In a previous work (Abstract data type systems, Theoret. Comput. Sci. 173 (2) (1997)), the last two authors presented a combined language made of a (strongly normalizing) algebraic rewrite system and a typed lambda-calculus enriched by pattern-matching definitions following a certain format, called the “General Schema”, which generalizes the usual recursor definitions for natural numbers and similar “basic inductive types”. This combined language was shown to be strongly normalizing. The purpose of this paper is to reformulate and extend the General Schema in order to make it easily extensible, to capture a more general class of inductive types, called “strictly positive”, and to ease the strong normalization proof of the resulting system. This result provides a computation model for the combination of an algebraic specification language based on abstract data types and of a strongly typed functional language with strictly positive inductive types.

在以前的工作（抽象数据类型系统，Theoret。Comput。Sci。173（2）（1997））中，最后两位作者介绍了一种由（高度规范化）代数重写系统和一个类型丰富的Lambda演算组成的组合语言。通过遵循某种格式的模式匹配定义（称为“通用模式”），该格式概括了自然数和类似的“基本归纳类型”的常规递归定义。事实证明，这种组合语言具有很强的规范性。本文的目的是重新构造和扩展通用模式，以使其易于扩展，捕获更通用的归纳类型，称为“严格正”，并简化所得系统的强大归一化证明。