Abstract
In this paper, we propose a new software design of an online judge system for interactive theorem proving. The distinctive feature of this architecture is that our online judge system is distributed on the network and especially involves volunteer computing. In volunteers' computers, network bots (software robots) are executed and donate computational resources to the central host of the online judge system. Our proposed design improves fault tolerance and security. We gave an implementation to two different styles of interactive theorem prover, Coq and ACL2, and evaluated our proposed architecture. From the experiment on the implementation, we concluded that our architecture is efficient enough to be used practically.
Highlights
1.1 A New Style of Distributed Computation, Volunteer computing Volunteer computing is a type of distributed computing in which computer owners (“volunteers”) donate their computing resources to projects
Volunteer computing systems must deal with problems related to correctness: z We cannot predict the number of volunteers and the volunteers are essentially anonymous; z Some volunteer computers are possibly overclocked and they occasionally do not work well and return incorrect results; z Some volunteers can intentionally return incorrect results
We propose a new design of an online judge system for interactive theorem proving in the style of
Summary
1.1 A New Style of Distributed Computation, Volunteer computing Volunteer computing is a type of distributed computing in which computer owners (“volunteers”) donate their computing resources to projects. 1.2 Interactive Theorem Provers An interactive theorem prover is a software system which assists in developing formal proofs through humanmachine collaboration. Interactive theorem provers provide automatic assistance for rigorous reasoning in such formal systems. The formal reasoning and proving process on the interactive theorem provers shed light on ambiguity in standard mathematics. The interactive theorem prover Coq is based on a higher-order type system with inductive definitions, Calculus of Inductive Constructions, which is powerful enough to describe definitions and proofs in mathematics and computer science. A proof of associativity of the list concatenation is written in Coq as follows The claim is automatically proved as (defthm triple-rev (equal (rev(rev(rev x))) (rev x)))
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