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Semantic Domains
, 1990
"... this report started working on denotational semantics in collaboration with Christopher Strachey. In order to fix some mathematical precision, he took over some definitions of recursion theorists such as Kleene, Nerode, Davis, and Platek and gave an approach to a simple type theory of highertype fu ..."
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Cited by 148 (3 self)
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this report started working on denotational semantics in collaboration with Christopher Strachey. In order to fix some mathematical precision, he took over some definitions of recursion theorists such as Kleene, Nerode, Davis, and Platek and gave an approach to a simple type theory of highertype functionals. It was only after giving an abstract characterization of the spaces obtained (through the construction of bases) that he realized that recursive definitions of types could be accommodated as welland that the recursive definitions could incorporate function spaces as well. Though it was not the original intention to find semantics of the socalled untyped calculus, such a semantics emerged along with many ways of interpreting a very large variety of languages. A large number of people have made essential contributions to the subsequent developments, and they have shown in particular that domain theory is not one monolithic theory, but that there are several different kinds of constructions giving classes of domains appropriate for different mixtures of constructs. The story is, in fact, far from finished even today. In this report we will only be able to touch on a few of the possibilities, but we give pointers to the literature. Also, we have attempted to explain the foundations in an elementary wayavoiding heavy prerequisites (such as category theory) but still maintaining some level of abstractionwith the hope that such an introduction will aid the reader in going further into the theory. The chapter is divided into seven sections. In the second section we introduce a simple class of ordered structures and discuss the idea of fixed points of continuous functions as meanings for recursive programs. In the third section we discuss computable functions and...
The complexity of type inference for higherorder typed lambda calculi
 In. Proc. 18th ACM Symposium on the Principles of Programming Languages
, 1991
"... We analyse the computational complexity of type inference for untyped X,terms in the secondorder polymorphic typed Xcalculus (F2) invented by Girard and Reynolds, as well as higherorder extensions F3,F4,...,/ ^ proposed by Girard. We prove that recognising the i^typable terms requires exponential ..."
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Cited by 28 (11 self)
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We analyse the computational complexity of type inference for untyped X,terms in the secondorder polymorphic typed Xcalculus (F2) invented by Girard and Reynolds, as well as higherorder extensions F3,F4,...,/ ^ proposed by Girard. We prove that recognising the i^typable terms requires exponential time, and for Fa the problem is nonelementary. We show as well a sequence of lower bounds on recognising the i^typable terms, where the bound for Fk+1 is exponentially larger than that for Fk. The lower bounds are based on generic simulation of Turing Machines, where computation is simulated at the expression and type level simultaneously. Nonaccepting computations are mapped to nonnormalising reduction sequences, and hence nontypable terms. The accepting computations are mapped to typable terms, where higherorder types encode reduction sequences, and firstorder types encode the entire computation as a circuit, based on a unification simulation of Boolean logic. A primary technical tool in this reduction is the composition of polymorphic functions having different domains and ranges. These results are the first nontrivial lower bounds on type inference for the Girard/Reynolds
A ModelTheoretic Semantics for Defeasible Logic
 Proc. Workshop on Paraconsistent Computational Logic
, 2002
"... Defeasible logic is an efficient logic for defeasible reasoning. ..."
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Cited by 18 (4 self)
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Defeasible logic is an efficient logic for defeasible reasoning.
This document in subdirectory RS/06/5 / Extending the Extensional Lambda Calculus with Surjective Pairing is Conservative ∗
, 2006
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS
Experimental Testing of Feature Structures and Unification
"... This paper presents two experiments where feature structures and unification provide an explanatory framework for what has been called illusory conjunctions in visual perception. Feature Structures and Unification has been successfully applied to computational analyses of natural languages. However, ..."
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This paper presents two experiments where feature structures and unification provide an explanatory framework for what has been called illusory conjunctions in visual perception. Feature Structures and Unification has been successfully applied to computational analyses of natural languages. However, this efficient computational technique has not been experimentally tested among human subjects. This is an attempt to show some psychological validity for the notion of feature structures and unification.
Mathematics and Information Science Directorate
, 2011
"... Unlimited distribution subject to the copyright. ..."