Towards "Mouldable Code" as a Better Approach to Synthesis of Efficient and Correct Software

优化代码生成器（特别是编译器中的代码生成器）的支持基础结构的重要部分由图的分析组成，特别是控制流图和数据流图。此外，通过这些分析实现的许多优化可以被理解为图形转换。******有趣的是，程序转换文献几乎完全集中于（高阶）抽象语法树的转换。这与编译器上下文中的通常方法相对应，首先将给定的程序解析为抽象语法树，然后从中提取必要的信息来构建用于数据流和控制流分析的图，同时仍然将抽象语法树视为程序的内部表示。******然而，许多用于代码优化的转换，特别是在编译器的后端，作用于可以被认为是图形模式的模式，并且由此产生的转换在文献中经常被解释为应用于控制流图和数据流图的图形转换。******在这个研究计划中，我的目标是通过将控制流和数据流语义理论与适当的图转换理论联系起来，为控制流图转换和数据流图转换创造理论依据，并在这些基础上建立一个用于嵌套代码图转换的机械化框架。******这个框架的目标是成为一类新的机械化环境的第一个代表，在这种环境中，专家可以用基于图的形式来设计特殊目的的优化通道，这种形式可以捕捉优化通道的直观的基于图的描述，因为它们在编译器文献中是习惯的。然而，虽然文献中基于图形的描述在技术上是完全非正式的，但设想的机械化系统将不仅支持捕获设计本身，而且还支持在概念上接近设计的级别上证明这些优化的正确性，并且最终还将自动生成这些优化通过的正确构造实现。

Important parts of the supporting infrastructure for optimising code generators, in particular in compilers, consist of analyses of graphs, especially control-flow graphs and data-flow graphs. In addition, many of the optimisations enabled by these analyses are usefully understood as graph transformations.******Interestingly, the program transformation literature almost exclusively concentrates on transformation of (higher-order) abstract syntax trees. This corresponds to the usual approach in a compiler context to first parse the given programs into abstract syntax trees, and then extract from these the necessary information to construct the graphs to be used for data-flow and control-flow analyses, while still considering the abstract syntax trees as the internal representation of the program.******However, many of the transformations that are used for code optimisation, in particular in the back-ends of compilers, act on patterns that can usefully be thought of as graph patterns, and the resulting transformations are frequently explained in the literature as graph transformations applied to control-flow graphs and data-flow graphs.******In this research programme, I aim to create the theoretical justifications for control-flow graph transformation and data-flow graph transformations by linking the theories of control-flow and data-flow semantics with appropriate theories of graph transformation and build on these foundations a mechanised framework for nested code graph transformation.******The goal of this framework is to be the first representative of a new class of mechanised environments in which experts can design special-purpose optimisation passes in a graph-based formalism that captures the intuitive graph-based descriptions of optimisation passes as they are customary in the compiler literature. However, while the graph-based descriptions in the literature are technically completely informal, the envisaged mechanised system will support not only capturing the design itself, but also proving the correctness of these optimisations at a level that is conceptually close to the design, and will finally also automatically generate correct-by-construction implementations of these optimisation passes.