MiniAgda: Integrating Sized and Dependent Types

• DOI: 10.4204/eptcs.43.2
• Publication Date: 2010-12-21T02:02:48Z
• Authors: Andreas Abel
• Keywords: FOS: Computer and information sciences; Computer Science - Logic in Computer Science; Computer Science - Programming Languages; QA75.5-76.95; 02 engineering and technology; Logic in Computer Science (cs.LO); Electronic computers. Computer science; QA1-939; 0202 electrical engineering, electronic engineering, information engineering; F.4.1; Mathematics; Programming Languages (cs.PL)

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.