Referential transparency

Let's delve a bit deeper to understand the consequences of being functional, as illustrated by the definitions given in the preceding section. Now, when we try to relate functions from both these worlds (mathematical and imperative programming), we see a strong disparity, as the latter mutates state with commands in the source language, thereby bringing in side effects (though desirable from an imperative programming standpoint). This violates one of the fundamental pre-requisites of functional programming - that of referential transparency, that is, the same expressions (when run at different times) yield different values with respect to the executing program's state. This affects the predictability of the program, which is definitely not desirable. On the other hand, pure functions (say f, one without such side effects) in the mathematical world would yield the same result f(x) each time with the same value of x, say sin(x). This characteristic is attributed to...