Containers: Constructing strictly positive types

  title={Containers: Constructing strictly positive types},
  author={Michael Gordon Abbott and Thorsten Altenkirch and Neil Ghani},
  journal={Theor. Comput. Sci.},
We introduce container functors as a representation of data types providing a new conceptual analysis of data structures and polymorphic functions. Our development exploits Type Theory as a convenient way to define constructions within locally cartesian closed categories. We show that container morphisms can be full and faithfully interpreted as polymorphic functions (i.e. natural transformations) and that in the presence of W-types all strictly positive types (including nested inductive and… CONTINUE READING
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