Information and Computation - Semantics of Data Types
Isomorphisms, hylomorphisms and hereditarily finite data types in Haskell
Proceedings of the 2009 ACM symposium on Applied Computing
A Groupoid of Isomorphic Data Transformations
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
An embedded declarative data transformation language
PPDP '09 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming
Hi-index | 0.01 |
We provide a "shared axiomatization" of natural numbers and hereditarily finite sets built around a polymorphic abstraction of bijective base-2 arithmetics. The "axiomatization" is described as a progressive refinement of Haskell type classes with examples of instances converging to an efficient implementation in terms of arbitrary length integers and bit operations. As an instance, we derive algorithms to perform arithmetic operations efficiently directly with hereditarily finite sets. The self-contained source code of the paper is available at http:// logic.cse.unt.edu/tarau/research/2010/unified.hs