Normalization for multimodal type theory
Abstract
We prove normalization for MTT, a general multimodal dependent type theory capable of expressing modal type theories for guarded recursion, internalized parametricity, and various other prototypical modal situations. We prove that deciding type checking and conversion in MTT can be reduced to deciding the equality of modalities in the underlying modal situation, immediately yielding a type checking algorithm for all instantiations of MTT in the literature. This proof uses a generalization of synthetic Tait computability -- an abstract approach to gluing proofs -- to account for modalities. This extension is based on MTT itself, so that this proof also constitutes a significant case study of MTT.
Fields of Study & Subjects
Logic
programming
and type systems
Semantic Web and Ontologies
Reasoning
and Knowledge
Publication details
- Journal / source
- Logical Methods in Computer Science
- Publisher
- Centre pour la Communication Scientifique Directe (CCSD)
- Volume
- Volume 22, Issue 1
- Publication date
- 17 March 2026
- Language
- EN