Elaborating Inductive Definitions

  title={Elaborating Inductive Definitions},
  author={Pierre-{\'E}variste Dagand and Conor McBride},
We present an elaboration of inductive definitions down to a universe of datatypes. The universe of datatypes is an internal presentation of strictly positive types within type theory. By elaborating an inductive definition – a syntactic artefact – to its code – its semantics – we obtain an internalised account of inductives inside the type theory itself: we claim that reasoning about inductive definitions could be carried in the type theory, not in the meta-theory as it is usually the case… CONTINUE READING
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Towards a practical programming language based on dependent type theory

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