Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tuple Interpretations for Higher-Order Rewriting   We develop a class of algebraic interpretations for many-sorted and
higher-order term rewriting systems that takes type information into account.
Specifically, base-type terms are mapped to \emph{tuples} of natural numbers
and higher-order terms to functions between those tuples. Tuples may carry
information relevant to the type; for instance, a term of type $\mathsf{nat}$
may be associated to a pair $(\mathsf{cost}, \mathsf{size})$ representing its
evaluation cost and size. This class of interpretations results in a more
fine-grained notion of complexity than runtime or derivational complexity,
which makes it particularly useful to obtain complexity bounds for higher-order
rewriting systems. We show that rewriting systems compatible with tuple
interpretations admit finite bounds on derivation height. Furthermore, we
demonstrate how to mechanically construct tuple interpretations and how to
orient $\beta$ and $\eta$ reductions within our technique. Finally, we relate
our method to runtime complexity and prove that specific interpretation shapes
imply certain runtime complexity bounds.

21
The categories of this paper are: adap-org
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: stat