Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tabled Typeclass Resolution   Typeclasses provide an elegant and effective way of managing ad-hoc
polymorphism in both programming languages and interactive proof assistants.
However, the increasingly sophisticated uses of typeclasses within proof
assistants, especially within Lean's burgeoning mathematics library, mathlib,
have elevated once-theoretical limitations of existing typeclass resolution
procedures into major impediments to ongoing progress. The two most devastating
limitations of existing procedures are exponential running times in the
presence of diamonds and divergence in the presence of cycles. We present a new
procedure, tabled typeclass resolution, that solves both problems by tabling,
which is a generalization of memoizing originally introduced to address similar
limitations of early logic programming systems. We have implemented our
procedure for the upcoming version (v4) of Lean, and have confirmed empirically
that our implementation is exponentially faster than existing systems in the
presence of diamonds. Although tabling is notoriously difficult to implement,
our procedure is notably lightweight and could easily be implemented in other
systems. We hope our new procedure facilitates even more sophisticated uses of
typeclasses in both software development and interactive theorem proving.

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The categories of this paper are: math
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
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The categories of this paper are: eess
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex