Extending MKM Formats at the Statement Level

Successful representation and markup languages find a good balance between giving the user freedom of expression, enforcing the fundamental semantic invariants of the modeling framework, and allowing machine support for the underlying semantic structures. MKM formats maintain strong invariants while trying to be foundationally unconstrained, which makes the induced design problem particularly challenging. In this situation, it is standard practice to define a minimal core language together with a scripting/macro facility for syntactic extensions that map into the core language. In practice, such extension facilities are either fully unconstrained (making invariants and machine support difficult) or limited to the object level (keeping the statement and theory levels fixed). In this paper we develop a general methodology for extending MKM representation formats at the statement level. We show the utility (and indeed necessity) of statement-level extension by redesigning the OMDoc format into a minimal, regular core language (strict OMDoc) and an extension (pragmatic OMDoc) that maps into strict OMDoc.