Implementing an Automatic Differentiator in ACL2

TL;DR

This paper presents an automated macro in ACL2 that simplifies the process of formalizing derivatives of functions, integrating differentiation rules and inverse functions to enhance proof automation.

Contribution

We developed a macro in ACL2 that automates the formalization of derivatives, streamlining the application of differentiation rules and handling inverse functions.

Findings

The macro automates derivative calculations in ACL2.

It integrates with existing ACL2 facilities for inverse functions.

Automation reduces manual effort in formal proofs of derivatives.

Abstract

The foundational theory of differentiation was developed as part of the original release of ACL2(r). In work reported at the last ACL2 Workshop, we presented theorems justifying the usual differentiation rules, including the chain rule and the derivative of inverse functions. However, the process of applying these theorems to formalize the derivative of a particular function is completely manual. More recently, we developed a macro and supporting functions that can automate this process. This macro uses the ACL2 table facility to keep track of functions and their derivatives, and it also interacts with the macro that introduces inverse functions in ACL2(r), so that their derivatives can also be automated. In this paper, we present the implementation of this macro and related functions.