A Compendium of Continuous Lattices
A Compendium of Continuous Lattices
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DOI：
10.1007/978-3-642-67678-9
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发表时间：
1980-12
期刊：
影响因子：
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通讯作者：
G. Gierz;K. Hofmann;K. Keimel;J. Lawson;M. Mislove;D. Scott
中科院分区：
文献类型：
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作者：
G. Gierz;K. Hofmann;K. Keimel;J. Lawson;M. Mislove;D. Scott
一本由六位作者合著的数学书可能是一件非常罕见的事情，以至于读者会问这样的合作是如何产生的。因此，我们首先要说几句，我们是如何在十年的时间里接触到这个问题的，在这十年的一段时间里，我们彼此并不认识。我们不打算在这里写连续格的历史，而是解释我们自己的个人参与。更恰当的意义上的历史是由参考书目和书中各章节后面的注释以及正文中的许多注释提供的。引言部分保留对整个研究的内容和动机的连贯讨论。1969年10月，Dana Scott受到计算机语言语义问题的启发，开始考虑函数空间的部分有序结构。用偏序来对应部分定义函数和泛函的空间的想法在递归函数理论中出现过好几次；然而，人们对连续泛函的结构并没有很持久的兴趣。这些是斯科特认为他需要的。他的第一个洞见是，用更现代的术语来说，代数格和（所谓的）斯科特连续函数的范畴是笛卡尔闭的。
A mathematics book with six authors is perhaps a rare enough occurrence to make a reader ask how such a collaboration came about. We begin, therefore, with a few words on how we were brought to the subject over a ten-year period, during part of which time we did not all know each other. We do not intend to write here the history of continuous lattices but rather to explain our own personal involvement. History in a more proper sense is provided by the bibliography and the notes following the sections of the book, as well as by many remarks in the text. A coherent discussion of the content and motivation of the whole study is reserved for the introduction. In October of 1969 Dana Scott was lead by problems of semantics for computer languages to consider more closely partially ordered structures of function spaces. The idea of using partial orderings to correspond to spaces of partially defined functions and functionals had appeared several times earlier in recursive function theory; however, there had not been very sustained interest in structures of continuous functionals. These were the ones Scott saw that he needed. His first insight was to see that-in more modern terminology-the category of algebraic lattices and the (so-called) Scott-continuous functions is cartesian closed.