FPCA '89 Proceedings of the fourth international conference on Functional programming languages and computer architecture
Substitution: a formal methods case study using monads and transformations
TAPSOFT '93 Selected papers of the colloquium on Formal approaches of software engineering
A Formalization of the Strong Normalization Proof for System F in LEGO
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Monadic Presentations of Lambda Terms Using Generalized Inductive Types
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Journal of Functional Programming
de Bruijn notation as a nested datatype
Journal of Functional Programming
Applicative programming with effects
Journal of Functional Programming
A fresh look at programming with names and binders
Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
Parametricity and dependent types
Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
A Computational Interpretation of Parametricity
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Verified programs with binders
Proceedings of the ACM SIGPLAN 2014 Workshop on Programming Languages meets Program Verification
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De Bruijn indices are a well known technique for programming with names and binders. They provide a representation that is both simple and canonical. However, programming errors tend to be really easy to make. We propose a safer programming interface implemented as a library. Whereas indexing the types of names and terms by a numerical bound is a famous technique, we index them by worlds, a different notion of index that is both finer and more abstract. While being more finely typed, our approach incurs no loss of expressiveness or efficiency. Via parametricity we obtain properties about functions polymorphic on worlds. For instance, well-typed world-polymorphic functions over open λ-terms commute with any renaming of the free variables. Our whole development is conducted within Agda, from the code of the library, to its soundness proof and the properties of external functions. The soundness of our library is demonstrated via the construction of a logical relations argument.