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The OBJ Family
OBJ refers to the language family, while OBJ2, OBJ3, CafeOBJ, BOBJ, etc. refer to particular members of the family. The OBJ languages are broad spectrum algebraic programming and specification languages, based on order sorted equational logic, possibly enriched with other logics
The Maude System
Maude is a high-performance reflective language and system supporting both equational and rewriting logic specification and programming for a wide range of applications. Maude has been influenced in important ways by the OBJ3 language, which can be regarded as an equational logic sublanguage
CafeOBJ and Maude are sister languages of OBJ and are also currently most advanced executable formal specification language systems. Professor Jose Meseguer is the leader of Maude project
OBJ3
OBJ3 is the last implemented version of OBJ language, and CafeOBJ is considered to be a direct successor to OBJ3

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