Tinderbox has a powerful internal scripting system (‘action code’), albeit not designed as a programming environment but rather for supporting real world use of the app. Over time, these have included HTML export, daybook, research data collection/analysis (primarily textual rather than mathematical), authoring books, system analysis plus there seems a healthy number people doing GTD and other todo-type tasks. Scrivener and DEVONThink seem popular in use alongside Tinderbox. Tinderbox’s map view is popular as being a powerful tool in investigating unstructured data. There seem to be a fair few programmers who are users, who may hopefully chip in here on their use of Tinderbox.
Tinderbox has powerful inheritance and supports incremental formalisation in a way that aids discovery and doesn’t force premature formalisation.
Besides internal action code, Tinderbox offers a fairly powerful export system allowing generation and export of a number of formats beside the original HTML export purpose. Besides the basic generic app support of AppleScript, Tinderbox does not have specific in-app AppleScript support.
Probably the largest single listing of data about the above is aTbRef (disclaimer: I’m the author). The website is generated entirely from a single TBX file. You can also download the TBX itself to see how that all works. If you browse through the listing of action code operators, you should get a feel for what’s possible.