Journal of Functional Programming
Formal certification of a compiler back-end or: programming a compiler with a proof assistant
Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Program-ing finger trees in Coq
ICFP '07 Proceedings of the 12th ACM SIGPLAN international conference on Functional programming
Proceedings of the 13th ACM SIGPLAN international conference on Functional programming
Dependently typed programming in Agda
AFP'08 Proceedings of the 6th international conference on Advanced functional programming
AMAST'10 Proceedings of the 13th international conference on Algebraic methodology and software technology
Dependently typed attribute grammars
IFL'10 Proceedings of the 22nd international conference on Implementation and application of functional languages
Guiding parallel array fusion with indexed types
Proceedings of the 2012 Haskell Symposium
Modular type-safety proofs in Agda
PLPV '13 Proceedings of the 7th workshop on Programming languages meets program verification
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Dependently typed languages have for a long time been used to describe proofs about programs. Traditionally, dependent types are used mostly for stating and proving the properties of the programs and not in defining the programs themselves. An impressive example is the certified compiler by Leroy (2006) implemented and proved correct in Coq (Bertot and Castéran 2004). Recently there has been an increased interest in dependently typed programming, where the aim is to write programs that use the dependent type system to a much higher degree. In this way a lot of the properties that were previously proved separately can be integrated in the type of the program, in many cases adding little or no complexity to the definition of the program. New languages, such as Epigram (McBride and McKinna 2004), are being designed, and existing languages are being extended with new features to accomodate these ideas, for instance the work on dependently typed programming in Coq by Sozeau (2007). This talk gives an overview of the Agda programming language (Norell 2007), whose main focus is on dependently typed programming. Agda provides a rich set of inductive types with a powerful mechanism for pattern matching, allowing dependently typed programs to be written with minimal fuss. To read about programming in Agda, see the lecture notes from the Advanced Functional Programming summer school (Norell 2008) and the work by Oury and Swierstra (2008). In the talk a number of examples of interesting dependently typed programs chosen from the domain of programming language implementation are presented as they are implemented in Agda.