Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Functional Hitchhiker's Guide to Hereditarily Finite Sets, Ackermann
  Encodings and Pairing Functions   The paper is organized as a self-contained literate Haskell program that
implements elements of an executable finite set theory with focus on
combinatorial generation and arithmetic encodings. The code, tested under GHC
6.6.1, is available at http://logic.csci.unt.edu/tarau/research/2008/fSET.zip .
  We introduce ranking and unranking functions generalizing Ackermann's
encoding to the universe of Hereditarily Finite Sets with Urelements. Then we
build a lazy enumerator for Hereditarily Finite Sets with Urelements that
matches the unranking function provided by the inverse of Ackermann's encoding
and we describe functors between them resulting in arithmetic encodings for
powersets, hypergraphs, ordinals and choice functions. After implementing a
digraph representation of Hereditarily Finite Sets we define {\em 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.
  Keywords: hereditarily finite sets, ranking and unranking functions,
executable set theory, arithmetic encodings, Haskell data representations,
functional programming and computational mathematics

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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: math
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The categories of this paper are: q-fin
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The categories of this paper are: nlin