A framework for defining logics
Journal of the ACM (JACM)
Set theory for verification. I: from foundations to functions
Journal of Automated Reasoning
A New Implementation of Automath
Journal of Automated Reasoning
Verifying and invalidating textbook proofs using scunak
MKM'06 Proceedings of the 5th international conference on Mathematical Knowledge Management
Combining type theory and untyped set theory
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Formal Representation of Mathematics in a Dependently Typed Set Theory
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
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We describe how a set-theoretic foundation for mathematics can be encoded in the new system Scunak. We then discuss an encoding of the construction of functions as functional relations in untyped set theory. Using the dependent type theory of Scunak, we can define object level application and lambda abstraction operators (in the spirit of higher-order abstract syntax) mediating between functions in the (meta-level) type theory and (object-level) functional relations. The encoding has also been exported to Automath and Twelf.