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(Almost) Affine Higher-Order Tree Transducers
- Publication Year :
- 2024
-
Abstract
- We investigate the tree-to-tree functions computed by \enquote{affine$\lambda$-transducers}: tree automata whose memory consists of an affine $\lambda$-term instead of a finite state. They can be seen as variations on Gallot, Lemay and Salvati's Linear High-Order Deterministic Tree Transducers. When the memory is almost purely affine (\textit{\`a la} Kanazawa), we show that these machines can be translated to tree-walking transducers (and with a purely affine memory, we get a reversible tree-walking transducer). This leads to a proof of an inexpressivity conjecture of \titocecilia on \enquote{implicit automata} in an affine $\lambda$-calculus. The key technical tool in our proofs is the Interaction Abstract Machine (IAM), an operational avatar of the \enquote{geometry of interaction} semantics of linear logic. We work with ad-hoc specializations to (almost) affine $\lambda$-terms of a tree-generating version of the IAM.
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2402.05854
- Document Type :
- Working Paper