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Efficient Mendler-Style Lambda-Encodings in Cedille
Book chapter

Efficient Mendler-Style Lambda-Encodings in Cedille

Denis Firsov, Richard Blair and Aaron Stump
Interactive Theorem Proving, pp.235-252
Lecture Notes in Computer Science, Springer International Publishing
07/04/2018
DOI: 10.1007/978-3-319-94821-8_14
url
https://arxiv.org/pdf/1803.02473View
Open Access

Abstract

It is common to model inductive datatypes as least fixed points of functors. We show that within the Cedille type theory we can relax functoriality constraints and generically derive an induction principle for Mendler-style lambda-encoded inductive datatypes, which arise as least fixed points of covariant schemes where the morphism lifting is defined only on identities. Additionally, we implement a destructor for these lambda-encodings that runs in constant-time. As a result, we can define lambda-encoded natural numbers with an induction principle and a constant-time predecessor function so that the normal form of a numeral requires only linear space. The paper also includes several more advanced examples.
Type theory Predecessor function Cedille Induction principle Inductive datatypes Lambda-encodings

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