General Theory and Tools for Proving Algorithms in Nominative Data Systems

• Published in: Formalized mathematics Vol. 28; no. 4; pp. 269 - 278
• Main Author: Jaszczak, Adrian
• Format: Journal Article
• Language: English
• Published: Bialystok Sciendo 01.12.2020; De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
• Subjects: 03B70; 68Q60; 68V20; inference rules; nominative data; program verification
• ISSN: 1898-9934; 1426-2630; 1898-9934
• DOI: 10.2478/forma-2020-0024

In this paper we introduce some new definitions for sequences of operations and extract general theorems about properties of iterative algorithms encoded in nominative data language [20] in the Mizar system [3], [1] in order to simplify the process of proving algorithms in the future. This paper continues verification of algorithms [10], [13], [12], [14] written in terms of simple-named complex-valued nominative data [6], [8], [18], [11], [15], [16]. The validity of the algorithm is presented in terms of semantic Floyd-Hoare triples over such data [9]. Proofs of the correctness are based on an inference system for an extended Floyd-Hoare logic [2], [4] with partial pre- and postconditions [17], [19], [7], [5].