Generic derivation of induction for impredicative encodings in Cedille

Denis Firsov, Aaron Stump
2018 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 fixed
more » ... oint of a signature functor. We consider Church-style and Mendler-style lambda-encodings. Moreover, the isomorphism of these encodings is proved. Also, we formalize Lambek's lemma as a consequence of expected laws of cancellation, reflection, and fusion.
doi:10.1145/3176245.3167087 fatcat:yoq7hshp6zhpvh2z4iie66hgx4