A Complete Term Rewriting System for Decimal

A Complete Term Rewriting System for Decimal Integer Arithmetic

We present a term rewriting system for decimal integers with addition and subtraction. We prove that the system is connuent and terminating.

Complete term rewrite systems for decimal arithmetic and other total recursive functions

We present a strongly normalising and confluent term rewrite system which describes addition, subtraction, and multiplication of positive and negative integers represented in base 10. We prove a general theorem giving an easily checkable syntactic condition on term rewrite systems which implies strong normalisation. The rewrite system for decimal arithmetic satisfies the condition. The method i...

Number representations and term rewriting

In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and termination in binary and decimal term rewriting systems for both append and tree constructor functions. We find that some of these term rewriting systems are no...

Three Datatype Defining Rewrite Systems for Datatypes of Integers each extending a Datatype of Naturals

Integer arithmetic is specified according to three views: unary, binary, and decimal notation. The binary and decimal view have as their characteristic that each normal form resembles common number notation, that is, either a digit, or a string of digits without leading zero, or the negated versions of the latter. The unary view comprises a specification of integer arithmetic based on 0, succes...

Complete Growth Series of Coxeter Groups with more than Three Generators