Maximilian Wuttke: Bachelor's Thesis

Saarland University Computer Science

Formalising Multi-Tape Turing Machines in Coq

Advisor: Yannick Forster

Abstract

We give a formalisation of multi-tape Turing machines in the proof assistant Coq. We make it concrete what it means that a machine is correct by using correctness relations following Asperti and Ricciotti. We implement basic machines and introduce building patterns like sequential composition, if-then-else, do-while, and match that can be used to easily build compound machines. Transformation operations can add new tapes or symbols, or can mirror the behaviour of a machine.
We introduce a class of encoding predicates to define what it means that a tape encodes a value of an encodable type. Using that class of predicates we define correctness relations to make it precise what it means that a machine computes a function.
We define machines that do pattern matching over lists, tuples, sum types, and natural numbers; and machines which can construct new values. We show that these machines can be used to define and prove correctness and termination of machines that compute addition and multiplication.

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Maximilian Wuttke, Tue Apr 17 22:08:04 2018