Algebra of programming
A Discipline of Programming
Journal of Functional Programming
Containers: constructing strictly positive types
Theoretical Computer Science - Applied semantics: Selected topics
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Algebra of programming in agda: Dependent types for relational program derivation
Journal of Functional Programming
Dependently typed programming in Agda
AFP'08 Proceedings of the 6th international conference on Advanced functional programming
Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
Epigram: practical programming with dependent types
AFP'04 Proceedings of the 5th international conference on Advanced Functional Programming
Monads need not be endofunctors
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
Transporting functions across ornaments
Proceedings of the 17th ACM SIGPLAN international conference on Functional programming
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Dependently typed programming is hard, because ideally dependently typed programs should share structure with their correctness proofs, but there are very few guidelines on how one can arrive at such integrated programs. McBride's algebraic ornamentation provides a methodological advancement, by which the programmer can derive a datatype from a specification involving a fold, such that a program that constructs elements of that datatype would be correct by construction. It is thus an effective method that leads the programmer from a specification to a dependently typed program. We enhance the applicability of this method by generalising algebraic ornamentation to a relational setting and bringing in relational algebraic methods, resulting in a hybrid approach that makes essential use of both dependently typed programming and relational program derivation. A dependently typed solution to the minimum coin change problem is presented as a demonstration of this hybrid approach. We also give a theoretically interesting "completeness theorem" of relational algebraic ornaments, which sheds some light on the expressive power of ornaments and inductive families.