This is a draft of the textbook/monograph that presents computability theory using string diagrams. The introductory chapters have been taught as graduate and undergraduate courses and evolved through 8 years of lecture notes. The later chapters contain new ideas and results about categorical computability and some first steps into computable category theory. The underlying categorical view of computation is based on monoidal categories with program evaluators, called *monoidal computers*. This categorical structure can be viewed as a single-instruction diagrammatic programming language called Run, whose only instruction is called RUN. This version: improved text, moved the final chapter to the next volume. (The final version will continue lots of exercises and workouts, but already this version has severely degraded graphics to meet the size bounds.)
翻译:这是一份使用字符串图表展现可计算理论的教材/专著草稿。导论部分已作为研究生和本科生课程教授,并通过8年的讲义演变而来。后面的章节包含了关于范畴可计算性的新思想和结果,以及一些关于可计算范畴论的开端。计算的潜在范畴观点基于具有程序评估器的单配范畴,称为*单配电脑*。这个范畴结构可以被视为一种名为RUN的单指令图形编程语言,其唯一指令称为RUN。这个版本:改进了文字,将最后一章移到下一卷中。(最终版本将继续有大量的练习和工作,但已经这个版本的图形已经严重降级以符合大小边界。)