A Weakly Initial Algebra for Higher-Order Abstract Syntax in Cedille

Aaron Stump
(The University of Iowa)

Cedille is a relatively recent tool based on a Curry-style pure type theory, without a primitive datatype system. Using novel techniques based on dependent intersection types, inductive datatypes with their induction principles are derived. One benefit of this approach is that it allows exploration of new or advanced forms of inductive datatypes. This paper reports work in progress on one such form, namely higher-order abstract syntax (HOAS). We consider the nature of HOAS in the setting of pure type theory, comparing with the traditional concept of environment models for lambda calculus. We see an alternative, based on what we term Kripke function-spaces, for which we can derive a weakly initial algebra in Cedille. Several examples are given using the encoding.

In Dale Miller and Ivan Scagnetto: Proceedings of the Fourteenth Workshop on Logical Frameworks and Meta-Languages: Theory and Practice (LFMTP 2019), Vancouver, Canada, 22nd June 2019, Electronic Proceedings in Theoretical Computer Science 307, pp. 55–67.
Published: 12th October 2019.

ArXived at: http://dx.doi.org/10.4204/EPTCS.307.6 bibtex PDF
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