These are two topics to which de Bruijn has made major contributions.

His contribution to the first topic was the today classic idea of `de Bruijn indices' as a technique to use in the computer implementation of variable binding operators. In recent years a variety of mathematical treatments of variable binding have been proposed and investigated. In the first part of my talk I will discuss the notion of a nested data type and its use in representing variable binding.

De Bruijn may be said to be the inventor of the idea of a logical framework in connection with his automath project. Today there are a variety of logical frameworks that have been proposed, often differing subtly by the features that they support. In the second part of my talk I will report on the ideas and results, of the PhD student Robin Adams, for classifying and comparing logical frameworks by the features that they support. In general adding a new feature to a logical framework often leads to a conservative extension.