Executable Set Theory and Arithmetic Encodings in Prolog

12 years 2 days ago
Executable Set Theory and Arithmetic Encodings in Prolog
The paper is organized as a self-contained literate Prolog program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The complete SWI-Prolog tested code is available at http://logic.csci. First, ranking and unranking functions for some "mathematically elegant" data types in the universe of Hereditarily Finite Sets with Urelements are provided, resulting in arithmetic encodings for powersets, hypergraphs, ordinals and choice functions. After implementing a digraph representation of Hereditarily Finite Sets we define decoration functions that can recover well-founded sets from encodings of their associated acyclic digraphs. We conclude with an encoding of arbitrary digraphs and discuss a concept of duality induced by the set membership relation. In the process, we uncover the surprising possibility of internally sharing isomorphic objects, independently of their lang...
Paul Tarau
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Where CORR
Authors Paul Tarau
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