Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abstract clones for abstract syntax   We give a formal treatment of simple type theories, such as the simply-typed
$\lambda$-calculus, using the framework of abstract clones. Abstract clones
traditionally describe first-order structures, but by equipping them with
additional algebraic structure, one can further axiomatize second-order,
variable-binding operators. This provides a syntax-independent representation
of simple type theories. We describe multisorted second-order presentations,
such as the presentation of the simply-typed $\lambda$-calculus, and their
clone-theoretic algebras; free algebras on clones abstractly describe the
syntax of simple type theories quotiented by equations such as $\beta$- and
$\eta$-equality. We give a construction of free algebras and derive a
corresponding induction principle, which facilitates syntax-independent proofs
of properties such as adequacy and normalization for simple type theories.
Working only with clones avoids some of the complexities inherent in
presheaf-based frameworks for abstract syntax.

8
The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg