Many program optimizations and analyses, such as arraybounds checking, termination analysis, depend on knowing the size of a function’s input and output. However, size information can be difficult to compute. Firstly, accurate size computation requires detecting a size relation between different inputs of a function. Secondly, size information may also be contained inside a collection (data structure with multiple elements). In this paper, we introduce some techniques to derive universal and existential size properties over collections of elements of recursive data structures. We shall show how a mixed constraint system could support the enhanced size type, and highlight examples where collection analysis are useful
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