Dan Doel wrote:
But, to get back to BASIC, or C, if the language you're extending is an empty language that does nothing, then remaining pure to it isn't interesting. I can't actually write significant portions of my program in such a language, so all I'm left with is the DSL, which doesn't (internally) have the nice properties.
I understand your argument to be the following: Functional languages are built upon the lambda calculus, so a *pure* functional language has to preserve the equational theory of the lambda calculus, including, for example, beta reduction. But since BASIC or C are not built upon any formal calculus with an equational theory, there is not notion of purity for these languages. I like your definition of purity, but I disagree with respect to your evaluation of BASIC and C. To me, they seem to be built upon the formal language of arithmetic expressions, so they should, to be "pure arithmetic expression languages", adhere to such equations as the commutative law for integers. forall x y : integer, x + y = y + x But due to possible side effects of x and y, languages like BASIC and C do not adhere to this, and many other laws. I would therefore consider them impure. They could be more pure by allowing side effects only in statements, but not in expressions. Tillmann