Term-Level Reasoning in Support of Bit-blasting

Abstract: GL is a verified tool for proving ACL2 theorems using Boolean methods such as BDD reasoning and satisfiability checking. In its typical operation, GL recursively traverses a term, computing a symbolic object representing the value of each subterm. In older versions of GL, such a symbolic object could use Boolean functions to compactly represent many possible values for integer and Boolean subfields, but otherwise needed to reflect the concrete structure of all possiblealues that its term might take. When a term has many possible values that can't share such a representation, this can easily cause blowups because GL must then case-split. To address this problem, we have added several features to GL that allow it to reason about term-like symbolic objects using various forms of rewriting. These features allow GL to be programmed with rules much like the ACL2 rewriter, so that users may choose a better normal form for terms for which the default, value-like representation would otherwise cause case explosions. In this paper we describe these new features; as a motivating example, we show how to program the rewriter to reason effectively about the theory of records.