2OBJ: a metalogical framework theroem prover based on equational logic

This paper describes 2OBJ, a tactic-based generic theorem prover that encodes object logics into equational logic via an abstract data type of object logic sentences and proofs. 2OBJ is built upon OBJ3, a term rewriting implementation of (order sorted conditional) equational logic. Because object logic proofs are explicitly represented, 2OBJ can not only reason with them, but also about them, as in arguments by symmetry and other metalogical devices of ordinary mathematics; this motivates the 'meta’ of ‘metalogical’ in the title. First-order equational logic has advantages in simplicity and efficiency over more complex framework logics, such as intuitionistic higher-order type theory, and also facilitates the definition of tactic languages. In addition, 2OBJ benefits from OBJ3’s powerful parametrized module system, and it has a convenient X window user interface. The paper concludes with a sketch of some semantic foundations based upon ruled parchments, charters, and institutions.