Abstract |
In this work we present a proof-theoretical justification for IT by means of the logical system Intersection Synchronous Logic (ISL). ISL builds equivalence classes of deductions of the implicative and conjunctive fragment of 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 |
@unpublished{Pim+Ron+Rov:ITRS08,
month = {March},
url = {http://www.di.unito.it/~rover/RESEARCH/PUBLICATIONS/2008-ITRS/PMR-ITRS08.pdf},
abstract = {In this work we present a proof-theoretical justification for IT
by means of the logical system Intersection Synchronous Logic
(ISL). ISL builds equivalence classes of deductions of the
implicative and conjunctive fragment of 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 = {{I}ntersection {T}ypes from a proof-theoretic perspective},
author = {Pimentel, E. and Ronchi Della Rocca, S. and Roversi, L.},
note = {Presented at the 4th Workshop on Intersection Types and Related
Systems (ITRS '08) -- Torino (Italy)},
year = {2008},
}
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