Formalizing the Halting Problem in a Constructive Type Theory

Authors:
Kristofer Johannisson
Affiliations:
-
Venue:
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Year:
2000

Citing 3
Cited 0

A Mechanical Proof of the Unsolvability of the Halting Problem

Journal of the ACM (JACM)
Introduction to Mathematical Theory of Computation

Introduction to Mathematical Theory of Computation
Abstract computability on algebraic structures

Proceedings on Algorithms in Modern Mathematics and Computer Science

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Abstract

We present a formalization of the halting problem in Agda, a language based on Martin-L枚f's intuitionistic type theory. The key features are: - We give a constructive proof of the halting problem. The "constructive halting problem" is a natural reformulation of the classic variant. - A new abstract model of computation is introduced, in type theory. - 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.