To make progress toward their vision (and or goal), all organizations require processes. "A process is a set of activities, ordered or structured to achieve a goal." One key contribution by Adam Smith's An Inquiry into the Nature and Causes of the Wealth of Nations, generally referred to by the short title The Wealth of Nations from the first chapter of book 1, is a model of process; the example he uses is of the production of pins to demonstrate that separating activities within a process streamlines the process, greatly increase the quality of the product produced while at the same time increasing the throughput of the process (This is one of the taproots of the assembly line and mass production). So the process must align with the organization's mission and strategies. This is the functional interface between process and control in the IDEF0 model.
As Adam Smith noted in his pin example, mechanisms or the tools that enable and support the process are process multipliers. The military considers tools, like 16" artillery pieces on Battleships--known as "Convincers"--to be force multipliers; they are tools of the process known as war. In the construction industry, the Steam Shovel replaced any number of laborers with picks and shovels, greatly multiplying the through of the digging process. And, in the "Information Age" computers initially enhanced the finance and accounting functions of the organization and has transformed nearly all financial transaction management, as witnesses by the speed and sheer throughput on Wall Street and other major markets globally.
While in Adam Smith's time, tools (mechanisms) only enabled and supported some of the processes, with the coming of automation and data networks (e.g., the Internet for one) tools have started to enable and support both the process and the control of the organization. Likewise, the choices made by management with regard to resources and policy, and the requirements of the processes directly affect the optimality of the investment in tools--which are the other interfaces in the IDEF0 model.