Formalizing computability theory via partial recursive functions

Mario Carneiro

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arXiv · 1810.08380

Formalizing computability theory via partial recursive functions

Mario Carneiro

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Abstract

We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and we use a constructive encoding of partial functions such that they are executable when the programs in question provably halt. Main theorems include the construction of a universal partial recursive function and a proof of the undecidability of the halting problem. Type class inference provides a transparent way to supply G\"{o}del numberings where needed and encapsulate the encoding details.

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Mario Carneiro. 2018-10-19. Formalizing computability theory via partial recursive functions. https://arxiv.org/abs/1810.08380

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