Functional programming is founded on the duality of functions and data: we treat functions as data, and often represent data as functions. But what does it mean to take a data-centric perspective within functional programming itself? This talk is an exploration of elevating finite maps—functions with finite, explicitly tabulated domains—to first-class status in the functional programming toolkit. Alongside the conventional lambda abstraction (𝜆𝑥.), we introduce a dual construct (Λ𝑥.) for constructing such data-centric functions, where the mapping is fully realized at definition time.

We demonstrate how this construct naturally supports functional array programming, relational query composition, and structured data manipulation—domains traditionally requiring ad hoc or external solutions in purely function-centric paradigms.

Tiark Rompf is an assistant professor at Purdue University. His work focuses on runtime code generation, advanced compiler technology, and associated language support. From 2008 to 2014 he was a member of Martin Odersky’s Scala team at EPFL where he developed the LMS compiler framework and made various contributions to the Scala language and toolchain (delimited continuations, efficient immutable data structures, compiler speedups, type system work).