Fracterms are introduced as a proxy for fractions. A precise definition of fracterms is formulated and on that basis reasonably precise definitions of various classes of fracterms are given. In the context of the meadow of rational numbers viewing fractions as fracterms... View more
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 J.A. Bergstra, Y. Hirshfeld, and J.V. Tucker. Meadows and the equational specification of division. Theoretical Computer Science, 410 (12), 1261-1271 (2009).
 J. A. Bergstra, I. Bethke, and A. Ponse. Cancellation meadows: a generic basis theorem and some applications. The Computer Journal, 56(1): 3-14, doi:10.1093/comjnl/bsx147 (2013).
 J.A. Bergstra and C.A. Middelburg. Inversive meadows and divisive meadows. Journal of Applied Logic, 9(3): 203-220 (2011).
 J.A. Bergstra and C.A. Middelburg. Division by zero in non-involutive meadows. Journal of Applied Logic, 13(1): 1-12 (2015).
 J.A. Bergstra and A. Ponse. Division by zero in common meadows. In R. de Nicola and R. Hennicker (editors), Software, Services, and Systems (Wirsing Festschrift), LNCS 8950, pages 46-61, Springer, 2015. Also available at arXiv:1406.6878v2 [math.RA], (2015).
 J.A. Bergstra and A. Ponse. Fracpairs: fractions over a reduced commutative ring. arXiv:1406.4410 [math.RA], (2014).
 J.A. Bergstra and A. Ponse. Three datatype defining rewrite systems for datatypes of integers each extending a datatype of naturals. arXiv:1406.3280 [math.LO], (2014).
 J.A. Bergstra and A. Ponse. Poly-infix operators and operator families. arXiv:1505.01087 [math.HO], (2015).