How Much Are Your Geraniums? Taking Graph Conditions Beyond First Order

Abstract

Previous work has shown how first-order logic can equivalently be expressed through nested graph conditions, also called condition trees, with surprisingly few ingredients. In this paper, we extend condition trees by adding set-based operators such as sums and products, calculated over operands that are themselves characterised by first-order logic formulas. This provides a greatly improved way to specify computations such as: given that the price of a geranium plant equals 2 per flower petal, return the average price of all geraniums with at least one flower .We claim the same level of expressive equivalence as before between (extended) condition trees and a certain class of logic formulas; we show that the latter go beyond what can be expressed in first-order logic.On the practical side, we evaluate the performance and usability of set-based operators by specifying and comparing the example geranium property, with and without set-based operators, in the graph transformation tool groove.1 Ehrig was also a leading researcher in algebraic data specification, i.e. [7]; in that capacity he was one of the founders of ACT-ONE, the data type specification language of LOTOS, the standardisation of which in [20] was one of Ed Brinksma's early scientific achievements.