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Abstract. We present a type system for a compile-time analysis of heap-space requirements of Java style object-oriented programs with explicit deallocation.Our system is based on an amortised complexity analysis: the data is arbitrarily assigned a potential related to its size and layout; allocations must be "payed for" from this potential. The potential of each input then furnishes an upper bound on the heap space usage for the computation on this input.We successfully treat inheritance, downcast, update and aliasing. Example applications for the analysis include destination-passing style and doubly-linked lists.Type inference is explicitly not included; the contribution lies in the system itself and the nontrivial soundness theorem. This extended abstract elides most technical lemmas and proofs, even nontrivial ones, due to space limitations. A full version is available at the authors' web pages.

We present a static analysis for determining the execution costs of lazily evaluated functional languages, such as Haskell. Time-and space-behaviour of lazy functional languages can be hard to predict, creating a significant barrier to their broader acceptance. This paper applies a type-based analysis employing amortisation and cost effects to statically determine upper bounds on evaluation costs. While amortisation performs well with finite recursive data, we significantly improve the precision of our analysis for co-recursive programs (i.e. dealing with potentially infinite data structures) by tracking self-references. Combining these two approaches gives a fully automatic static analysis for both recursive and co-recursive definitions. The analysis is formally proven correct against an operational semantic that features an exchangeable parametric cost-model. An arbitrary measure can be assigned to all syntactic constructs, allowing to bound, for example, evaluation steps, applications, allocations, etc. Moreover, automatic inference only relies on first-order unification and standard linear programming solving. Our publicly available implementation demonstrates the practicability of our technique on editable non-trivial examples.

We describe a new automatic static analysis for determining upper-bound functions on the use of quantitative resources for strict, higher-order, polymorphic, recursive programs dealing with possibly-aliased data. Our analysis is a variant of Tarjan's manual amortised cost analysis technique. We use a type-based approach, exploiting linearity to allow inference, and place a new emphasis on the number of references to a data object. The bounds we infer depend on the sizes of the various inputs to a program. They thus expose the impact of specific inputs on the overall cost behaviour.The key novel aspect of our work is that it deals directly with polymorphic higher-order functions without requiring source-level transformations that could alter resource usage. We thus obtain safe and accurate compile-time bounds. Our work is generic in that it deals with a variety of quantitative resources. We illustrate our approach with reference to dynamic memory allocations/deallocations, stack usage, and worst-case execution time, using metrics taken from a real implementation on a simple micro-controller platform that is used in safety-critical automotive applications.