NARROWING THE DOMAINS OF DEFINITION AS A PATH TO IMPROVING SOFTWARE CORRECTNESS

Abstract

The article explores the problem of partial functions that arise in the process of modeling and software development due to insufficiently defined or non-formalized domains of model inputs. In complex domain-oriented systems—where models are often integrated from diverse sources or developed by interdisciplinary teams—narrowing the range of admissible input values is a critical tool for ensuring consistency, correctness, and predictability of software components.
It is shown that the narrowing of function domains in programming arises as a result of mathematical, technical, and domain-specific (contextual) constraints.
The focus is placed on cases where such constraints are not explicitly defined or exist only as part of an engineer’s implicit intuition. In these cases, constraints are neither reflected in type systems nor encoded in the logic, making automatic validation, model reuse, or transfer to other domains impossible, unreliable or even hazardous. The lack of formal domain specifications can lead to violations of system logic and the generation of incorrect or contradictory results—risks that are especially critical in high-stakes applications such as healthcare, autonomous systems, and energy infrastructures.
A particular emphasis is placed on the interdisciplinary nature of the problem, where models created in one application domain are transferred to another without adequately revisiting the original domain assumptions. Such transfer often preserves implicit constraints that are no longer valid or even harmful in the new context. As a result, systems that appeared stable may exhibit partial or unpredictable behavior, potentially disrupting critical processes.
The article proposes methodological approaches to the formal narrowing of input domains as a means of improving software reliability. This includes the specification of admissible values, domain boundaries, and edge-case handling within the programming and modeling infrastructure. The work contributes an interdisciplinary perspective on the correctness of software models operating with partial functions and outlines practical strategies for mitigating related issues through domain constraint formalization.