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A pure function is a function where the return value is only determined by its arguments without any side effects.

Currying is the process of taking a function with multiple arguments and turning it into a sequence of functions each with only a single argument. Therefor with currying you take a n-ary function and you turn it into a unary function:

…y of a number of arguments accepted by a function. Unary function (i.e. monadic) is a function that accepts exactly one argument.