Monad的一种自动生成技术

Monad程序的核心是一组Monad定义.Monad定义分为MAP型和BIND型.如果在Monad库中已有所需要的Monad定义型,则可以直接使用,而不需要重新构造;否则,需要重新构造.但如果在Monad程序设计环境中增加从一类Monad构造另一类Monad的自动生成器,那么既方便了用户也扩充了1倍原有的Monad库.鉴于这种思想,用支持Monad程序设计的高阶函数语言Haskell实现了一个Monad的自动生成系统.另外,用户构造Monad不仅要花费较多的时间,而且写出的Monad多态函数往往不满足Monad所需满足的几条公理,因此,从这方面也可以看出,从一种类型的Monad自动产生另一种类型的Monad的重要意义.     

非确定性Monad

纯函数式语言缺乏处理非确定性的功能，本文给出了一个非确定性Ｍｏｎａｄ，用此Ｍｏｎａｄ在纯函数式语言中描述了非确定性进程网，证明了一些有用的代数性质。     

Infinite trees and completely iterative theories: a coalgebraic view

Infinite trees form a free completely iterative theory over any given signature—this fact, proved by Elgot, Bloom and Tindell, turns out to be a special case of a much more general categorical result exhibited in the present paper. We prove that whenever an endofunctor H of a category has final coalgebras for all functors H( _ )+X, then those coalgebras, TX, form a monad. This monad is completely iterative, i.e., every guarded system of recursive equations has a unique solution. And it is a free completely iterative monad on H. The special case of polynomial endofunctors of the category is the above mentioned theory, or monad, of infinite trees.

This procedure can be generalized to monoidal categories satisfying a mild side condition: if, for an object H, the endofunctor H_+I has a final coalgebra, T, then T is a monoid. This specializes to the above case for the monoidal category of all endofunctors.     

Combining a monad and a comonad

We give a systematic treatment of distributivity for a monad and a comonad as arises in giving category theoretic accounts of operational and denotational semantics, and in giving an intensional denotational semantics. We do this axiomatically, in terms of a monad and a comonad in a 2-category, giving accounts of the Eilenberg–Moore and Kleisli constructions. We analyse the eight possible relationships, deducing that two pairs are isomorphic, but that the other pairs are all distinct. We develop those 2-categorical definitions necessary to support this analysis.     

基于Monad的纯函数式语言通道系统设计

本文通过状态转换器来定义I／O的文件系统，并用非确定性Monad描述了操作系统的进程同，从而给出了通道系统的语义。     

一种基于组合Monad的纯函数式通道系统操作

Monad作为构造纯函数式语言的工具,能构造出诸如错误处理、状态、IO等非纯函数式语言的特征。该文通过组合状态转换Monad和异常处理Monad来定义纯函数式语言通道系统操作,给出了通道系统操作的操作语义。     

平行哲学与智能科学:从莱布尼茨的Monad到区块链之DAO

本文从新的角度回顾科学和哲学的本源,认为需要以新的思想发展人工智能和智能技术及其相应的智慧社会.围绕卡尔·波普尔的三个交织世界的现实观,提出面向描述知识、预测知识和引导知识的平行哲学理念,使关于智能的哲学之研究对象从Being,Becoming到Believing,并讨论结合区块链DAO技术与范畴数学理论的可能实施途径.     

一种基于Z规范的纯函数式程序设计方法

状态、输入和输出是Z规范的基础,引入Monad的纯函数式语言特别适合用来实现用Z规范说明的系统.通过将状态、输入和输出封装在一个Monad内,提出一种基于Z规范的纯函数式程序设计方法.     

基于Monad的纯函数式程序设计

ＰｈｉｌｉｐＷａｄｌｅｒ在探讨用Ｍｏｎａｄ构造纯函数式程序时，介绍了一个简单的词法分析程序的构造过程．本文进一步研究了这种方法，并用这种方法构造出一个能进行复杂的ｌａｙｏｕｔ分析、词法分析与语法分析的纯函数式分析程序.