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Universes for Generic Programs and Proofs in Dependent Type Theory
 Nordic Journal of Computing
, 2003
"... We show how to write generic programs and proofs in MartinL of type theory. To this end we consider several extensions of MartinL of's logical framework for dependent types. Each extension has a universes of codes (signatures) for inductively defined sets with generic formation, introductio ..."
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Cited by 42 (2 self)
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We show how to write generic programs and proofs in MartinL of type theory. To this end we consider several extensions of MartinL of's logical framework for dependent types. Each extension has a universes of codes (signatures) for inductively defined sets with generic formation, introduction, elimination, and equality rules. These extensions are modeled on Dybjer and Setzer's finitely axiomatized theories of inductiverecursive definitions, which also have a universe of codes for sets, and generic formation, introduction, elimination, and equality rules.
How to Comprehend Queries Functionally
, 1999
"... Compilers and optimizers for declarative query languages use some form of intermediate language to represent userlevel queries. The advent of compositional query languages for orthogonal type systems (e.g. OQL) calls for internal query representations beyond extensions of relational algebra. This w ..."
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Cited by 11 (3 self)
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Compilers and optimizers for declarative query languages use some form of intermediate language to represent userlevel queries. The advent of compositional query languages for orthogonal type systems (e.g. OQL) calls for internal query representations beyond extensions of relational algebra. This work adopts a view of query processing which is greatly influenced by ideas from the functional programming domain. A uniform formal framework is presented which covers all query translation phases, including userlevel query language compilation, query optimization, and execution plan generation. We pursue the typebased design  based on initial algebras  of a core functional language which is then developed into an intermediate representation that ts the needs of advanced query processing. Based on the principle of structural recursion we extend the language by monad comprehensions (which provide us with a calculusstyle sublanguage that proves to be useful during the optimization of nested...
Modeling Context Effect in Perceptual Domains
"... In this paper we present a formal approach to modelling context effect in perceptual domains: namely how the perception of an object is effected by other objects. Our approach is operational and perceptually motivated in the sense that we focus on how objects are perceived as being constructed f ..."
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Cited by 2 (1 self)
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In this paper we present a formal approach to modelling context effect in perceptual domains: namely how the perception of an object is effected by other objects. Our approach is operational and perceptually motivated in the sense that we focus on how objects are perceived as being constructed from certain components. Based on a psychological theory of perception, called Structural Information Theory, we develop an algebraic model for context sensitive perception. We illustrate our model by using the domain of alphabetic strings and discuss its extension to the domain of visual objects. Finally, we remark on how this approach can be applied to model context effect in nonperceptual situation, and then make some observations on the general problem of context.
Combining a Monad and a Comonad
"... We give a systematic treatment of distributivity for a monad and a comonad as arises in giving category theoretic accounts of operational and denotational semantics, and in giving an intensional denotational semantics. We do this axiomatically, in terms of a monad and a comonad in a 2category, givi ..."
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Cited by 2 (0 self)
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We give a systematic treatment of distributivity for a monad and a comonad as arises in giving category theoretic accounts of operational and denotational semantics, and in giving an intensional denotational semantics. We do this axiomatically, in terms of a monad and a comonad in a 2category, giving accounts of the EilenbergMoore and Kleisli constructions. We analyse the eight possible relationships, deducing that two pairs are isomorphic, but that the other pairs are all distinct. We develop those 2categorical denitions necessary to support this analysis. This work is supported by EPSRC grants GR/J84205: Frameworks for programming language semantics and logic and GR/M56333: The structure of programming languages : syntax and semantics, and British Council grant 747 FCS R34807: Data and program renement using algebraic structure. y The author acknowledges the support of STA through COE budget for Global Information Processing Project. 1 1 Introduction In recent years, th...
Schmidt: Towards a Structured Specification Language for Database Applications
 Proc. Int. Workshop on the Specification of Database Systems, Springer WICS
, 1991
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An Evaluation Semantics for NarrowingBased Functional Logic Languages
, 2000
"... We introduce a semantic characterization of narrowing, the computational engine of many functional logic languages. We use a functional domain for giving a denotation to the narrowing space associated to a given initial expression under an arbitrary narrowing strategy. Such a semantic description hi ..."
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Cited by 1 (1 self)
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We introduce a semantic characterization of narrowing, the computational engine of many functional logic languages. We use a functional domain for giving a denotation to the narrowing space associated to a given initial expression under an arbitrary narrowing strategy. Such a semantic description highlights (and favours) the operational notion of evaluation instead of the more usual modeltheoretic notion of interpretation semantics which encodes information about the real operational framework used by a given (narrowingbased) functional logic language. Our aim is to provide a general, suitable, and accurate framework for the analysis of functional logic programs.
Closure Induction in a Zlike Language
, 2000
"... Simplytyped settheoretic languages such as Z and B are widely used for program and system specifications. The main technique for reasoning about such specifications is induction. However, while partiality is an important concept in these languages, many standard approaches to automating induct ..."
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Simplytyped settheoretic languages such as Z and B are widely used for program and system specifications. The main technique for reasoning about such specifications is induction. However, while partiality is an important concept in these languages, many standard approaches to automating induction proofs rely on the totality of all occurring functions. Reinterpreting the second author's recently proposed induction technique for partial functional programs, we introduce in this paper the new principle of "closure induction" for reasoning about the inductive properties of partial functions in simplytyped settheoretic languages. In particular, closure induction allows us to prove partial correctness, that is, to prove those instances of conjectures for which designated partial functions are explicitly defined.
www.elsevier.com/locate/tcs A hidden agenda(
"... This paper publicly reveals, motivates, and surveys the results of an ambitious hidden agenda for applying algebra to software engineering. The paper reviews selected literature, introduces a new perspective on nondeterminism, and features powerful hidden coinduction techniques for proving behaviora ..."
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This paper publicly reveals, motivates, and surveys the results of an ambitious hidden agenda for applying algebra to software engineering. The paper reviews selected literature, introduces a new perspective on nondeterminism, and features powerful hidden coinduction techniques for proving behavioral properties of concurrent systems, especially renements; some proofs are given using OBJ3. We also discuss where modularization, bisimulation, transition systems and combinations of the object, logic, constraint and functional paradigms t into our hidden agenda.