A type-based complexity analysis of Object Oriented programs

Abstract

A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound and complete characterization of the set of polynomial time computable functions is obtained. As a consequence, the heap-space and the stack-space requirements of typed programs are also bounded polynomially. This type system is inspired by previous works on Implicit Computational Complexity, using tiering and non-interference techniques. The presented methodology has several advantages. First, it provides 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 features like inheritance, overload, override and recursion. Moreover it can deal with loops guarded by objects and can also be extended to statements that alter the control flow like break or return. Init ::= BList b := new BList (); BList c := new BList ( true , b ); B d := new B ( c ); A e := new A (c , c );

ComplexityParser: An Automatic Tool for Certifying Poly-Time Complexity of Java Programs

“…Stages of type inference. Tiers and typing judgments of [15] are implemented in an object hierarchy. The class Tier contains the constants T0, T1 and None for representing the tiers 0, 1, and "undefined", plus some useful static methods on tiers.…”

“…For example, the code of the while statement visitor is provided in Figure 3. It implements the following rule (rephrased rule (Wh) from [15]) enforcing any while statement to be controlled by a tier T1 expression: Γ ⊢ env ctx.expression() : T1 Γ ⊢ ctx.statement() : st env, st ∈ {T0, T1} Γ ⊢ while(ctx.expression()){ctx.statement()} : T1…”

“…This problem has been solved by the cornerstone work of [25] that has exhibited and studied the relations between tiering and non-interference on imperative programs. It has been extended to fork processes [13], object-oriented programs [24,14,15], and type-2 polynomial time [12], hence showing its portability and paving the way for practical implementations.…”

“…Contribution. This paper describes the architecture of ComplexityParser, a tier-based automatic cost analyzer for Java programs implementing the type system of [14,15] in Java, built using Maven, and whose source code is fully available at https://gitlab.inria.fr/hainry/complexityparser. The application receives as input a text file program and infers a type (called tier) as output.…”

“…The implemented analyses [25,14,15] are complete for the class of polynomial time computable functions, i.e. capture all functions.…”