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\title{A Hoare Logic for Diverging Programs}
\author{Johannes \AA{}man Pojhola, Magnus O. Myreen, Miki Tanaka}
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\begin{abstract}

  This submission contains:
  (1) a formalisation of a small While language with support for output;
  (2) a standard total-correctness Hoare logic that has been proved sound and complete; and
  (3) a new Hoare logic for proofs about programs that diverge: this new logic has also been proved sound and complete.

\end{abstract}

\section*{Background}

The theories in this submission are a port of
\href{https://github.com/HOL-Theorem-Prover/HOL/tree/develop/examples/Hoare-for-divergence}{a similar formalisation in HOL4},
which, in turn, is a simplified version of a program logic for nonterminating CakeML programs~\cite{ITP19} (which was not complete).

The HOL4 version of these theories was developed by Myreen with some lemmas proved by \AA{}man Pojhola.
The Isabelle/HOL theories were developed by Tanaka with some input from \AA{}man Pojhola.

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