Purity vs Referential transparency

Question

The terms do appear to be defined differently, but I\'ve always thought of one implying the other; I can\'t think of any case when an expression is referentially t

Answer 1

I'm somewhat unsure of the answer I give here, but surely somebody will point us in some direction. :-)

"Purity" is generally considered to mean "lack of side-effects". An expression is said to be pure if its evaluation lacks side-effects. What's a side-effect then? In a purely functional language, side-effect is anything that doesn't go by the simple beta-rule (the rule that to evaluate function application is the same as to substitute actual parameter for all free occurrences of the formal parameter).

For example, in a functional language with linear (or uniqueness, this distinction shouldn't bother at this moment) types some (controlled) mutation is allowed.

So I guess we have sorted out what "purity" and "side-effects" might be.

Referential transparency (according to the Wikipedia article you cited) means that variable can be replaced by the expression it denotes (abbreviates, stands for) without changing the meaning of the program at hand (btw, this is also a hard question to tackle, and I won't attempt to do so here). So, "purity" and "referential transparency" are indeed different things: "purity" is a property of some expression roughly means "doesn't produce side-effects when executed" whereas "referential transparency" is a property relating variable and expression that it stands for and means "variable can be replaced with what it denotes".

Hopefully this helps.