Abstract

We describe an alternative schema of induction for the programming logic TK based on safe positive induction. This replaces the original schema based on the well founded part of a relation. We show how the new schema can be included into the realizability definition and how the soundness of realizability can be extended to allow for the derivation of recursive programs from proofs of specifications which use the new schema. We further show how systems of mutual induction can be handled naturally with the new schema. In particular we show how useful systems of mutually recursive combinators can be derived which realize the principles of mutual induction. 2 Introduction The apparatus which a programming logic provides for inductive types is, perhaps, its most important component. This is because we rely on inductive types for the definition of many recursive types ubiquitous in programming languages: natural numbers, lists, trees, and so on. Moreover, it is from proofs which involve in...

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