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Encodings of Turing machines in linear logic

Published online by Cambridge University Press:  10 June 2020

James Clift  and
Daniel Murfet Open the ORCID record for Daniel Murfet [Opens in a new window]
James Clift
Affiliation:
Department of Mathematics, University of Melbourne, Melbourne, Australia
Daniel Murfet*
Affiliation:
Department of Mathematics, University of Melbourne, Melbourne, Australia
*
*Corresponding author. Email: d.murfet@unimelb.edu.au
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Abstract

The Sweedler semantics of intuitionistic differential linear logic takes values in the category of vector spaces, using the cofree cocommutative coalgebra to interpret the exponential and primitive elements to interpret the differential structure. In this paper, we explicitly compute the denotations under this semantics of an interesting class of proofs in linear logic, introduced by Girard: the encodings of step functions of Turing machines. Along the way we prove some useful technical results about linear independence of denotations of Church numerals and binary integers.

Keywords

linear logicdifferential linear logicTuring machines
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 30 , Issue 4 , April 2020 , pp. 379 - 415
Copyright
© The Author(s) 2020. Published by Cambridge University Press

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