An Implementation Kernel for Theorem Proving with Equality Clauses

keywords: Automated theorem proving, rst-order clauses with equality. Abstract We provide a standard abstract architecture around which high-performance theorem provers for full clausal logic with equality can be built. A WAM-like heap structure for storing terms (as DAG's, with structure sharing) and several substitution trees Gra95b] are central in the architecture. These two data structures turn out to be surprisingly well combinable due to conceptual similarities. Indexing techniques based on substitution trees outperform previous methods, and are integrated in such a way that e.g. no writing on the heap is needed during (many-to-one) term uniication. Static clause (sub)sets can be compiled in this framework into eecient abstract machine code for inference computation and redundancy proving. Finally, as an example, a toy equational completion system based on the framework is described.