Automatic Type Inference for Amortised Heap-Space Analysis

Abstract

Abstract. We present a fully automatic, sound and modular heap-space analysis for object-oriented programs. In particular, we provide type inference for the system of refinement types RAJA, which checks upper bounds of heap-space usage based on amortised analysis. Until now, the refined RAJA types had to be manually specified. Our type inference increases the usability of the system, as no user-defined annotations are required.The type inference consists of constraint generation and solving. First, we present a system for generating subtyping and arithmetic constraints based on the RAJA typing rules. Second, we reduce the subtyping constraints to inequalities over infinite trees, which can be solved using an algorithm that we have described in previous work. This paper also enriches the original type system by introducing polymorphic method types, enabling a modular analysis.

Towards the Typing of Resource Deployment

“…In these regards, we plan to explore the adoption of behavioural types that depends [3] on the input data of conditions in if-statements. We observe, anyway, that the generalisation of the results in [11,12] to a concurrent setting has not been investigated.…”

“…A type inference technique for resource analysis has been developed in [11,12]. They study the problem of worst-case heap usage in functional and (sequential) object-oriented languages and their tool returns functions on the size of inputs of every method that highlight the heap consumption.…”

“…On the contrary, our technique returns upper bounds disregarding input sizes. However, we think it is possible to extend our types to enable a transition system model that support the expressivity of [12] (our current analysis of behavioural types is preliminary and must be considered as a proof-of-concept). In these regards, we plan to explore the adoption of behavioural types that depends [3] on the input data of conditions in if-statements.…”

Automatic amortized analysis

“…Furthermore, the compositionality of amortized complexity makes it suitable for integration with type systems. This research has led to several systems for the automatic analysis of functional [4] and objectoriented programs [8,11]. There have also been applications to resource usage certification [1,3], to the analysis of low-level systems code [2,12] and to lazy functional programming [16] and to term rewriting [9].…”

Decidable linear list constraints

“…The constraint systems appearing in this analysis have finitely many variables and can be reduced to linear programming. The same was true for subsequent extensions to higher-order functions and more complex potential functions [3,4,5,6,7]. The extension of this method to object-oriented programs in a language RAJA (Resource Aware JAva, a fragment of Java with inheritance, recursive methods and extended with resource annotations in the types) [8,9,10,1] led to the use of constraints involving infinite lists or trees whose entries are numerical variables.…”