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==Definition==
Purely functional data structures are often represented in a different way than their [[imperative programming|imperative]] counterparts.<ref>[http://www.cambridge.org/us/academic/subjects/computer-science/algorithmics-complexity-computer-algebra-and-computational-g/purely-functional-data-structures ''Purely functional data structures''] by [[Chris Okasaki]], [[Cambridge University Press]], 1998, {{ISBN|0-521-66350-4}}</ref> For example, an array can be replaced by a [[Map (computer science)|map]], a random access list, or a tree, which admits a purely functional implementation, but access and update operations may run in [[logarithmic time]]. [[Persistent data structure|Persistent data structures]] have the property of keeping previous versions of themselves unmodified, and are used as functional alternatives to their
==Ensuring that a data structure is purely functional==
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