Efficient execution in an automated reasoning environment

Abstract

We describe a method to permit the user of a mathematical logic to write elegant logical definitions while allowing sound and efficient execution. We focus on the ACL2 logic and automated reasoning environment. ACL2 is used by industrial researchers to describe microprocessor designs and other complicated digital systems. Properties of the designs can be formally established with the theorem prover. But because ACL2 is also a functional programming language, the formal models can be executed as simulation engines. We implement features that afford these dual applications, namely formal proof and execution on industrial test suites. In particular, the features allow the user to install, in a logically sound way, alternative executable counterparts for logically-defined functions. These alternatives are often much more efficient than the logically equivalent terms they replace. We discuss several applications of these features.

Data Refinement in Isabelle/HOL

“…ACL2 also seems to provide for data refinement based on invariants [4], but the exact relationship is unclear. In Coq [1], parametrized modules support a form of data refinement [3]: perform your development inside the context of a specification of finite sets (or whatever abstract type you have), and later instantiate the module with some implementation of finite sets that has been proved to satisfy the finite set axioms.…”

“…4 Function Morph p gives us the concrete morphism according to the polarity: Morph + (κ) = Abs κ and Morph − (κ) = rep κ .…”

Code Generation via Higher-Order Rewrite Systems

“…ACL2 allows replacement of subterms at code generation time with other provably equal subterms [5]. Coq also allows replacement of one function by another at code generation time but this is completely unchecked.…”

“…-The language of the theorem prover ACL2 is (almost) a subset of Common Lisp, i.e. the translation is (almost) the identity function [5]. -PVS allows evaluation of ground terms by translation to Common Lisp [4].…”

Mechanized Certification of Secure Hardware Designs

“…ACL2 provides a mechanism, called guards [13] to enable the use of the Common Lisp counterpart only on ground terms where the arguments for each function f are in the intended domain of application of f . ACL2 contains contains several other constructs to support efficient executability, such as (1) single-threaded objects [6], and (2) mbe [9]. Single-threaded objects enable destructive updates to certain data structures in an applicative context.…”