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Generic derivation of induction for impredicative encodings in Cedille
Conference proceeding   Open access

Generic derivation of induction for impredicative encodings in Cedille

Denis Firsov and Aaron Stump
Proceedings of the 7th ACM SIGPLAN International Conference on certified programs and proofs, Vol.2018-, pp.215-227
CPP 2018
01/08/2018
DOI: 10.1145/3167087
url
https://doi.org/10.1145/3167087View
Published (Version of record) Open Access

Abstract

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 point 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.
Cedille datatypes impredicativity induction lambda encodings

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