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Random Access to Abstract Data Types
 8th Int. Conf. on Algebraic Methodology and Software Technology. LNCS 1816
, 2000
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Finitary construction of free algebras for equational systems
, 2008
"... The purpose of this paper is threefold: to present a general abstract, yet practical, notion of equational system; to investigate and develop the finitary construction of free algebras for equational systems; and to illustrate the use of equational systems as needed in modern applications. Key words ..."
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The purpose of this paper is threefold: to present a general abstract, yet practical, notion of equational system; to investigate and develop the finitary construction of free algebras for equational systems; and to illustrate the use of equational systems as needed in modern applications. Key words: Equational system; algebra; free construction; monad. 1
A Summary of Refinement Theory
, 1994
"... this paper we have no opportunity to exploit the di#erence. A context A with another context B plugged into the hole is again a context: the nesting of B within A . Formally it is the functional composition of A with B , which we denote by juxtaposition: ..."
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this paper we have no opportunity to exploit the di#erence. A context A with another context B plugged into the hole is again a context: the nesting of B within A . Formally it is the functional composition of A with B , which we denote by juxtaposition:
When is an abstract data type a functor?
"... A parametric algebraic data type is a functor when we can apply a function to its data components while satisfying certain equations. We investigate whether parametric abstract data types can be functors. We provide a general definition for their map operation that needs only satisfy one equation. T ..."
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A parametric algebraic data type is a functor when we can apply a function to its data components while satisfying certain equations. We investigate whether parametric abstract data types can be functors. We provide a general definition for their map operation that needs only satisfy one equation. The definability of this map depends on properties of interfaces and is a sufficient condition for functoriality. Instances of the definition for particular abstract types can then be constructed using their axiomatic semantics. The definition and the equation can be adapted to determine, necessarily and sufficiently, whether an ADT is a functor for a given implementation. 1
Equational Systems and Free Constructions (Extended Abstract)
"... Abstract. The purpose of this paper is threefold: to present a general abstract, yet practical, notion of equational system; to investigate and develop a theory of free constructions for such equational systems; and to illustrate the use of equational systems as needed in modern applications, specif ..."
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Abstract. The purpose of this paper is threefold: to present a general abstract, yet practical, notion of equational system; to investigate and develop a theory of free constructions for such equational systems; and to illustrate the use of equational systems as needed in modern applications, specifically to the theory of substitution in the presence of variable binding and to models of namepassing process calculi. 1
Generic Accumulations for Program Calculation
, 2004
"... Accumulations are recursive functions widely used in the context of functional programming. They maintain intermediate results in additional parameters, called accumulators, that may be used in later stages of computing. In a former work [Par02] a generic recursion operator named afold was presented ..."
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Accumulations are recursive functions widely used in the context of functional programming. They maintain intermediate results in additional parameters, called accumulators, that may be used in later stages of computing. In a former work [Par02] a generic recursion operator named afold was presented. Afold makes it possible to write accumulations defined by structural recursion for a wide spectrum of datatypes (lists, trees, etc.). Also, a number of algebraic laws were provided that served as a formal tool for reasoning about programs with accumulations. In this work, we present an extension to afold that allows a greater flexibility in the kind of accumulations that may be represented. This extension, in essence, provides the expressive power to allow accumulations to have more than one recursive call in each subterm, with different accumulator values —something that was not previously possible. The extension is conservative, in the sense that we obtain similar algebraic laws for the extended operator. We also present a case study that illustrates the use of the algebraic laws in a calculational setting and a technique for the improvement of fused programs
Towards a Theory of Moa
, 2000
"... Introduction 1 Monet. Whereas in traditional relational database applications, data is most often needed "by rows at a time" (of one person all its attributes) , there also exist database applications, such as datamining and information retrieval, where data is needed "by entire columns at a time" ..."
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Introduction 1 Monet. Whereas in traditional relational database applications, data is most often needed "by rows at a time" (of one person all its attributes) , there also exist database applications, such as datamining and information retrieval, where data is needed "by entire columns at a time" (of all persons just one attribute). For such applications the mainmemory database system Monet [3, 4] has been developed; it is optimised for manipulating (traversing and aggregating) entire columns at a time. In fact, Monet has only binary tables, so that fetching a column is fetching a table (and this is manipulated entirely in main memory, and stored consecutively on disk). 2 Moa. Moa [4] is a language (a datamodel, to be used at the "logical" level in between the "external" enduser level and the lowlevel "physical" level of Monet) for defining data representations that exploit Monet's capabilities of e#ciently traversing and aggregating ent
TA: set
, 2008
"... Map and Reduce are generic, useful notions for computing science; together they are equally expressive as simple inductive definitions over trees/lists/bags/sets. 1. Datatypes Let A be a set. Consider the datatype of finite binary trees over A; it consists of a set TA and two constructors tip and jo ..."
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Map and Reduce are generic, useful notions for computing science; together they are equally expressive as simple inductive definitions over trees/lists/bags/sets. 1. Datatypes Let A be a set. Consider the datatype of finite binary trees over A; it consists of a set TA and two constructors tip and join: join
Background info for Map and Reduce
, 2010
"... What I will discuss falls in the range of Functional Programming––Theory of Datatypes, and is meant to be background info for the MapReduce paradigm. ..."
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What I will discuss falls in the range of Functional Programming––Theory of Datatypes, and is meant to be background info for the MapReduce paradigm.