Graphical Primitive Recursion For String Diagrams
summary
Provides a concrete way to add primitive recursion to diagrams in a symmetric monoidal setting, with a proof‑of‑concept Haskell eDSL that converts recursive diagrams into runnable circuits and compiles down to KASM. Defines two formal semantics — translation to endofunctor algebras enabling paramorphisms (so recursive boxes keep their index and admit algebraic laws) and an alternative view as a composition of coends. Demonstrates by encoding the Quantum Fourier Transform, running and simplifying mirrored/inverse circuits automatically using the paramorphic equations.
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chapters (10)
- 0:00Introduction
- 1:07Scalable ZX calculus
- 2:35Quantum Fourier transform example
- 5:01Semantics in symmetric monoidal categories
- 8:13Recursion schemes and paramorphisms
- 12:57Paramorphic semantics for diagrams
- 14:21Haskell implementation
- 15:47Applications and future work
- 16:30Live QFT code
- 17:12Q&A
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