When I initially challenged myself with building a dataframe implementation, I began by looking at what already existed for inspiration. Spark was my initial reference. Then pandas. Then Polars, R’s data.table, Julia’s DataFrames.jl. Each one had its own take on the API. Early on, my main challenge was trying to figure out which operations I actually needed to implement to call what I had a “dataframe”. The surface area felt enormous. Do I need pivot and melt as separate things? Is apply different from map? What about transform, agg, applymap, pipe? Some of these seemed like the same operation wearing different hats. Others seemed genuinely distinct. I didn’t have a good framework for telling them apart.

Lobsters is a community-driven platform for sharing and discussing links to articles, tutorials, and projects related to technology and programming. Readers can learn about a wide range of topics, from software development and system administration to cybersecurity and artificial intelligence. With user submissions, comments, and voting, Lobsters provides a platform for collaborative learning and knowledge sharing among technology enthusiasts.

Lobsters

A developer building a custom dataframe library explores the theoretical foundations of dataframe operations. Starting from Petersohn et al.'s dataframe algebra (15 operators covering 200+ pandas methods), the author discovers that the relational core maps onto exactly three categorical patterns: Delta (restructuring/projection), Sigma (merging/groupby), and Pi (pairing/join). These correspond to an adjoint triple Σ ⊣ Δ ⊣ Π from Fong and Spivak's category theory work, explaining why these three operations compose correctly. The post shows how this framework guides API design in a typed Haskell dataframe library where schema transitions are verified at compile time, and how the algebraic laws enable safe query optimization like predicate pushdown and filter fusion.

What Category Theory Teaches Us About DataFrames

Designing an API around the three patterns