In this paper, a new formulation of the central ideas of the well-established theory of Boden about creativity is presented. This new formulation redefines some terms and reviews the formal mechanisms of exploratory and transformational creativity. The presented approach is based on the conceptual space proposed by Boden and formalized by other authors in a way that facilitates the implementation of these mechanisms. The presented formulation is applied to a the real case of creative designing in which a new combination of chocolate and fruit is desired. The experimentation has been conducted jointly with a Spanish chocolate chef. Data collected from the chef has been used to validate the proposed system. Experimental results show that the formulation presented is not only useful for understanding how the creative mechanisms of design works, but also facilitates its implementation in real cases to support creativity processes.