Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Delta-calculus: syntax and types   We present the Delta-calculus, an explicitly typed lambda-calculus with
strong pairs, projections and explicit type coercions. The calculus can be
parametrized with different intersection type theories T, e.g. the
Coppo-Dezani, the Coppo-Dezani-Salle', the Coppo-Dezani-Venneri and the
Barendregt-Coppo-Dezani ones, producing a family of Delta-calculi with related
intersection type systems. We prove the main properties like Church-Rosser,
unicity of type, subject reduction, strong normalization, decidability of type
checking and type reconstruction. We state the relationship between the
intersection type assignment systems a` la Curry and the corresponding
intersection type systems a` la Church by means of an essence function
translating an explicitly typed Delta-term into a pure lambda-term one. We
finally translate a Delta-term with type coercions into an equivalent one
without them; the translation is proved to be coherent because its essence is
the identity. The generic Delta-calculus can be parametrized to take into
account other intersection type theories as the ones in the Barendregt et al.
book.

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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: math
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex