Tuplix Calculus

TL;DR

This paper introduces the Tuplix Calculus, a formal system for expressions called tuplices that generalize matrices and vectors, with applications in financial budgeting and modular design.

Contribution

It presents the core calculus CTC, extends it with new operators, and proves its relative completeness with respect to a standard model.

Findings

CTC is relatively complete with respect to its standard model.

Extended calculus includes operators for choice, hiding, scalar multiplication, clearing, and encapsulation.

Applications demonstrated in financial budgeting and modular design.

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.