Second-Order Functions and Theorems in ACL2

• Main Author: Alessandro Coglio
• Format: Article
• Language: English
• Published: Open Publishing Association 2015-09-01
• Series: Electronic Proceedings in Theoretical Computer Science
• Online Access: http://arxiv.org/pdf/1509.06080v1

SOFT ('Second-Order Functions and Theorems') is a tool to mimic second-order functions and theorems in the first-order logic of ACL2. Second-order functions are mimicked by first-order functions that reference explicitly designated uninterpreted functions that mimic function variables. First-order theorems over these second-order functions mimic second-order theorems universally quantified over function variables. Instances of second-order functions and theorems are systematically generated by replacing function variables with functions. SOFT can be used to carry out program refinement inside ACL2, by constructing a sequence of increasingly stronger second-order predicates over one or more target functions: the sequence starts with a predicate that specifies requirements for the target functions, and ends with a predicate that provides executable definitions for the target functions.