It's a rather traditional type system; the specification is here: http://software.rochus-keller.ch/busy_spec.html. The main advantage are the combination of modularization, types and formal declarations, so that if you make a change in a large build (such as my https://github.com/rochus-keller/LeanQt or https://github.com/rochus-keller/LeanCreator systems) incompatibilites are immediately found by the compiler. Without these features you can never be sure whether all effects were checked.
Which tool did you use to create that busy_spec.html file? They remind me of Engelbart's blue numbering system for documents, if I remember the name correctly.