Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First-order natural deduction in Agda   Agda is a dependently-typed functional programming language, based on an
extension of intuitionistic Martin-L\"of type theory. We implement first order
natural deduction in Agda. We use Agda's type checker to verify the correctness
of natural deduction proofs, and also prove properties of natural deduction,
using Agda's proof assistant functionality. This implementation corresponds to
a formalisation of natural deduction in constructive type theory, and the
proofs are verified by Agda to be correct (under the assumption that Agda
itself is correct).

19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio