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Generic Properties of Datatypes
, 2002
"... Generic programming adds a new dimension to the parametrisation of programs by allowing programs to be dependent on the structure of the data that they manipulate. ..."
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Generic programming adds a new dimension to the parametrisation of programs by allowing programs to be dependent on the structure of the data that they manipulate.
This research was supported by NASA grant NAG54301 and NSF grant AST9619552 to AW. MK was supported by KBN grant 2.P03D.006.1. Arecibo Observatory is part of the National Astronomy and Ionosphere Center, which is operated by Cornell University under cont
, 2005
"... A partial component is a process which fails or dies at some stage, thus exhibiting a finite, more ephemeral behaviour than expected (e.g. operating system crash). Partiality — which is the rule rather than exception in formal modelling — can be treated mathematically via totalization techniques. In ..."
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A partial component is a process which fails or dies at some stage, thus exhibiting a finite, more ephemeral behaviour than expected (e.g. operating system crash). Partiality — which is the rule rather than exception in formal modelling — can be treated mathematically via totalization techniques. In the case of partial functions, totalization involves error values and exceptions. In the context of a coalgebraic approach to component semantics, this paper argues that the behavioural counterpart to such functional techniques should extend behaviour with tryagain cycles preventing from component collapse, thus extending totalization or transposition from the algebraic to the coalgebraic context. We show that a refinement relationship holds between original and totalized components which is reasoned about in a coalgebraic approach to component refinement expressed in the pointfree binary relation calculus. As part of the pragmatic aims of this research, we also address the factorization of every such totalized coalgebra into two coalgebraic components — the original one and an added frontend — which cooperate in a clientserver style. Key words: partial components, tryagain cycles, refinement, coalgebra 1
Polytypic Recursion Patterns
, 2000
"... Recursive schemes over inductive data structures have been recognized as categorytheoretic universals, yielding a handful of equational laws for program construction and transformation. This paper introduces the implementation of such recursion patterns as type parametric, or polytypic, functionals ..."
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Recursive schemes over inductive data structures have been recognized as categorytheoretic universals, yielding a handful of equational laws for program construction and transformation. This paper introduces the implementation of such recursion patterns as type parametric, or polytypic, functionals in the Camila prototyping language. Several examples are discussed.
Logical Relations and Galois Connections
, 2002
"... Algebraic properties of logical relations on partially ordered sets are studied. It is shown how to construct a logical relation that extends a collection of base Galois connections to a Galois connection of arbitrary higherorder type. "Theoremsforfree" is used to show that the construction ensur ..."
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Algebraic properties of logical relations on partially ordered sets are studied. It is shown how to construct a logical relation that extends a collection of base Galois connections to a Galois connection of arbitrary higherorder type. "Theoremsforfree" is used to show that the construction ensures safe abstract interpretation of parametrically polymorphic functions.
DomainSpecific Embedded Languages
, 2002
"... A domainspecific embedded language (DSEL) is a domainspecific programming language with no concrete syntax of its own. Defined as a set of combinators encapsulated in a module, it borrows the syntax and tools (such as typecheckers and compilers) of its host language; hence it is economical to des ..."
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A domainspecific embedded language (DSEL) is a domainspecific programming language with no concrete syntax of its own. Defined as a set of combinators encapsulated in a module, it borrows the syntax and tools (such as typecheckers and compilers) of its host language; hence it is economical to design, introduce, and maintain. Unfortunately, this economy is counterbalanced by a lack of room for growth. DSELs cannot match sophisticated domainspecific languages that offer tools for domainspecific errorchecking and optimisation. These tools are usually based on syntactic analyses, so they do not work on DSELs. Abstract interpretation is a technique ideally suited to the analysis of DSELs, due to its semantic, rather than syntactic, approach. It is based upon the observation that analysing a program is equivalent to evaluating it over an abstract semantic domain. The mathematical properties of the abstract domain are such that evaluation reduces to solving a mutually recursive set of equations. This thesis shows how abstract interpretation can be applied to a DSEL by replacing it with an abstract implementation
UML Model Refactoring as Refinement: A Coalgebraic Perspective
"... Abstract—Although increasingly popular, Model Driven Architecture (MDA) still lacks suitable formal foundations on top of which rigorous methodologies for the description, analysis and transformation of models could be built. This paper aims to contribute in this direction: building on previous work ..."
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Abstract—Although increasingly popular, Model Driven Architecture (MDA) still lacks suitable formal foundations on top of which rigorous methodologies for the description, analysis and transformation of models could be built. This paper aims to contribute in this direction: building on previous work by the authors on coalgebraic refinement for software components and architectures, it discusses refactoring of models within a coalgebraic semantic framework. Architectures are defined through aggregation based on a coalgebraic semantics for (subsets of) UML. On the other hand, such aggregations, no matter how large and complex they are, can always be dealt with as coalgebras themselves. This paves the way to a discipline of models’ transformations which, being invariant under either behavioural equivalence or refinement, are able to formally capture a large number of refactoring patterns. The main ideas underlying this research are presented through a detailed example in the context of refactoring of UML class diagrams. I.
Meeting a Fanclub: A Lattice of Generic Shape Selectors 1
"... The “fan ” of a datatype F is a relation that holds between a value x and an arbitrary F structure in which the only stored value is x. Fans make precise the notion of the shape of a data structure. We formulate two different representations of shape selectors and exploit the properties of fans to p ..."
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The “fan ” of a datatype F is a relation that holds between a value x and an arbitrary F structure in which the only stored value is x. Fans make precise the notion of the shape of a data structure. We formulate two different representations of shape selectors and exploit the properties of fans to prove that the two representations are order isomorphic and that shape selectors are closed under set intersection. For arbitrary datatypes F, G and H, we consider six different ways of composing their fans in order to construct F structures of G structures of H structures; each of the six imposes a different requirement on the shape of the substructures. We catalogue the relation between different combinations of the constructions. We apply the result to a problem that arose in a generic theory of dynamic programming concerning the shape properties of a natural transformation from G structures to F G structures.