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Pure type systems with explicit substitutions

Part of: JFP Research Articles

Published online by Cambridge University Press:  09 November 2015

DANIEL FRIDLENDER  and
MIGUEL PAGANO
DANIEL FRIDLENDER
Affiliation:
FaMAF, Universidad Nacional de Córdoba, Córdoba, Argentina (e-mail: fridlend@famaf.unc.edu.ar, pagano@famaf.unc.edu.ar)
MIGUEL PAGANO
Affiliation:
FaMAF, Universidad Nacional de Córdoba, Córdoba, Argentina (e-mail: fridlend@famaf.unc.edu.ar, pagano@famaf.unc.edu.ar)
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Abstract

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We introduce a new formulation of pure type systems (PTSs) with explicit substitution and de Bruijn indices and formally prove some of its meta-theory. Using techniques based on Normalisation by Evaluation, we prove that untyped conversion can be typed for predicative PTSs. Although this equivalence was settled by Siles and Herbelin for the conventional presentation of PTSs, we strongly conjecture that our proof method can also be applied to PTSs with η.

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Journal of Functional Programming , Volume 25 , 2015 , e19
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Copyright © Cambridge University Press 2015 

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