Theoretical Computer Science
Theorem Proving via General Matings
Journal of the ACM (JACM)
Focusing and polarization in linear, intuitionistic, and classical logics
Theoretical Computer Science
Embedding pure type systems in the lambda-pi-calculus modulo
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
The open theory standard theory library
NFM'11 Proceedings of the Third international conference on NASA Formal methods
Least and Greatest Fixed Points in Linear Logic
ACM Transactions on Computational Logic (TOCL)
A proposal for broad spectrum proof certificates
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
A modular integration of SAT/SMT solvers to coq through proof witnesses
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Programming with Higher-Order Logic
Programming with Higher-Order Logic
LFP: a logical framework with external predicates
Proceedings of the seventh international workshop on Logical frameworks and meta-languages, theory and practice
Foundational proof certificates: making proof universal and permanent
Proceedings of the Eighth ACM SIGPLAN international workshop on Logical frameworks & meta-languages: theory & practice
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It is the exception that provers share and trust each others proofs. One reason for this is that different provers structure their proof evidence in remarkably different ways, including, for example, proof scripts, resolution refutations, tableaux, Herbrand expansions, natural deductions, etc. In this paper, we propose an approach to foundational proof certificates as a means of flexibly presenting proof evidence so that a relatively simple and universal proof checker can check that a certificate does, indeed, elaborate to a formal proof. While we shall limit ourselves to first-order logic in this paper, we shall not limit ourselves in many other ways. Our framework for defining and checking proof certificates will work with classical and intuitionistic logics and with proof structures as diverse as resolution refutations, matings, and natural deduction.