In this paper, aimed at dependently typed programmers, we present a novel connection between automated and interactive theorem proving paradigms. The novelty is that the connection offers a better trade-off between usability, efficiency and soundness when compared to existing techniques. This technique allows for a powerful interactive proof framework that facilitates efficient verification of finite domain theorems and guided construction of the proof of infinite domain theorems. Such situations typically occur with industrial verification. As a case study, an embedding of SAT and CTL model checking is presented, both of which have been implemented for the dependently typed proof assistant Agda. Finally, an example of a real world railway control system is presented, and shown using our proof framework to be safe with respect to an abstract model of trains not colliding or derailing. We demonstrate how to formulate safety directly and show using interactive theorem proving that signalling principles imply safety. Therefore, a proof by an automated theorem prover that the signalling principles hold for a concrete system implies the overall safety. Therefore, instead of the need for domain experts to validate that the signalling principles imply safety they only need to make sure that the safety is formulated correctly. Therefore, some of the validation is replaced by verification using interactive theorem proving.

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The Decision Problem for Exponential Diophantine Equations

A light-weight integration of automated and interactive theorem proving

/pdf/a-binomial-representation-of-the-3x-1-problem-qhrjqgurox.pdf

A binomial representation of the 3x + 1 problem

Diophantine representations of the sequence of solutions of the Pell equation

CrystalBall: Gazing in the Black Box of SAT Solving.

This is a survey of a century long history of interplay between Hilbert's tenth problem (about solvability of Diophantine equations) and different notions and ideas from the Computability Theory.

The Decision Problem for Exponential Diophantine Equations

Citations

A light-weight integration of automated and interactive theorem proving

A binomial representation of the 3x + 1 problem

Diophantine representations of the sequence of solutions of the Pell equation

CrystalBall: Gazing in the Black Box of SAT Solving.

Hilbert's tenth problem and paradigms of computation

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