Inductive Data Type Systems: Strong Normalization
نویسندگان
چکیده
This paper is concerned with the foundations of Inductive Data Type Systems, an extension of pure type systems by inductive data types. IDTS generalize (inductive) types equipped with primitive recursion of higher-type, by providing de nitions of functions by pattern matching of a form which is general enough to capture recursor de nitions for strictly positive inductive types. IDTS also generalize the rst-order framework of abstract data types by providing function types and higher-order rewrite rules. The main result of the paper is the strong normalization property of inductive data type systems, in case of a simple type discipline.
منابع مشابه
Inductive-data-type systems
In a previous work (“Abstract Data Type Systems”, TCS 173(2), 1997), the last two authors presented a combined language made of a (strongly normalizing) algebraic rewrite system and a typed λ-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 ...
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