Brian Hulley wrote: ] Here is another example. Consider two functions f and g which, given the ] same inputs, always return the same outputs as each other such as: ] ] f x = x + 2 ] g x = x + 1 + 1 ] ] Now since f and g compute the same results for the same inputs, anywhere in ] a program that you can use f you could just replace f by g and the ] observable behaviour of the program would be completely unaffected. This is ] what referential transparency means. ] ] However, if you allowed a function such as superShow, superShow f == "x + ] 2" and superShow g == "x + 1 + 1" so superShow f /= superShow g thus you ] could no longer just use f and g interchangeably, since these expressions ] have different results. Hmm. It must be a little more complicated than that, right? Since after all you can print out *some* functions. That's what section 5 of _Fun with Phantom Types_ is about. Here's a slightly different example, using the AbsNum module from... http://www.haskell.org/hawiki/ShortExamples_2fSymbolDifferentiation
import AbsNum
f x = x + 2 g x = x + 1 + 1
y :: T Double y = Var "y"
main = do print (f y) print (g y)
...which results in... *Main> main (Var "y")+(Const (2.0)) (Var "y")+(Const (1.0))+(Const (1.0)) ...is this competely unrelated? Thanks, Greg Buchholz