Wireless systems are expanding their purposes, from merely connecting humans and things to connecting intelligence and opportunistically sensing of the environment through radio-frequency signals. In this paper, we introduce the concept of triple-functional networks in which the same infrastructure and resources are shared for integrated sensing, communications, and (edge) Artificial Intelligence (AI) inference. This concept opens up several opportunities, such as devising non-orthogonal resource deployment and power consumption to concurrently update multiple services, but also challenges related to resource management and signaling cross-talk, among others. The core idea of this work is that computation-related aspects, including computing resources and AI models availability, should be explicitly considered when taking resource allocation decisions, to address the conflicting goals of the services coexistence. After showing the natural coupling between theoretical performance bounds of the three services, we formulate a service coexistence optimization problem that is solved optimally, and showcase the advantages against a disjoint allocation strategy.