First-class function
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As one can test most literals and values for equality, it is natural to ask whether a programming language can support testing functions for equality. On further inspection, this question appears more difficult and one has to distinguish between several types of function equality:cite-ref-7[7]
Two functions f and g are considered extensionally equal if they agree on their outputs for all inputs (∀x. f(x) = g(x)). Under this definition of equality, for example, any two implementations of a stable sorting algorithm, such as insertion sort and merge sort, would be considered equal. Deciding on extensional equality is undecidable in general and even for functions with finite domains often intractable. For this reason no programming language implements function equality as extensional equality.
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