This paper addresses the problem of abstracting a set of affine transformers $$\overrightarrow{v}' = \overrightarrow{v} \cdot C + \overrightarrow{d}$$v→′=v→·C+d→, where $$\overrightarrow{v}$$v→ and $$\overrightarrow{v}'$$v→′ represent the pre-state and post-state, respectively. We introduce a framework to harness any base abstract domain $$\mathcal {B}$$B in an abstract domain of affine transformations. Abstract domains are usually used to define constraints on the variables of a program. In this paper, however, abstract domain $$\mathcal {B}$$B is re-purposed to constrain the elements of C and $$\overrightarrow{d}$$d→—thereby defining a set of affine transformers on program states. This framework facilitates intra- and interprocedural analyses to obtain function and loop summaries, as well as to prove program assertions.

中文翻译：

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仿射变换器的新抽象框架

本文解决了抽象一组仿射变换器 $$\overrightarrow{v}' = \overrightarrow{v} \cdot C + \overrightarrow{d}$$v→′=v→·C+d→ 的问题，其中$$\overrightarrow{v}$$v→ 和 $$\overrightarrow{v}'$$v→′ 分别代表前状态和后状态。我们引入了一个框架来利用仿射变换的抽象域中的任何基本抽象域 $$\mathcal {B}$$B。抽象域通常用于定义对程序变量的约束。然而，在本文中，抽象域 $$\mathcal {B}$$B 被重新用于约束 C 和 $$\overrightarrow{d}$$d→ 的元素，从而在程序上定义一组仿射变换器状态。该框架有助于过程内和过程间分析，以获得函数和循环摘要，以及证明程序断言。