Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formalizing computability theory via partial recursive functions   We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem
prover formalizing the foundations of computability theory. We use primitive
recursive functions and partial recursive functions as the main objects of
study, and we use a constructive encoding of partial functions such that they
are executable when the programs in question provably halt. Main theorems
include the construction of a universal partial recursive function and a proof
of the undecidability of the halting problem. Type class inference provides a
transparent way to supply G\"{o}del numberings where needed and encapsulate the
encoding details.

25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th