HasCASL中的自举电感和共电感类型
Bootstrapping Inductive and Coinductive Types in HasCASL
摘要：
我们讨论了处理的初始数据集和最终的进程类型的广谱语言HasCASL。特别是，我们提出的规范，说明了如何datatures和进程类型出现的自举概念，使用HasCASL的类型类机制，我们描述了有限和无限树的类型，建立保守性的datatype和进程类型声明坚持一定的合理格式的建设。后者相当于从HOL修改已知的结构，以避免唯一的选择;在分类术语，这意味着我们建立了拟对内部自然数对象支持初始代数和最终余代数的多项式函子的范围，从而部分概括相应的结果从拓扑理论。此外，我们提出了类似的建设范畴的内部完全偏序拟。
英文摘要：
We discuss the treatment of initial datatypes and final process types in the wide-spectrum language HasCASL. In particular, we present specifications that illustrate how datatypes and process types arise as bootstrapped concepts using HasCASL's type class mechanism, and we describe constructions of types of finite and infinite trees that establish the conservativity of datatype and process type declarations adhering to certain reasonable formats. The latter amounts to modifying known constructions from HOL to avoid unique choice; in categorical terminology, this means that we establish that quasitoposes with an internal natural numbers object support initial algebras and final coalgebras for a range of polynomial functors, thereby partially generalising corresponding results from topos theory. Moreover, we present similar constructions in categories of internal complete partial orders in quasitoposes.
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