<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Alexandra Silva</style></author><author><style face="normal" font="default" size="100%">Jan Rutten</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Behavioural differential equations and coinduction for binary trees</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the Workshop on Logic, Language, Information and Computation 2007 (WoLLIC 2007)</style></secondary-title><tertiary-title><style face="normal" font="default" size="100%">Lecture Notes in Computer Science</style></tertiary-title></titles><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">July</style></date></pub-dates></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://haslab.uminho.pt/sites/default/files/xana/files/wollic2007.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">Springer</style></publisher><pub-location><style face="normal" font="default" size="100%">Rio de Janeiro, Brazil</style></pub-location><volume><style face="normal" font="default" size="100%">4576</style></volume><pages><style face="normal" font="default" size="100%">322 – 336</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study the set TA of infinite binary trees with nodes labelled in a semiring A from a coalgebraic perspective. We present coinductive definition and proof principles based on the fact that TA carries a final coalgebra structure. By viewing trees as formal power series, we develop a calculus where definitions are presented as behavioural differential equations. We present a general format for these equations that guarantees the existence and uniqueness of solutions. Although technically not very difficult, the resulting framework has surprisingly nice applications, which is illustrated by various concrete examples.&lt;/p&gt;
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