Interval Term Rewriting System: Toward A Formal Model for Interval Computation - Carvalho, A.X.; Santiago, R.H.N. (Trends in Computational and Applied Mathematics, 2006)
We present a term rewriting system for interval arithmetic (addition, subtraction and multiplication), toward a mathematical model for interval compu- tation. We start presenting a term rewriting system whose rules (directed equa- tions) perform binary floating-point arithmetic, which is based on IEEE-754 Stan- dard. Next, this primitive system is extended with rules for interval arithmetic. Finally, correctness and termination of our system are both discussed.