Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lambda-calculus and Reversible Automatic Combinators   In 2005, Abramsky introduced various linear/affine combinatory algebras of
partial involutions over a suitable formal language, to discuss reversible
computation in a game-theoretic setting. These algebras arise as instances of
the general paradigm explored by Haghverdi (Abramsky's Programme), which
amounts to defining a lambda-algebra starting from a GoI Situation in a traced
symmetric monoidal category. We investigate this construction from the point of
view of the model theory of lambda-calculus. We focus on the strictly linear
and affine parts of Abramsky's Affine Combinatory Algebras, sketching how to
encompass the full algebra. The gist of our approach is that the GoI
interpretation of a term based on involutions is dual to the principal type of
the term, w.r.t. the type discipline for a linear/affine lambda-calculus. In
the general case the type discipline and the calculus need to be extended,
resp., with intersection, !-types, and !-abstractions. Our analysis unveils
three conceptually independent, but ultimately equivalent, accounts of
application in the lambda-calculus: beta-reduction, the GoI application of
involutions based on symmetric feedback (Girard's Execution Formula), and
unification of principal types. Thus we provide an answer, in the strictly
affine case, to the question raised in [1] of characterising the partial
involutions arising from bi-orthogonal pattern matching automata, which are
denotations of affine combinators, and we point to the answer to the full
question. Furthermore, we prove that the strictly linear combinatory algebra of
partial involutions is a strictly linear lambda-algebra, albeit not a
combinatory model, while both the strictly affine combinatory algebra and the
full affine combinatory algebra are not. To check all the equations involved in
the definition of affine lambda-algebra, we implement in Erlang application of
involutions.

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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: math
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin