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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 52 (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.
Categorybased Semantics for Equational and Constraint Logic Programming
, 1994
"... This thesis proposes a general framework for equational logic programming, called categorybased equational logic by placing the general principles underlying the design of the programming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equation ..."
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Cited by 25 (10 self)
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This thesis proposes a general framework for equational logic programming, called categorybased equational logic by placing the general principles underlying the design of the programming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equational deduction to an arbitrary category satisfying certain natural conditions; completeness is proved under a hypothesis of quantifier projectivity, using a semantic treatment that regards quantifiers as models rather than variables, and regards valuations as model morphisms rather than functions. This is used as a basis for a model theoretic categorybased approach to a paramodulationbased operational semantics for equational logic programming languages. Categorybased equational logic in conjunction with the theory of institutions is used to give mathematical foundations for modularisation in equational logic programming. We study the soundness and completeness problem for module imports i...
Extended ML: an institutionindependent framework for formal program development
 PROC. WORKSHOP ON CATEGORY THEORY AND COMPUTER PROGRAMMING
, 1986
"... The Extended ML specification language provides a framework for the formal stepwise development of modular programs in the Standard ML programming language from specifications. The object of this paper is to equip Extended ML with a semantics which is completely independent of the logical system use ..."
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Cited by 20 (12 self)
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The Extended ML specification language provides a framework for the formal stepwise development of modular programs in the Standard ML programming language from specifications. The object of this paper is to equip Extended ML with a semantics which is completely independent of the logical system used to write specifications, building on Goguen and Burstall's work on the notion of an institution as a formalisation of the concept of a logical system. One advantage of this is that it permits freedom in the choice of the logic used in writing specifications; an intriguing sideeffect is that it enables Extended ML to be used to develop programs in languages other than Standard ML since we view programs as simply Extended ML specifications which happen to include only "executable" axioms. The semantics of Extended ML is defined in terms of the primitive specificationbuilding operations of the ASL kernel specification language which itself has an institutionindependent semantics. It is no...
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...
A Survey of Formal Software Development Methods
 SOFTWARE ENGINEERING
, 1988
"... This paper is a survey of the current state of the art of research on methods for formal software development. The scope of this paper is necessarily restricted so as to avoid discussion of a great many approaches at a very superficial level. First, although some of the ideas discussed below could b ..."
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Cited by 9 (0 self)
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This paper is a survey of the current state of the art of research on methods for formal software development. The scope of this paper is necessarily restricted so as to avoid discussion of a great many approaches at a very superficial level. First, although some of the ideas discussed below could be (and have been) applied to hardware development as well as to software development, this topic will not be treated here. Second, the special problems involved in the development of concurrent systems will not be discussed here although again many of the approaches mentioned below could be applied in this context. Third, no attempt is made to treat programming methodologies such as Jackson's method and program development systems such as the MIT Programmer's Apprentice which are not formally based. Finally, this survey does not claim to be fully exhaustive although an attempt has been made to cover most of the main approaches. Many of the technical details of the different approaches discussed have been glossed over or simplified for the purposes of this presentation; full details may be found in the cited references.
Formal Transformations from GraphicallyBased ObjectOriented Representations to TheoryBased Specifications
, 1996
"... Approved for public release; distribution unlimited The views expressed in this dissertation are those of the author and do not re
ect the ocial policy or position of the Department of Defense or the U. S. Government. AFIT/DS/ENG/9605 ..."
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Cited by 8 (3 self)
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Approved for public release; distribution unlimited The views expressed in this dissertation are those of the author and do not re
ect the ocial policy or position of the Department of Defense or the U. S. Government. AFIT/DS/ENG/9605
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 3 (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...