A formula system can transform a formula natural language representation (“NLR”) into a representation which shows the formula in traditional mathematical notation. This transformation can include creating a state machine with transition mappings between states that match to initial parts of the NLR. These transition mappings can include global transition mappings that are first attempted to be matched to the beginning of the NLR and then state specific transition mappings can be matched to the NLR. The formula system can consume the NLR, transitioning from state to state as indicated by the transition mappings and removing the matched initial part from the NLR, until the NLR has been fully consumed. In some cases, the formula system can recursively or iteratively create additional state machines to consume portions of the NLR. Some states provide a result (e.g. portion of a formula representation) which are combined to create the final formula representation.