Abstract |
In this work we present a proof-theoretical justification for the intersection type assignment system (IT) by means of the logical system Intersection Synchronous Logic (ISL). ISL builds classes of equivalent deductions of the implicative and conjunctive fragment of the intuitionistic logic (NJ). ISL results from decomposing intuitionistic conjunction into two connectives: a synchronous conjunction, that can be used only among equivalent deductions of NJ, and an asynchronous one, that can be applied among any sets of deductions of NJ. A term decoration of ISL exists so that it matches both: the IT assignment system, when only the synchronous conjunction is used, and the simple types assignment with pairs and projections, when the asynchronous conjunction is used. Moreover, the proof of strong normalization property for ISL is a simple consequence of the same property in NJ and hence strong normalization for IT comes for free. |
@article{Pimentel+Ronchi+Roversi:2012-FI,
number = {1-4},
volume = {121},
month = {Dicember},
author = {Pimentel, Elaine and {Ronchi della Rocca}, Simonetta and Roversi,
Luca},
url = {http://www.di.unito.it/~rover/RESEARCH/PUBLICATIONS/2012-FI/PimentelRonchiRoversi2012FI.pdf},
abstract = {In this work we present a proof-theoretical justification for the
intersection type assignment system (IT) by means of the logical
system Intersection Synchronous Logic (ISL). ISL builds classes of
equivalent deductions of the implicative and conjunctive fragment
of the intuitionistic logic (NJ). ISL results from decomposing
intuitionistic conjunction into two connectives: a synchronous
conjunction, that can be used only among equivalent deductions of
NJ, and an asynchronous one, that can be applied among any sets of
deductions of NJ. A term decoration of ISL exists so that it
matches both: the IT assignment system, when only the synchronous
conjunction is used, and the simple types assignment with pairs
and projections, when the asynchronous conjunction is used.
Moreover, the proof of strong normalization property for ISL is a
simple consequence of the same property in NJ and hence strong
normalization for IT comes for free.},
title = {Intersection Types from a proof-theoretic perspective},
year = {2012},
pages = {253 --- 274},
journal = {{F}undamenta {I}nformaticae},
}
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