Abstract

Abstract. We study the set TA of infinite binary trees with nodes labelledinasemiringA 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. 1

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