<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">José Nuno Oliveira</style></author><author><style face="normal" font="default" size="100%">C. Rodrigues</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Pointfree Factorization of Operation Refinement</style></title><secondary-title><style face="normal" font="default" size="100%">FM - Formal Methods 2006 </style></secondary-title><tertiary-title><style face="normal" font="default" size="100%">LNCS</style></tertiary-title></titles><dates><year><style  face="normal" font="default" size="100%">2006</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer-Verlag</style></publisher><pub-location><style face="normal" font="default" size="100%">Ontario, Canada</style></pub-location><volume><style face="normal" font="default" size="100%">4085</style></volume><pages><style face="normal" font="default" size="100%">236–251</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The standard operation refinement ordering is a kind of “meet of op- posites”: non-determinism reduction suggests “smaller” behaviour while increase of definition suggests “larger” behaviour. Groves’ factorization of this ordering into two simpler relations, one per refinement concern, makes it more mathe- matically tractable but is far from fully exploited in the literature. We present a pointfree theory for this factorization which is more agile and calculational than the standard set-theoretic approach. In particular, we show that factorization leads to a simple proof of structural refinement for arbitrary parametric types and ex- ploit factor instantiation across different subclasses of (relational) operation. The prospect of generalizing the factorization to coalgebraic refinement is discussed.&lt;/p&gt;
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