35 citations · 57 across the 5 of their papers we have counts for
5 papers
Probability functions in the context of signed involutive meadows
Jan A. Bergstra, Alban Ponse
The Kolmogorov axioms for probability functions are placed in the context of signed meadows. A completeness theorem is stated and proven for the resulting equational theory of prob…
An Instruction Sequence Semigroup with Involutive Anti-Automorphisms
Jan A. Bergstra, Alban Ponse
We introduce an algebra of instruction sequences by presenting a semigroup C in which programs can be represented without directional bias: in terms of the next instruction to be e…
Periodic Single-Pass Instruction Sequences
Jan A. Bergstra, Alban Ponse
A program is a finite piece of data that produces a (possibly infinite) sequence of primitive instructions. From scratch we develop a linear notation for sequential, imperative pro…
Differential Meadows
Jan A. Bergstra, Alban Ponse
A meadow is a zero totalised field (0^{-1}=0), and a cancellation meadow is a meadow without proper zero divisors. In this paper we consider differential meadows, i.e., meadows equ…
Cancellation Meadows: a Generic Basis Theorem and Some Applications
Jan A. Bergstra, Inge Bethke, Alban Ponse
Let Q_0 denote the rational numbers expanded to a "meadow", that is, after taking its zero-totalized form (0^{-1}=0) as the preferred interpretation. In this paper we consider "can…