# Automated Sized-Type Inference and Complexity Analysis

## TL;DR

This paper presents an automated methodology for size-type inference and complexity analysis of higher-order functional programs, combining advanced type systems, transformations, and constraint solving, capable of handling complex examples.

## Contribution

It introduces a fully automated approach with an abstract index language and index polymorphism, enabling analysis of complex higher-order programs beyond existing methods.

## Key findings

- Successfully analyzes complex higher-order programs
- Automated process reduces manual effort
- Prototype implementation demonstrates practical applicability

## Abstract

This paper introduces a new methodology for the complexity analysis of higher-order functional programs, which is based on three components: a powerful type system for size analysis and a sound type inference procedure for it, a ticking monadic transformation and a concrete tool for constraint solving. Noticeably, the presented methodology can be fully automated, and is able to analyse a series of examples which cannot be handled by most competitor methodologies. This is possible due to various key ingredients, and in particular an abstract index language and index polymorphism at higher ranks. A prototype implementation is available.