A functional representation of data structures with a hole

Data structures with a hole, in other words data structures with an uninitialized field, are useful to write efficient programs: they enable us to construct functional data structures flexibly and write functions such as append and map as tail recursive functions. In this paper we present an approach to introducing data structures with a hole into call-by-value functional programming languages like ML. Data structures with a hole are formalized as a new form of ¿-abstraction called hole abstraction. The novel features of hole abstraction are that expressions inside hole abstraction are evaluated and application is implemented by destructive update of a hole. We present a simply typed call-by-value ¿-calculus extended with hole abstractions. Then we show a compilation method of hole abstraction and prove correctness of the compilation.

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