Sorry to barge in in the middle of your discussion here..
On 4/5/06, Robert Dockins
There is a fair bit of disagreement about what referential transparency means. I found the following link after googling around a bit; it seems to address some of these issues.
Do you have any reference to the fact that there is any diagreement about the term? I know it has been used sloppily at times but I think it is pretty well defined. See section 4 of the following paper: http://www.dina.kvl.dk/~sestoft/papers/SondergaardSestoft1990.pdf Readers digest: First we need a denotational semantics and a corresponding equality which I call '='. A language is then referentially transparent if for all expressions e,e1 and e2, if e1 = e2 then e[x:=e1] = e[x:=e2]. Here e[x:=e'] denotes substitution where the variable x is replaced with e' in the expression e. So it's a standard substitutivity property. The only problem here is that Haskell has a pretty hairy denotational semantics and I don't think anyone has spelled it out in detail. The thing which I think comes closest is the following paper which investigates the denotational implications of have seq as a primitive: http://www.crab.rutgers.edu/~pjohann/seqFinal.pdf Cheers, /Josef