# Algorithmic Eta-reduction in Type-theory of Acyclic Recursion

### Roussanka Loukanova

#### Abstract

The paper extends the standard reduction calculus of the higher-order Type-theory of Acyclic Recursion to Î·-reduction. This is achieved by adding a restricted Î·-rule, which is applicable only to terms in canonical forms satisfying certain conditions. Canonical forms of terms determine the iterative algorithms for computing the semantic denotations of the terms. Unnecessary Î»-abstractions and corresponding functional applications in canonical forms contribute to algorithmic complexity. The Î·-rule provides a simple way to reduce complexity by maintenance of essential algorithmic structure of computations.

Download#### Paper Citation

#### in Harvard Style

Loukanova R. (2020). **Algorithmic Eta-reduction in Type-theory of Acyclic Recursion**.In *Proceedings of the 12th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,* ISBN 978-989-758-395-7, pages 1003-1010. DOI: 10.5220/0009182410031010

#### in Bibtex Style

@conference{icaart20,

author={Roussanka Loukanova},

title={Algorithmic Eta-reduction in Type-theory of Acyclic Recursion},

booktitle={Proceedings of the 12th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},

year={2020},

pages={1003-1010},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0009182410031010},

isbn={978-989-758-395-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 12th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,

TI - Algorithmic Eta-reduction in Type-theory of Acyclic Recursion

SN - 978-989-758-395-7

AU - Loukanova R.

PY - 2020

SP - 1003

EP - 1010

DO - 10.5220/0009182410031010