MiniAgda: Integrating Sized and Dependent Types

16 pages•Published: May 15, 2012

Abstract

Sized types are a modular and theoretically well-understood tool for checking termination of recursive and productivity of corecursive definitions. The essential idea is to track structural descent and guardedness in the type system to make termination checking robust and suitable for strong abstractions like higher-order functions and polymorphism.

To study the application of sized types to proof assistants and programming languages based on dependent type theory, we have implemented a core language with explicit handling of sizes. New considerations were necessary to soundly integrate sized types with dependencies and pattern matching, which was made possible by modern concepts such as inaccessible patterns and parametric function spaces.

Keyphrases: dependent types, pattern matching, productivity, sized types, termination

In: Ekaterina Komendantskaya, Ana Bove and Milad Niqui (editors). PAR-10. Partiality and Recursion in Interactive Theorem Provers, vol 5, pages 18-33.

Links:	https://easychair.org/publications/paper/RM
	https://doi.org/10.29007/322q

BibTeX entry

@inproceedings{PAR-10:MiniAgda_Integrating_Sized_Dependent,
  author    = {Andreas Abel},
  title     = {MiniAgda: Integrating Sized and Dependent Types},
  booktitle = {PAR-10. Partiality and Recursion in Interactive Theorem Provers},
  editor    = {Ekaterina Komendantskaya and Ana Bove and Milad Niqui},
  series    = {EPiC Series in Computing},
  volume    = {5},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/RM},
  doi       = {10.29007/322q},
  pages     = {18-33},
  year      = {2012}}

Download PDF Open PDF in browser