Tuplix Calculus

Abstract

We introduce a calculus for tuplices, which are expressions that generalize matrices and vectors. Tuplices have an underlying data type for quantities that are taken from a zero-totalized field. We start with the core tuplix calculus CTC for entries and tests, which are combined using conjunctive composition. We define a standard model and prove that CTC is relatively complete with respect to it. The core calculus is extended with operators for choice, information hiding, scalar multiplication, clearing and encapsulation. We provide two examples of applications; one on incremental financial budgeting, and one on modular financial budget design. * Thanks are due to Sanne Nolst Trenité (UvA, Faculty of Science) for many discussions and for helping to clarify the usefulness and necessity of formalization in budget calculations.

Towards a formalization of budgets

“…We have motivated our interest in a formal theory of budgets, and we have proposed a simple algebraic theory of budgets based on the tuplix calculus [2]. Quantities are expressed as functions on the rational numbers, which we have modeled as a totalized field [3].…”

“…We present a simple algebra for rational budgets. This algebra is an application of the so-called tuplix calculus [2]. A tuplix (plural: tuplices) is a datastructure that collects attribute-value pairs.…”

“…One EC stands for 28 hours of work. 2 Mark Burgess (see for instance [4]) advocates the mechanism of autonomous agents making promises which constrain their actions on a voluntary basis only. A budget proposal might be viewed as a promise conditional under the counter promise by other parties that they will go along with it.…”

“…In Section 3 we reflect on the formalization of budgets, and this is followed by a simple theory of budgets in Section 4. We use the so-called tuplix calculus [2] to model budgets. In Section 5 we present a case study on the educational budget of a university department offering master programs.…”

Tuplix Calculus Specifications of Financial Transfer Networks

“…In [3] we described the application of Tuplix Calculus (TC, see [6]) in the formalization of financial budgets. Here, we explore this application further starting with the definition of financial transfer networks.…”