AllSameBy

AllSameBy[{e₁,e₂,…},f]

tests whether all the f[e_i] are the same.

represents an operator form of AllSameBy that can be applied to an expression.

Details

AllSameBy applies f sequentially from the first element to the last until the result is different from the ones before, i.e. it short-circuits whenever possible.
When {e_n} has length 0 or 1, True is automatically returned without f being applied.

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Test whether all numbers have the same parity:

Test if all the numbers have the same magnitude:

Check if numbers are all prime or all composite:

AllSameBy can be implemented by applying f to all elements and then checking whether the results are all the same:

The difference becomes apparent when there are side effects.

AllSameBy will cease evaluation if any variation in f[e_n] is found:

Whereas Map would evaluate on all elements prior to checking SameQ:

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