Algorithms for Equality and Unification in the Presence of Notational Definitions

Notational definitions are pervasive in mathematical practice and are therefore supported in most automated theorem proving systems such as Coq [B+98], PVS [ORS92], Lego [LP92], or Isabelle [Pau94]. Semantically, notational definitions are transparent, that is, one obtains the meaning of an expression by interpreting the result of expanding all definitions. Pragmatically, however, expanding all definitions as they are encountered is unsatisfactory, since it can be computationally expensive and complicate the user interface.

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