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Sometimes a member function of a class template (possibly one of an overloaded set) only makes sense for certain template parameters. The enable_if idiom uses SFINAE to eliminate unwanted functions before overload resolution.
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One use of enable_if is in implementing requirements such as that on the (size_type, value_type) constructor of a standard container, which has special behavior if the value_type is an integral type. More primitive solutions exist, but enable_if is elegant in this context.