On Thu, 2009-04-09 at 12:31 -0400, Brandon S. Allbery KF8NH wrote:
On 2009 Apr 9, at 11:47, Mark Spezzano wrote:
How exactly do monads “solve” the problem of referential transparency? I understand RT to be such that a function can be replaced with a actual value.
Since a monad could potentially encapsulate any other value—say, data read from a keyboard—doesn’t that violate the assumption of RT on monads?
Monads provide a way to carry extra data or operations around with their values. IO passes an opaque "world state" around in the background, conceptually I/O operations modify the "world state" and it is in fact always valid to replace the monadified version with the unwrapped version --- ignoring IORefs, IO is just a simple state monad.
I'm not sure what you mean by that, but semantically IO is definitely *not* a state monad. Under any circumstances or any set of assumptions. GHC *implements* IO as a state monad, but not because it semantically is. Rather, GHC's back-end language (STG) is an *impure* lazy functional language, supplying primitive functions with (ultimate) result type (# State# s, alpha #) , for some alpha,[1] that are side-effectful. The intention is that the State# s component (which has almost no run-time representation) is used to ensure a strict sequencing of the evaluation of these expressions --- which intention can be violated by using the operations unsafePerformIO and unsafeInterleaveIO --- allowing the language to be both side-effectful and lazy without the programmer necessarily effectively losing the ability to control what the outcome of running the program will be. But that has nothing to do with referential transparency, because the language those tricks are used in is not referentially transparent. It's just an implementation technique for implementing a referentially transparent source language on a non-referentially transparent imperative stored-memory computer. jcc [1] As pointed out in another thread a couple of weeks ago, the order of these components is reversed: they should be (# alpha, State# s #) It's probably too late to change it now, though.