1. A domain-specific symbolic computing apparatus comprising: first circuitry configured to receive input via an interface; second circuitry configured to generate an input symbol based on the input; third circuitry configured to validate that a value of the input symbol is valid according to a first domain, wherein the first domain is one of a plurality of domains embedded into hardware of the domain-specific symbolic computing apparatus; fourth circuitry configured to generate an output symbol by mapping the input symbol from the first domain to a second domain of the plurality of domains; fifth circuitry configured to generate data based on the output symbol; and sixth circuitry configured to transmit the data to another apparatus.