This work introduces collected size semantics of strict functional programs over lists. The collected size semantics of a function definition is a multivalued size function that collects the dependencies between every possible output size and the corresponding input sizes. Such functions annotate standard types and are defined by conditional rewriting rules generated during type inference. We focus on the connection between the rewriting rules and lower and upper bounds on the multivalued size functions, when the bounds are given by piecewise polynomials. We show how, given a set of conditional rewriting rules, one can infer bounds that define an indexed family of polynomials that approximates the multivalued size function. Using collected size semantics we are able to infer non-monotonic and non-linear lower and upper polynomial bounds for many functional programs. As a feasibility study, we use the procedure to infer lower and upper polynomial size-bounds on typical functions of a list library.

Abstract. Security automata are a convenient way to describe security policies. Their typical use is to monitor the execution of an application, and to interrupt it as soon as the security policy is violated. However, run-time adherence checking is not always convenient. Instead, we aim at developing a technique to verify adherence to a security policy statically. To do this, we consider a security automaton as specification, and we generate JML annotations that inline the monitor -as a specificationinto the application. We describe this translation and prove preservation of program behaviour, i.e., if monitoring does not reveal a security violation, the generated annotations are respected by the program. The correctness proofs are formalised using the PVS theorem prover. This reveals several subtleties to be considered in the definition of the translation algorithm and in the program requirements.

Abstract. Size analysis can be an important part of heap consumption analysis. This paper is a part of ongoing work about typing support for checking output-on-input size dependencies for function definitions in a strict functional language. A significant restriction for our earlier results is that inner data structures (e.g. in a list of lists) all must have the same size. Here, we make a big step forwards by overcoming this limitation via the introduction of higher-order size annotations such that variate sizes of inner data structures can be expressed. In this way the analysis becomes applicable for general, polymorphic nested lists.

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