Source-Level Proof Reconstruction for Interactive Theorem Proving

Paulson, Lawrence C.; Susanto, Kong Woei

doi:10.1007/978-3-540-74591-4_18

Cited by 51 publications

(48 citation statements)

References 17 publications

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“…The HOL Light [35] system is probably the first among the existing well-known interactive theorem provers (ITPs) which has integrated and extensively used a general ATP procedure, the MESON tactic [37]. Hurd has developed and benchmarked early bridges [40,41] between HOL and external systems, and his Metis system [42] has also become a significant part of the Isabelle/Sledgehammer bridge to ATPs [61]. Using the very detailed Otter/Ivy [54] proof objects, Harrison also later implemented a bridge from HOL Light to Prover9 [53].…”

Section: Introductionmentioning

confidence: 99%

Learning-Assisted Automated Reasoning with Flyspeck

2014

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The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the Flyspeck proofs, producing an AI system capable of proving a wide range of mathematical conjectures automatically. The performance of this architecture is evaluated in a bootstrapping scenario emulating the development of Flyspeck from axioms to the last theorem, each time using only the previous theorems and proofs. It is shown that 39 % of the 14185 theorems could be proved in a push-button mode (without any high-level advice and user interaction) in 30 seconds of real time on a fourteen-CPU workstation. The necessary work involves: (i) an implementation of sound translations of the HOL Light logic to ATP formalisms: untyped first-order, polymorphic typed first-order, and typed higher-order, (ii) export of the dependency information from HOL Light and ATP proofs for the machine learners, and (iii) choice of suitable representations and methods for learning from previous proofs, and their integration as advisors with HOL Light. This work is described and discussed here, and an initial analysis of the body of proofs that were found fully automatically is provided.

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Section: Introductionmentioning

confidence: 99%

Learning-Assisted Automated Reasoning with Flyspeck

2014

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“…Several approaches have been proposed to integrate new decision procedures in sceptical proof assistants for various theories. First-order provers have been integrated in Isabelle [25], HOL [18] or Coq [9]. These works rely generally on resolution proof trees.…”

Section: Related Workmentioning

confidence: 99%

Modular SMT Proofs for Fast Reflexive Checking Inside Coq

Besson¹,

Cornilleau²,

Pichardie³

2011

Certified Programs and Proofs

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“…2). There are several works on increasing the degree of automation in interactive theorem provers by integrating external automated tools [15,26,14,24,19]. These works have in common that they integrate generic tools like SAT or SMT tools.…”

Section: Related and Future Workmentioning

confidence: 99%

Integrating Automated and Interactive Protocol Verification

Brucker¹,

Mödersheim

2010

Formal Aspects in Security and Trust

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Abstract. A number of current automated protocol verification tools are based on abstract interpretation techniques and other over-approximations of the set of reachable states or traces. The protocol models that these tools employ are shaped by the needs of automated verification and require subtle assumptions. Also, a complex verification tool may suffer from implementation bugs so that in the worst case the tool could accept some incorrect protocols as being correct. These risks of errors are also present, but considerably smaller, when using an LCF-style theorem prover like Isabelle. The interactive security proof, however, requires a lot of expertise and time. We combine the advantages of both worlds by using the representation of the over-approximated search space computed by the automated tools as a "proof idea" in Isabelle. Thus, we devise proof tactics for Isabelle that generate the correctness proof of the protocol from the output of the automated tools. In the worst case, these tactics fail to construct a proof, namely when the representation of the search space is for some reason incorrect. However, when they succeed, the correctness only relies on the basic model and the Isabelle core.

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Source-Level Proof Reconstruction for Interactive Theorem Proving

Cited by 51 publications

References 17 publications

Learning-Assisted Automated Reasoning with Flyspeck

Learning-Assisted Automated Reasoning with Flyspeck

Modular SMT Proofs for Fast Reflexive Checking Inside Coq

Integrating Automated and Interactive Protocol Verification

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