Step-indexed models of call-by-name: a tutorial example

In this tutorial paper we show how to construct a step-indexed logical relation for a call-by-name programming language with recursive types and show that it is complete with respect to contextual equivalence. We then show how the same constructions can be used to define a step-indexed model, in the standard categorical sense, of the language. We hope that this will make step-indexed techniques more readily available for researchers interested in call-by-name or call-by-need based languages (such as Haskell) and make it clear that step-indexed models can indeed be seen as (operationally-based) models in the technical sense (and not only as a reasoning technique for reasoning about contextual equivalence).