SYMEVAL: A theorem prover based on the experimental logic

Abstract

SYMEVAL is a theorem prover which is based on a rather simple, yet effective principle about deduction, namely that deduction is fundamentally a process of replacing expressions by logically equivalent simpler expressions. To facilitate this principle, an experimental logic called Symmetric Logic has been developed. The symmetric logic is a collection of rewrite rules regarding propositional and quantificational logic, equality and abstraction logic. The deduction process is implicitly controlled by the way the rewrite rules of the system are constructed. In particular, quantification rules of the symmetric logic are designed so as to reduce the scope of quantifiers in order to eliminate them. [Brown1] gives a detailed description of the symmetric logic, the theorem prover SYMEVAL, the user interface and some example runs. S~WIEVAL is implemented in Zetalisp on a Symbolics lisp machine.