Conference Paper/Proceeding/Abstract 81 views
Implicit automata in λ-calculi III: affine planar string-to-string functions
Cécilia Pradic 
,
Ian Price
,
Ian Price
Mathematical Foundations of Programming Semantics 2024
Swansea University Authors:
Cécilia Pradic , Ian Price
Abstract
We prove a characterization of first-order string-to-string transduction via λ-terms typed in non-commutative affine logic that compute with Church encoding, extending the analogous known characterization of star-free languages. We show that every first-order transduction can be computed by a λ-term...
| Published in: | Mathematical Foundations of Programming Semantics 2024 |
|---|---|
| Published: |
Oxford
2024
|
| URI: | https://cronfa.swan.ac.uk/Record/cronfa68303 |
| Abstract: |
We prove a characterization of first-order string-to-string transduction via λ-terms typed in non-commutative affine logic that compute with Church encoding, extending the analogous known characterization of star-free languages. We show that every first-order transduction can be computed by a λ-term using a known Krohn-Rhodes-style decomposition lemma. The converse direction is given by compiling λ-terms into two-way reversible planar transducers. The soundness of this translation involves showing that the transition functions of those transducers live in a monoidal closed category of diagrams in which we can interpret purely affine λ-terms. One challenge is that the unit of the tensor of the category in question is not a terminal object. As a result, our interpretation does not identify β-equivalent terms, but it does turn β-reductions into inequalities in a poset-enrichment of the category of diagrams. |
|---|---|
| College: |
Faculty of Science and Engineering |