4 citations · 23 across the 11 of their papers we have counts for
12 papers
Universality of Univariate Mixed Fractions in Divisive Meadows
Jan A. Bergstra, Inge Bethke, Dimitri Hendriks
Univariate fractions can be transformed to mixed fractions in the equational theory of meadows of characteristic zero.
A negative result on algebraic specifications of the meadow of rational numbers
Jan A. Bergstra, Inge Bethke
- the involutive meadow of the rational numbers - is the field of the rational numbers where the multiplicative inverse operation is made total by imposing $0^{-1}=0…
Note on paraconsistency and reasoning about fractions
Jan A. Bergstra, Inge Bethke
We apply a paraconsistent logic to reason about fractions.
Equations for formally real meadows
Jan A. Bergstra, Inge Bethke, Alban Ponse
We consider the signatures of meadows and of signed meadows. We give two complete axiomatizations of the equational theories of…
On the contribution of backward jumps to instruction sequence expressiveness
Jan A. Bergstra, Inge Bethke
We investigate the expressiveness of backward jumps in a framework of formalized sequential programming called program algebra. We show that - if expressiveness is measured in term…
Straight-line instruction sequence completeness for total calculation on cancellation meadows
Jan A. Bergstra, Inge Bethke
A combination of program algebra with the theory of meadows is designed leading to a theory of computation in algebraic structures which use in addition to a zero test and copying…