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Here are are a couple good introductions to semirings: https://www.youtube.com/watch?v=Gd_VT_Nj8Xw https://www.youtube.com/watch?v=Gd_VT_Nj8Xw https://www.you

• espeed 8y ago
  Hi Michel - You're working on a GraphBLAS Postgres implementation [0] -- here's an open question I've been pondering... [0] Postgres GraphBLAS https://github.com/michelp/pggraphblas https://github.com/michelp/pggraphblas Now that we have SOTA linear algebra models for graphs [1], logic [2] and the lambda calculus [3] that are being optimized for vectorized parallel compute on modern CPU/GPU/TPUs -- do we have the makings for a unified linear algebra model that obsoletes the relational algebra model in relational DBs? [1] Graph Algorithms in the Language of Linear Algebra (2011) https://epubs.siam.org/doi/book/10.1137/1.9780898719918 https://epubs.siam.org/doi/book/10.1137/1.9780898719918 Mathematical Foundations of the GraphBLAS (2016) https://arxiv.org/pdf/1606.05790.pdf https://arxiv.org/pdf/1606.05790.pdf [2] A Linear Algebraic Approach to Datalog Evaluation (2017) [pdf] https://arxiv.org/abs/1608.00139 https://arxiv.org/abs/1608.00139 A Linear Algebraic Approach to Logic Programming (2018) https://www.imperial.ac.uk/media/imperial-college/faculty-of-engineering/computing/public/1718-pg-projects/AspisY-Logical-Abduction-via-Linear-Algebraic-Methods.pdf https://www.imperial.ac.uk/media/imperial-college/faculty-of... [3] Lineal: A linear-algebraic Lambda-calculus (2017) https://arxiv.org/pdf/quant-ph/0612199.pdf https://arxiv.org/pdf/quant-ph/0612199.pdf The Vectorial λ-Calculus (2017) https://arxiv.org/pdf/1308.1138.pdf https://arxiv.org/pdf/1308.1138.pdf Simple λΠ-interpreter for matrix computation (2017) http://cs242.stanford.edu/assets/projects/2017/nykh.pdf http://cs242.stanford.edu/assets/projects/2017/nykh.pdf Algebra and the Lambda Calculus https://people.csail.mit.edu/jaffer/lambda.txt https://people.csail.mit.edu/jaffer/lambda.txt