Using Information Systems to Solve Recursive Domain Equations Effectively
Using Information Systems to Solve Recursive Domain Equations Effectively
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DOI：
10.1007/3-540-13346-1_5
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发表时间：
1984-06
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影响因子：
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通讯作者：
G. Winskel;K. Larsen
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文献类型：
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作者：
G. Winskel;K. Larsen
由Dana Scott和Christopher Strachey建立的编程语言语义的数学理论是基于信息的偏序。就像我们考虑计算一个整数或一个最终状态一样，我们也可以考虑计算一个更抽象的信息偏序中的元素。就像从输入状态到输出状态的计算一样，也可以从一个信息偏序的输入计算另一个信息偏序的输出，最常用的偏序是完全偏序（缩写为cpos）。一个cpo有一个最小的元素I，叫做”bottom”，它代表零信息，并且满足我们试图激励的完备性公理。想象一下，计算一个像部分函数一样的信息元素。信息不一定是一个不可分割的整体，而是可以表现为信息元素的递增链，信息随着时间的推移而积累，在cpo中，信息的积累，即使是在无限长的时间内，也可以用偏序元素来表示。形式上，cpo必须满足条件，如果x 0~ xI ~.~ xn~..是递增e-链，则它在偏序中有最小上界（lub）UnE x。
The mathematical theory of semantics of programming languages founded by Dana Scott and Christopher Strachey has been based on partial orders of information. Just as one thinks of computing an integer or a final state so can one think of computing an element in the more abstract partial orders of information. And just as one has computations from input states to output states one can have computations which from input in one partial order of information compute output in another.The most general partial orders in use are complete partial orders (abbreviated to cpos). A cpo has a least element I, called" bottom", which stands for null information, and satisfies a completeness axiom which we try to motivate. Imagine computing an element of information like a partial function. The information need not come in one indivisible lump but may instead be presented as an increasing chain of elements of information, with information accumulating as time goes on. In a cpo the accumulation of this information, even over infinite time, is represented by an element of the partial order too. Formally, a cpo must satisfy the condition that if x 0~ x I~...~ xn~.. is an increasing e-chain then it has a least upper bound (lub) UnE x in the partial order.