Meadow based Fraction Theory

Preprint English OPEN
Bergstra, Jan A. (2015)
  • Subject: Mathematics - History and Overview
    acm: TheoryofComputation_GENERAL

In the context of an involutive meadow a precise definition of fractions is formulated and on that basis formal definitions of various classes of fractions are given. The definitions follow the fractions as terms paradigm. That paradigm is compared with two competing paradigms for storytelling on fractions: fractions as values and fractions as pairs.
  • References (34)
    34 references, page 1 of 4

    [2] J.A. Bergstra. (2011).

    [3] J.A. Bergstra, I. Bethke. Note on paraconsistency and reasoning about fractions. J. of Applied Non-Classical Logics. http://dx.doi.org/10.1080/11663081.2015.1047232 (2015).

    [4] J.A. Bergstra, Y. Hirshfeld, and J.V. Tucker. Meadows and the equational specification of division. Theoretical Computer Science, 410 (12), 1261-1271 (2009).

    [5] 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).

    [6] J.A. Bergstra and C.A. Middelburg. Inversive meadows and divisive meadows. Journal of Applied Logic, 9(3): 203-220 (2011).

    [7] J.A. Bergstra and C.A. Middelburg. Division by zero in non-involutive meadows. Journal of Applied Logic, 13(1): 1-12 (2015).

    [8] 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).

    [9] J.A. Bergstra and A. Ponse. Fracpairs: fractions over a reduced commutative ring. arXiv:1406.4410 [math.RA], (2014).

    [10] 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).

    [11] J.A. Bergstra and A. Ponse. Poly-infix operators and operator families. arXiv:1505.01087 [math.HO], (2015).

  • Metrics
    No metrics available
Share - Bookmark