Linear Dependent Types for Domain Specific Program Analysis (Extended Abstract)

TL;DR

This paper explores how combining linear and dependent types can enhance the analysis of higher-order programs, especially for properties like complexity and sensitivity, by capturing control flow and function behavior.

Contribution

It introduces a novel approach integrating linear and dependent types for program analysis, demonstrating its usefulness through complexity and sensitivity analysis examples.

Findings

Effective description of function properties using combined types

Application to complexity and sensitivity analysis

Potential for generalization to other program properties

Abstract

In this tutorial I will present how a combination of linear and dependent type can be useful to describe different properties about higher order programs. Linear types have been proved particularly useful to express properties of functions; dependent types are useful to describe the behavior of the program in terms of its control flow. This two ideas fits together well when one is interested in analyze properties of functions depending on the control flow of the program. I will present these ideas with example taken by complexity analysis and sensitivity analysis. I will conclude the tutorial by arguing about the generality of this approach.