# A Diagrammatic Calculus for a Functional Model of Natural Language Semantics

arXiv: https://arxiv.org/abs/2507.00782 · HTML: https://mlsanity.com/paper/2507.00782/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 11 references that are in the map.
- First posted on arXiv 1 Jul 2025.

## Builds on (most cited first, 6 of 6)

- [Mathematical Structure of Syntactic Merge](https://mlsanity.com/paper/2305.18278/) (2023)
- [The categorical contours of the Chomsky-Sch"utzenberger representation theorem](https://mlsanity.com/paper/2405.14703/) (2023)
- [Normalization for planar string diagrams and a quadratic equivalence algorithm](https://mlsanity.com/paper/1804.07832/) (2018)
- [Higher-Order DisCoCat (Peirce-Lambek-Montague semantics)](https://mlsanity.com/paper/2311.17813/) (2023)
- [The Algebraic Structure of Morphosyntax](https://mlsanity.com/paper/2507.00244/) (2025)
- [Effect-driven interpretation: Functors for natural language composition](https://mlsanity.com/paper/2504.00316/) (2025)

## Abstract (arXiv)

In this paper, we study a functional programming approach to natural language semantics, allowing us to increase the expressiveness of a more traditional denotation style. We will formalize a category based type and effect system to represent the semantic difference between syntactically equivalent expressions. We then construct a diagrammatic calculus to model parsing and handling of effects, providing a method to efficiently compute the denotations for sentences.