V2EX complete partial order

Complete Partial Order

释义 Definition

完全偏序(CPO):一种偏序集(poset),通常要求包含最小元(⊥),并且对任意有向子集(directed set),都存在其上确界/最小上界(supremum, lub)。常用于域论(domain theory)程序语义中,用来刻画“逐步逼近的计算过程”。

发音 Pronunciation

/kmplit prl rdr/

例句 Examples

A complete partial order is used to model computation with limits.
完全偏序常用来刻画带“极限”的计算过程。

In denotational semantics, a complete partial order guarantees that iterative definitions have a well-defined least fixed point.
在指称语义中,完全偏序保证迭代定义具有良好定义的最小不动点。

词源 Etymology

该术语由三部分构成:complete(完备的)+ partial(部分的/非全的)+ order(序)。其中“partial order(偏序)”指元素之间并非都可比较;“complete”在这里不是“全序(total order)”的意思,而是指特定集合(尤其是有向集)上,上确界存在,从而满足语义学与不动点理论所需的“完备性”。

相关词 Related Words

文献作品 Literary Works

  • Domain Theory(Samson Abramsky & Achim Jung)
  • The Formal Semantics of Programming Languages: An Introduction(Glynn Winskel)
  • A Compendium of Continuous Lattices(G. Gierz 等)
  • Introduction to Lattices and Order(B. A. Davey & H. A. Priestley)
  • Categories for the Working Mathematician(Saunders Mac Lane)
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