论文标题
$ \ aleph $微积分
The $\aleph$ Calculus
论文作者
论文摘要
引入了$ \ aleph $ cyculus的动机，需要适合布朗分子体系结构的可逆计算模型。这个新颖的模型是声明性的，并发和基于术语的 - 包含有关单个结构中程序数据和状态的所有信息，以消除对von Neumann式的离散计算“机器”的需求，这是分子环境中的挑战。该名称的灵感来自希腊语“不忘记”，因为强调（可逆地）学习和对不同变量的学习知识。为了为此目的证明其实用性以及作为编程语言的优雅性，呈现了许多例子。这些示例中有两个，加法/减法和平方/平方根，配有用于抽象分子实现的设计。这些例子和随附的句法糖的自然副产品是设计成熟的编程语言Alethe的设计，该语言也与口译员一起呈现。在确定性计算机上有效地模拟$ \ aleph $，需要对Alethe解释器中的程序进行一些静态分析，以使声明程序顺序呈现。最后，提出了适合这种可逆的声明性计算模型的类型系统。
Motivated by a need for a model of reversible computation appropriate for a Brownian molecular architecture, the $\aleph$ calculus is introduced. This novel model is declarative, concurrent, and term-based--encapsulating all information about the program data and state within a single structure in order to obviate the need for a von Neumann-style discrete computational 'machine', a challenge in a molecular environment. The name is inspired by the Greek for 'not forgotten', due to the emphasis on (reversibly) learning and un-learning knowledge of different variables. To demonstrate its utility for this purpose, as well as its elegance as a programming language, a number of examples are presented; two of these examples, addition/subtraction and squaring/square-rooting, are furnished with designs for abstract molecular implementations. A natural by-product of these examples and accompanying syntactic sugar is the design of a fully-fledged programming language, alethe, which is also presented along with an interpreter. Efficiently simulating $\aleph$ on a deterministic computer necessitates some static analysis of programs within the alethe interpreter in order to render the declarative programs sequential. Finally, work towards a type system appropriate for such a reversible, declarative model of computation is presented.
