Abstract
We formalise results from computability theory in the theorem prover Isabelle/HOL. Following the textbook by Boolos et al, we formalise Turing machines and relate them to abacus machines and recursive functions. We “tie the know” between these three computational models by formalising a universal function and obtaining from it a universal Turing machine by our verified translation from recursive functions to abacus programs and from abacus programs to Turing machine programs. Hoare-style reasoning techniques allow us to reason about concrete Turing machine and abacus programs.
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Xu, J., Zhang, X., Urban, C. (2013). Mechanising Turing Machines and Computability Theory in Isabelle/HOL. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds) Interactive Theorem Proving. ITP 2013. Lecture Notes in Computer Science, vol 7998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39634-2_13
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DOI: https://doi.org/10.1007/978-3-642-39634-2_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39633-5
Online ISBN: 978-3-642-39634-2
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