A Type-Based Complexity Analysis of Object Oriented Programs

TL;DR

This paper introduces a type system for object-oriented languages that infers resource bounds, ensuring polynomial time computability and bounded memory usage, while being expressive and decidable.

Contribution

It presents a novel type-based complexity analysis framework for object-oriented programs that guarantees polynomial resource bounds and supports key language features.

Findings

Programs have polynomial time computability.

Heap and stack space are polynomially bounded.

Type checking is decidable in polynomial time.

Abstract

A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound andcomplete characterization of the set of polynomial time computable functions is obtained. As a consequence, the heap-space and thestack-space requirements of typed programs are also bounded polynomially. This type system is inspired by previous works on ImplicitComputational Complexity, using tiering and non-interference techniques. The presented methodology has several advantages. First, itprovides explicit big $O$ polynomial upper bounds to the programmer, hence its use could allow the programmer to avoid memory errors.Second, type checking is decidable in polynomial time. Last, it has a good expressivity since it analyzes most object oriented featureslike inheritance, overload, override and recursion. Moreover it can deal with loops guarded by objects and can also be extended tostatements that alter the control flow like break or return.