Characterizing algorithmic solutions via language decompositions

Determine whether different algorithmic solutions to the same problem within a fixed programming language can be characterized by distinct semigroupoid decompositions of that programming language, such that differences in computational strategies are reflected in differences between the decompositions.

Background

The paper proposes applying algebraic hierarchical decompositions—generalized from semigroups to semigroupoids—to programming languages, with a focus on concatenative functional languages. The goal is to use these decompositions to understand and classify computational processes and coding styles.

Within this framework, the authors hypothesize that different solutions to the same problem (e.g., recursion versus folding on a sequence) manifest as different decompositions of the programming language’s semigroupoid representation, thereby offering a precise algebraic lens on program differences.