类型系统搜索的两个算法
Two algorithms in search of a type system
摘要：
作者的ATR编程形式主义是复杂性理论驱动的类型系统下的按值调用PCF的一个版本。ATR程序运行在2型多项式时间内，所有标准的2型基本可行泛函都是ATR可定义的（ATR类型被限制在0、1和2级）。原始版本的ATR的一个局限性是，唯一可直接表达的递归是尾递归。在这里，我们扩展ATR，使广泛的仿射递归直接表达。特别是，修改后的ATR可以相当自然地表达经典的插入和选择排序算法，从而克服了大多数以前的隐复杂性为基础的形式主义的症结。本文的主要工作是在提炼原来的时间复杂度语义ATR表明，这些新的递归计划不会导致的可行性领域。
英文摘要：
The authors' ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-definable (ATR types are confined to levels 0, 1, and 2). A limitation of the original version of ATR is that the only directly expressible recursions are tail-recursions. Here we extend ATR so that a broad range of affine recursions are directly expressible. In particular, the revised ATR can fairly naturally express the classic insertion- and selection-sort algorithms, thus overcoming a sticking point of most prior implicit-complexity-based formalisms. The paper's main work is in refining the original time-complexity semantics for ATR to show that these new recursion schemes do not lead out of the realm of feasibility.
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