Programming and automating mathematics in the Tarski–Kleene hierarchy

Alasdair Armstrong, Georg Struth, Tjark Weber
<span title="">2014</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/75odiq25o5gtzcy4h7mdcztb5y" style="color: black;">Journal of Logical and Algebraic Methods in Programming</a> </i> &nbsp;
We present examples from a reference implementation of variants of Kleene algebras and Tarski's relation algebras in the theorem proving environment Isabelle/HOL. For Kleene algebras we show how models can be programmed, including sets of traces and paths, languages, binary relations, max-plus and min-plus algebra, matrices, formal power series. For relation algebras we discuss primarily proof automation in a comprehensive library and present an advanced formalisation example.
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