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arXiv · 1811.11961

Course-of-Value Induction in Cedille

Denis Firsov·Larry Diehl·Christopher Jenkins·Aaron Stump
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Abstract

In the categorical setting, histomorphisms model a course-of-value recursion scheme that allows functions to be defined using arbitrary previously computed values. In this paper, we use the Calculus of Dependent Lambda Eliminations (CDLE) to derive a lambda-encoding of inductive datatypes that admits course-of-value induction. Similar to course-of-value recursion, course-of-value induction gives access to inductive hypotheses at arbitrary depth of the inductive arguments of a function. We show that the derived course-of-value datatypes are well-behaved by proving Lambek's lemma and characterizing the computational behavior of the induction principle. Our work is formalized in the Cedille programming language and also includes several examples of course-of-value functions.

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Denis Firsov, Larry Diehl, Christopher Jenkins, Aaron Stump. 2018-11-29. Course-of-Value Induction in Cedille. https://arxiv.org/abs/1811.11961

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