Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The duality of computation under focus   We review the close relationship between abstract machines for (call-by-name
or call-by-value) lambda-calculi (extended with Felleisen's C) and sequent
calculus, reintroducing on the way Curien-Herbelin's syntactic kit expressing
the duality of computation. We use this kit to provide a term language for a
presentation of LK (with conjunction, disjunction, and negation), and to
transcribe cut elimination as (non confluent) rewriting. A key slogan here,
which may appear here in print for the first time, is that commutative cut
elimination rules are explicit substitution propagation rules. We then describe
the focalised proof search discipline (in the classical setting), and narrow
down the language and the rewriting rules to a confluent calculus (a variant of
the second author's focalising system L). We then define a game of patterns and
counterpatterns, leading us to a fully focalised finitary syntax for a
synthetic presentation of classical logic, that provides a quotient on
(focalised) proofs, abstracting out the order of decomposition of negative
connectives.

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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
2
The categories of this paper are: math
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con