corpus. Two main levels are identified, respectively called the linear and functional level. The ..."
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Abstract. We discuss the mathematical structure of various levels of representation of Sanskrit text in order to guide the design of computer aids aiming at useful processing of the digitalised Sanskrit corpus. Two main levels are identified, respectively called the linear and functional level. The design space of these two levels is sketched, and the computational implications of the main design choices are discussed. Current solutions to the problems of mechanical segmentation, tagging, and parsing of Sanskrit text are briefly surveyed in this light. An analysis of the requirements of relevant linguistic resources is provided, in view of justifying standards allowing interoperability of computer tools. This paper does not attempt to provide definitive solutions to the representation of Sanskrit at the various levels. It should rather be considered as a survey of various choices, allowing an open discussion of such issues in a formally precise general framework. 1