Generalized Rewriting in Type Theory

While type theories such as Nuprl are expressive logics for theorem proving, they present diiculties for designers of term rewriting systems. The two most serious diiculties are: 1) They do not provide a global equality. Instead users rewrite over arbitrary user-deened relations. 2) Each rewrite step must be proved valid. In general, these proofs cannot be recursively generated. We have overcome these diiculties and designed a package for the Nuprl system that works well in practice. Our solution is an extensible set of functions for directing and validating relational inferences. The heart of our package is a set of operators that use a user-supplied lemma database to create new rewrites from old ones. These routines place no restrictions on relations; a rewrite's success depends on the strength of the database. Overall, the package allows rewrites to be pieced together in numerous ways, providing the user with a tool to construct sophisticated rewrite strategies.