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The calculus of dependent lambda eliminations*

Part of: JFP Research Articles

Published online by Cambridge University Press:  09 May 2017

AARON STUMP
AARON STUMP*
Affiliation:
Computer Science, The University of Iowa, Iowa City, IA, USA (e-mail: astump@acm.org)

Abstract

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Modern constructive type theory is based on pure dependently typed lambda calculus, augmented with user-defined datatypes. This paper presents an alternative called the Calculus of Dependent Lambda Eliminations, based on pure lambda encodings with no auxiliary datatype system. New typing constructs are defined that enable induction, as well as large eliminations with lambda encodings. These constructs are constructor-constrained recursive types, and a lifting operation to lift simply typed terms to the type level. Using a lattice-theoretic denotational semantics for types, the language is proved logically consistent. The power of CDLE is demonstrated through several examples, which have been checked with a prototype implementation called Cedille.

Information

Type
Articles
Information
Journal of Functional Programming , Volume 27 , 2017 , e14
Copyright
Copyright © Cambridge University Press 2017 

Footnotes

*

I gratefully acknowledge NSF support of this project under award 1524519, and DoD support under award FA9550-16-1-0082 (MURI program).

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