A coinductive calculus of streams
A coinductive calculus of streams
复制标题
流的共归纳演算
DOI：
10.1017/s0960129504004517
复制
发表时间：
2005
影响因子：
0.5
通讯作者：
J. Rutten
中科院分区：
文献类型：
--
作者：
J. Rutten
我们开发了一个coinductive演算流的基础上存在的一个最终的余代数结构的流（无限序列的真实的数字）。主要成分是流导数的概念，它可以用来制定共同归纳证明和定义。在密切的类比经典分析，后者提出的行为微分方程。微积分的一些应用，包括差分方程，分析微分方程，连分数，和一些问题，从离散数学和组合数学。
We develop a coinductive calculus of streams based on the presence of a final coalgebra structure on the set of streams (infinite sequences of real numbers). The main ingredient is the notion of stream derivative, which can be used to formulate both coinductive proofs and definitions. In close analogy to classical analysis, the latter are presented as behavioural differential equations. A number of applications of the calculus are presented, including difference equations, analytical differential equations, continued fractions, and some problems from discrete mathematics and combinatorics.