A Dependent Type Theory for Meta-programming with Intensional Analysis

In this paper, we introduce DeLaM, a dependent layered modal type theory which enables meta-programming in Martin-Löf type theory (MLTT) with recursion principles on open code. DeLaM includes three layers: the layer of static syntax objects of MLTT without any computation; the layer of pure MLTT wit...

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Bibliographic Details
Published in:Proceedings of ACM on programming languages Vol. 9; no. POPL; pp. 416 - 445
Main Authors: Hu, Jason Z. S., Pientka, Brigitte
Format: Journal Article
Language:English
Published: New York, NY, USA ACM 07.01.2025
Subjects:
Functional languages
Software and its engineering
Theory of computation
Type theory
logical relations
contextual types
meta-programming
dependent types
intensional analysis
modal type theory
ISSN:2475-1421, 2475-1421
Online Access:Get full text
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Summary:In this paper, we introduce DeLaM, a dependent layered modal type theory which enables meta-programming in Martin-Löf type theory (MLTT) with recursion principles on open code. DeLaM includes three layers: the layer of static syntax objects of MLTT without any computation; the layer of pure MLTT with the computational behaviors; the meta-programming layer extends MLTT with support for quoting an open MLTT code object and composing and analyzing open code using recursion. We can also execute a code object at the meta-programming layer. The expressive power strictly increases as we move up in a given layer. In particular, while code objects only describe static syntax, we allow computation at the MLTT and meta-programming layer. As a result, DeLaM provides a dependently typed foundation for meta-programming that supports both type-safe code generation and code analysis. We prove the weak normalization of DeLaM and the decidability of convertibility using Kripke logical relations.
ISSN:2475-1421
2475-1421
DOI:10.1145/3704851