Implementing an Automatic Differentiator in ACL2
نویسندگان
چکیده
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.
منابع مشابه
Automatic Differentiation in ACL2
In this paper, we describe recent improvements to the theory of differentiation that is formalized in ACL2(r). First, we show how the normal rules for the differentiation of composite functions can be introduced in ACL2(r). More important, we show how the application of these rules can be largely automated, so that ACL2(r) can automatically define the derivative of a function that is built from...
متن کاملUsing a Single-Threaded Object to Speed a Verified Graph Pathfinder
We have written hardware simulators in ACL2 in order to unify highspeed simulators and formal analysis models [2, 7]. The techniques used for these simulators extend to other kinds of software, which we demonstrate in this paper by implementing a much faster version of an algorithm for graph path nding previously veri ed by J Moore using ACL2 [5]. This exercise also highlights a weakness in ACL...
متن کاملMatrices in ACL2
This paper describes some initial work on a formalization of matrices in ACL2. The current work is focused on creating an executable implementation that is simple to mechanically reason with and complete enough to be capable of analyzing real problems in linear algebra. A number of basic operations have been defined including matrix addition, transposition and multiplication by a scalar, a vect...
متن کاملMolecular Computation Models in ACL2: a Simulation of Lipton’s Experiment Solving
In this paper we present an ACL2 formalization of a molecular computing model: Adleman’s restricted model [2]. This is a first step to formalize unconventional models of computation in ACL2. As an application of this model, an implementation of Lipton’s experiment solving SAT [7] is described, based on the formalization given in [6]. We use ACL2 to make a formal proof of the completeness and so...
متن کاملPythia: Automatic Generation of Counterexamples for ACL2 using Alloy
A key research problem in automated theorem proving is generating examples and counterexamples to guide the discovery of proofs. We present Pythia, a framework that connects ACL2 with the SAT-based Alloy Analyzer, a tool for solving formulas in first-order logic with transitive closure using bounded exhaustive checking. Pythia takes as inputs an Alloy model of the ACL2 type system together with...
متن کامل