Abstract

This case study shows how non-ACL2 programs can be combined with ACL2 functions in such a way that useful properties can be proved about the composite programs. Nothing is proved about the non-ACL2 programs. Instead, the results of the non-ACL2 programs are checked at run time by ACL2 functions, and properties of these checker functions are proved. The application is resolution/paramodulation automated theorem proving for first-order logic. The top ACL2 function takes a conjecture, preprocesses the conjecture, and calls a non-ACL2 program to search for a proof or countermodel. If the non-ACL2 program succeeds, ACL2 functions check the proof or countermodel. The top ACL2 function is proved sound with respect to finite interpretations. Introduction Our ACL2 project arose from a different kind of automated theorem proving. We work with fully automatic resolution/paramodulation theo- This work was supported by the Mathematical, Information, and Computational Sciences Division subprogram...

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