An introduction to the theory of lists
Proceedings of the NATO Advanced Study Institute on Logic of programming and calculi of discrete design
Algorithmic skeletons: structured management of parallel computation
Algorithmic skeletons: structured management of parallel computation
A Discipline of Programming
Parallelizing functional programs by generalization
Journal of Functional Programming
Journal of Functional Programming
Automatic inversion generates divide-and-conquer parallel programs
Proceedings of the 2007 ACM SIGPLAN conference on Programming language design and implementation
The third homomorphism theorem on trees: downward & upward lead to divide-and-conquer
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A short cut to parallelization theorems
Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
| Hi-index | 0.00 |
The third list-homomorphism theorem says that a function is a list homomorphism if it can be described as an instance of both a foldr and a foldl. We prove a dual theorem for unfolds and generalise both theorems to trees: if a function generating a list can be described both as an unfoldr and an unfoldl, the list can be generated from the middle, and a function that processes or builds a tree both upwards and downwards may independently process/build a subtree and its one-hole context. The point-free, relational formalism helps to reveal the beautiful symmetry hidden in the theorem.