Indexed containers

We show that the syntactically rich notion of strictly positive families can be reduced to a core type theory with a fixed number of type constructors exploiting the novel notion of indexed containers. As a result, we show indexed contain-ers provide normal forms for strictly positive families in much the same way that containers provide normal forms for strictly positive types. Interestingly, this step from containers to indexed containers is achieved without having to extend the core type theory. Most of the construction presented here has been formalized using the Agda system – the missing bits are due to the current shortcomings of the Agda system.