Joachim Durchholz wrote:
This "identity is equality under change" definition captures not just two objects at identical addresses, but also proxies, network objects, files, and whatever there is.
Step 3: Realize that if you have an immutable object, there is no relevant difference between equality and identity anymore. (You can make various formal statements about this.)
Is that what is called "extensional equality"? Values a,b :: A are extensionally equal if they behave the same in all contexts. That is, there is no type X and no function f :: A -> X such that f a can be observed to be different from f b, e.g. f a throws an exception and f b does not, or X is in Eq and f a /= f b. Can one write a function (even using reallyUnsafePtrEquality#) that distinguishes the following? a = Add (Val 1) (Val 1) b = let v = Val 1 in Add v v I tried: import GHC.Exts peq :: a -> a -> Bool peq x y = I# (reallyUnsafePtrEquality# x y) == 1 f :: Ex -> Bool f (Val _) = False f (Add x y) = peq x y But I get (even when I make the fields of Add strict): peq a a == True f a == False f b == False Olaf