Evaluating Linear Functions to Symmetric Monoidal Categories
summary
Arrows lose needed parallelism because they force tuple-shaped inputs, so encoding box-and-wire diagrams as arrows wastes CPU; the claim is that symmetric monoidal categories are the right model and can be encoded in Haskell using LinearTypes. The implementation represents each box as a linear function from ports-as-typed-pairs to ports, embeds the SMC into a free cartesian category, then performs an encode/decode runtime elimination of projections and pairings so no duplication occurs. Result: readable code that restores exact parallelism for long-running workflows; requires some metaprogramming tradeoffs.
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chapters (7)
- 0:00Introduction to box diagrams
- 2:02The limitations of arrows
- 5:57Symmetric monoidal categories
- 12:39Linear types as a solution
- 16:51Implementing the library
- 20:40Defining ports and syntax
- 25:33Q&A and closing remarks
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