On the ambiguation of Polish notation (Q549208)

Unique reading theorems for Polish notation show how structure of terms in this notation can be recovered. The author proposes another interpretation strategy: the free monoid of all strings is interpreted in a certain semantic algebra which also is a monoid. To construct the latter, the author introduces the notion of Polish composition over a category; under one extra condition, this composition is essentially an extension of the partial composition operation \(g \circ f\) to the cases where codomain of \(f\) differs from the domain of \(f\). The language of category theory is used throughout the study; the reader is supposed to have some knowledge of basic category theory. However, the main tool, strictly r-monoidal categories, is explained in the paper.