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Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2018
This paper presents generic derivations of induction for impredicatively typed lambda-encoded datatypes, in the Cedille type theory. Cedille is a pure type theory extending the Curry-style Calculus of Constructions with implicit products, primitive heterogeneous equality, and dependent intersections. All data erase to pure lambda terms, and there is no built-in notion of datatype. The derivations are generic in the sense that we derive induction for any datatype which arises as the least fixeddoi:10.1145/3176245.3167087 fatcat:yoq7hshp6zhpvh2z4iie66hgx4