Algebraic Graphs with Class (functional pearl)

Mokhov, A

doi:10.1145/3122955.3122956

Algebraic Graphs with Class (functional pearl)

Lookup NU author(s): Dr Andrey Mokhov

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This is the authors' accepted manuscript of a conference proceedings (inc. abstract) that has been published in its final definitive form by ACM, 2017.

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Abstract

The paper presents a minimalistic and elegant approach to workingwith graphs in Haskell. It is built on a rigorousmathematical foundation --- an algebra of graphs --- that allows us to applyequational reasoning for proving the correctness of graph transformationalgorithms. Algebraic graphs let us avoid partial functions typicallycaused by `malformed graphs' that contain an edge referring toa non-existent vertex. This helps to liberate APIs of existing graph librariesfrom partial functions.The algebra of graphs can represent directed, undirected, reflexiveand transitive graphs, as well as hypergraphs, by appropriately choosingthe set of underlying axioms. The flexibility of the approach isdemonstrated by developing a library for constructingand transforming polymorphic graphs.