Abstract
We present a formalization of the halting problem in Agda, a language based on Martin-Löf’s intuitionistic type theory. The key features are:
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We give a constructive proof of the halting problem. The “constructive halting problem” is a natural reformulation of the classic variant.
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A new abstract model of computation is introduced, in type theory.
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The undecidability of the halting problem is proved via a theorem similar to Rice’s theorem.
The central idea of the formalization is to abstract from the details of specific models of computation. This is accomplished by formulating a number of axioms which describe an abstract model of computation, and proving that the halting problem is undecidable in any model described by these axioms.
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Johannisson, K. (2002). Formalizing the Halting Problem in a Constructive Type Theory. In: Callaghan, P., Luo, Z., McKinna, J., Pollack, R., Pollack, R. (eds) Types for Proofs and Programs. TYPES 2000. Lecture Notes in Computer Science, vol 2277. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45842-5_10
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DOI: https://doi.org/10.1007/3-540-45842-5_10
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