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Explore the development of a domain-specific language for tensor mathematics in this 26-minute conference presentation from ICFP 2025. Learn how researchers Jean-Philippe Bernardy and Patrik Jansson from the University of Gothenburg and Chalmers University of Technology address the gap between mathematical tensor notation and functional programming by creating an embedded DSL in Haskell. Discover the challenges with existing tensor algebra languages, which either lack enforcement of tensor properties or require unwieldy point-free notation, and understand how standard tensor notation presents exotic properties from lambda calculi perspectives. Examine the design of their embedded domain-specific language that closely captures index notation for tensors while maintaining semantics defined through algebraic structures that represent tensors in full generality. Gain insights into how this approach bridges theoretical tensor mathematics with practical scientific computing applications, providing both a computational tool and an educational vehicle for expressing tensor theory and applications within the functional programming paradigm.
