(以上定义来源于“A Taste of Category Theory for Computer Scientists ”) 两个最常见的函子是 和。例如是一个集合,所以的“值域”永远是集合范畴。也一样,唯一的差别在于两者作用在同一范畴上后,得到的集合范畴的的内部箭头(态射)全体要调个方向,所以又称为反变函子,又称为协变函子。关于箭头的反向,笔者会...
原文category theory for programmers 最后更新于2021-11-23 Category: The Essence of Composition composition定理 ( essence of programming) 1.1 Arrows as Functions 在一个category中, 如果有arrow从A得到B,另外一arrow从B得到C,那么有arrow从A到C. // TSconstf=(a:A)=>(returnb:B)constg=(b:B)=>(re...
Category theory for programmers这本书阅读有俩障碍,一是英文,二是数学概念比较难理解。翻译成中文工作量大又很有可能出错。于是乎我还是作为一个中国js程序员角度对文章每段写个我的理解,既轻松,又应该有点用。 Presface写了作者写这本书的原因和解释了一波为什么程序员要学范畴论。 文章格式:: [ 原文一段 ++...
(以上定义来源于“A Taste of Category Theory for Computer Scientists ”) 看完以上定义后你的感受是? A. B. 选B的话就可以继续前进啦! 当然选A似乎也可以。。 我们甚至可以进一步把这些概念具体化,例如每当我们提到范畴时,可以参照两个实例: 群范畴或线性空间范畴,那么态射就是群之间的同态或线性空间之间的...
1. Programming is Math. 2. Object-Oriented is based onSet Theorywhich has 2 weaknesses: ◇ Set has contradiction: The famous“Russell’s Barber Paradox”. ◇Data Immutabilityfor Concurrent Processing : OO can’t control the mutable state of objects, making debugging impossible. ...
It might therefore come as a shock that the basic concepts of category theory can be explained in relatively simple terms to anybody with some experience in programming. That's because, just like programming, category theory is about structure. Mathematicians discover structure in mathematical ...
Category Theory: A Programming Language Oriented Introduction This book explains the following topics: Categories, functors, natural transformations, String diagrams, Kan extensions, Algebras, coalgebras, bialgebras, Lambda-calculus and categories. Computational...
Category theory is the kind of math that is particularly well suited for the minds of programmers. It deals with the kind of structure that makes programs composable. And I will argue strongly that composition is the essence of programming. I will illustrate all major concepts using computer cod...
Category Theory for Programmers:'Category Theory for Programmers' 非官方 PDF 和 LaTeX 源-开源 这是Bartosz Milewski 撰写的“程序员类别理论”的非官方 PDF 版本,从他的博文系列(经许可)转换而来。 程序员类别理论于 2019 年 8 月 12 日发布。基于发布标签 v1.3.0。 有关自打印以来的更改和修复,请参阅...
Category Theory For Programmers AnunofficialPDF version of "CategoryTheoryForProgrammers" byBartosz Milewski, converted from hisblogpost series(with permission!). Standard edition in full-color hardcover print Publish date: 12 August, 2019. Based off release tagv1.3.0. Seeerrata-1.3.0for changes an...