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Roots of Refactoring
 In: Tenth OOPSLA Workshop on Behavioral Semantics
, 2001
"... Refactoring is a new name for a transformational approach to iterative software development. Originally focused on class diagrams, it is now commonly associated with objectoriented programming languages like Java. In this article, we trace some of the conceptual roots and the ideas behind refactori ..."
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Refactoring is a new name for a transformational approach to iterative software development. Originally focused on class diagrams, it is now commonly associated with objectoriented programming languages like Java. In this article, we trace some of the conceptual roots and the ideas behind refactoring, and sketch its relation to other techniques, such as behavioral and structural refinement or compiler optimization. Based on these observations, we firmly believe that improved and adapted refactoring techniques will belong to the methodical tool set of tomorrow's software engineers.
Computers, Reasoning and Mathematical Practice
"... ion in itself is not the goal: for Whitehead [117]"it is the large generalisation, limited by a happy particularity, which is the fruitful conception." As an example consider the theorem in ring theory, which states that if R is a ring, f(x) is a polynomial over R and f(r) = 0 for every element of ..."
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ion in itself is not the goal: for Whitehead [117]"it is the large generalisation, limited by a happy particularity, which is the fruitful conception." As an example consider the theorem in ring theory, which states that if R is a ring, f(x) is a polynomial over R and f(r) = 0 for every element of r of R then R is commutative. Special cases of this, for example f(x) is x 2 \Gamma x or x 3 \Gamma x, can be given a first order proof in a few lines of symbol manipulation. The usual proof of the general result [20] (which takes a semester's postgraduate course to develop from scratch) is a corollary of other results: we prove that rings satisfying the condition are semisimple artinian, apply a theorem which shows that all such rings are matrix rings over division rings, and eventually obtain the result by showing that all finite division rings are fields, and hence commutative. This displays von Neumann's architectural qualities: it is "deep" in a way in which the symbol manipulati...
Varieties of Mathematical Prose
 Primus
, 1997
"... This article begins the development of a taxonomy of mathematical prose, describing the precise function and meaning of specific types mathematical exposition. This article further discusses the merits and demerits of a style of mathematical writing that labels each passage according to its function ..."
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This article begins the development of a taxonomy of mathematical prose, describing the precise function and meaning of specific types mathematical exposition. This article further discusses the merits and demerits of a style of mathematical writing that labels each passage according to its function as described in the taxonomy. Key words Mathematical exposition, writing style, mathematical argument, formal reasoning, symbolic logic, definitions, proofs, terminology, hypertext. 1 Introduction 1.1 Rationale Many students of mathematics are not experienced in reading mathematics texts. They may not understand the nature and use of definitions. Even if they do, they may not easily distinguish between a definition and an informal discussion of a topic. They may not pick up on the use of a word such as "group" that has a meaning in ordinary discourse but that has been given a special technical meaning in their text. They may not distinguish a plausibility argument from a careful proof, an...
On the Parity of Graph Spanning Tree Numbers
, 1996
"... Any bipartite Eulerian graph, any Eulerian graph with evenly many vertices, ..."
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Any bipartite Eulerian graph, any Eulerian graph with evenly many vertices,
The Mathematician as a Formalist
 in Truth in Mathematics (H.G. Dales and
, 1998
"... Introduction The existence of this meeting bears testimony to the anodyne remark that there is a continuing debate about what it means to say of a statement in mathematics that it is `true'. This debate began at least 2500 years ago, and will presumably continue at least well into the next millenni ..."
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Introduction The existence of this meeting bears testimony to the anodyne remark that there is a continuing debate about what it means to say of a statement in mathematics that it is `true'. This debate began at least 2500 years ago, and will presumably continue at least well into the next millennium; it would be implausible and perhaps presumptuous to suppose that even the union of the talented and distinguished speakers that have been assembled here in Mussomeli will approach any solution to the problem, or even arrive at a consensus of what a solution would amount to. In the end, it falls to the philosophers, with their professional expertise and training, to carry forward the debate and to move us to a fuller understanding of this subtle and elusive matter. Indeed, we are hearing at this meeting a variety of contributions to the debate from different philosophical points of view; also, there is a good number of recent published contributions to the debate (see (Maddy 1990)
Philosophy of Mathematics: Making a Fresh Start
"... ABSTRACT: The paper distinguishes between two kinds of mathematics, natural mathematics which is a result of biological evolution and artificial mathematics which is a result of cultural evolution. On this basis, it outlines an approach to the philosophy of mathematics which involves a new treatment ..."
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ABSTRACT: The paper distinguishes between two kinds of mathematics, natural mathematics which is a result of biological evolution and artificial mathematics which is a result of cultural evolution. On this basis, it outlines an approach to the philosophy of mathematics which involves a new treatment of the method of mathematics, the notion of demonstration, the questions of discovery and justification, the nature of mathematical objects, the character of mathematical definition, the role of intuition, the role of diagrams in mathematics, and the effectiveness of mathematics in natural science.