Exploring the Properties of Finit Coproduct in the Category of Riesz Modules: A Semantic Approach to Denotational Semantics in Functional Programming Languages

The relationship between Riesz modules and functional programming languages lies in their shared mathematical structures and use of category theory. This paper discusses the utilization of Riesz spaces and modules in functional programming, including the frameworks proposed by Lucas and Mio for modeling Riesz spaces and the exploration of probabilistic logic by Furber, Mardare, and Mio. Foundational work by De Jonge and Van Rooij establishes the understanding of Riesz spaces and Banach lattices, while Kozen examines formal methods in probabilistic programs. Riesz spaces are valuable for representing complex mathematical structures in functional programming, and Riesz modules provide an ideal semantic category for facilitating mathematical proofs and logical reasoning. The paper focuses on the properties of finite coproduct in the category of Riesz modules and provides proofs of their existence and uniqueness.