Introducing a Calculus of Effects and Handlers for Natural Language Semantics
This work addresses a foundational issue in natural language semantics for researchers, but it appears incremental as it builds on existing monadic observations and effect handler techniques.
The paper tackles the problem of compositional model-theoretic semantics by introducing an extension of the simply-typed lambda calculus using effect handlers to exploit the monadic pattern in lambda terms and denotations, resulting in a modular semantics for a fragment with multiple semantic phenomena and proven formal properties.
In compositional model-theoretic semantics, researchers assemble truth-conditions or other kinds of denotations using the lambda calculus. It was previously observed that the lambda terms and/or the denotations studied tend to follow the same pattern: they are instances of a monad. In this paper, we present an extension of the simply-typed lambda calculus that exploits this uniformity using the recently discovered technique of effect handlers. We prove that our calculus exhibits some of the key formal properties of the lambda calculus and we use it to construct a modular semantics for a small fragment that involves multiple distinct semantic phenomena.