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| class   | std::const_mem_fun1_ref_t< _Ret, _Tp, _Arg > | 
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| class   | std::const_mem_fun1_t< _Ret, _Tp, _Arg > | 
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| class   | std::const_mem_fun_ref_t< _Ret, _Tp > | 
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| class   | std::const_mem_fun_t< _Ret, _Tp > | 
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| class   | std::mem_fun1_ref_t< _Ret, _Tp, _Arg > | 
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| class   | std::mem_fun1_t< _Ret, _Tp, _Arg > | 
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| class   | std::mem_fun_ref_t< _Ret, _Tp > | 
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| class   | std::mem_fun_t< _Ret, _Tp > | 
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template<typename _Ret , typename _Tp >  | 
| mem_fun_t< _Ret, _Tp >  | std::mem_fun (_Ret(_Tp::*__f)()) | 
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template<typename _Ret , typename _Tp , typename _Arg >  | 
| mem_fun1_t< _Ret, _Tp, _Arg >  | std::mem_fun (_Ret(_Tp::*__f)(_Arg)) | 
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template<typename _Ret , typename _Tp >  | 
| mem_fun_ref_t< _Ret, _Tp >  | std::mem_fun_ref (_Ret(_Tp::*__f)()) | 
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template<typename _Ret , typename _Tp , typename _Arg >  | 
| mem_fun1_ref_t< _Ret, _Tp, _Arg >  | std::mem_fun_ref (_Ret(_Tp::*__f)(_Arg)) | 
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There are a total of 8 = 2^3 function objects in this family. (1) Member functions taking no arguments vs member functions taking one argument. (2) Call through pointer vs call through reference. (3) Const vs non-const member function.
All of this complexity is in the function objects themselves. You can ignore it by using the helper function mem_fun and mem_fun_ref, which create whichever type of adaptor is appropriate.