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For questions on the formal system in mathematical logic for expressing effective functions, programs and computation, and proofs, using abstract notions of functions and combining them through binding and substitution.
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Univalence and higher inductive types in the lambda calculus model of type theory
In appendix A1 of the homotopy type theory book by the Univalent Foundations Project, the authors give a formal presentation of Martin-Löf type theory in lambda calculus. However, they did not give an …