[Haskell-cafe] Proof that Haskell is RT

Ryan Ingram ryani.spam at gmail.com
Wed Nov 12 13:47:22 EST 2008

On a totally non-theory side, Haskell isn't referentially transparent.
 In particular, any code that calls unsafePerformIO or
unsafeInterleaveIO is not necessarily RT.  Given that getContents and
interact use unsafeInterleaveIO, this includes most toy programs as
well as almost every non-toy program; almost all use unsafePerformIO

That said, the situations in which these functions are RT are not that
hard to meet, but they would muddy up any formal proof significantly.

Personally, I'm happy with the hand-wavy proof that goes like this:

1) "pure" functions don't have side effects.
2) side-effect free functions can be duplicated or shared without
affecting the results of the program that uses them (in the absence of
considerations of resource limitation like running out of memory)
3) any function that only uses other pure functions is pure
4) all Haskell98 functions that don't use unsafe* are pure
5) therefore Haskell98 minus unsafe functions is referentially transparent.

Note that I am including I/O actions as "pure" when observed as the
GHC implementation of IO a ~~ World -> (World, a); the function result
that is the value of "main" is pure.  It is only the observation of
that function by the runtime that causes side effects.

  -- ryan

On Wed, Nov 12, 2008 at 2:11 AM, Andrew Birkett <andy at nobugs.org> wrote:
> Hi,
> Is a formal proof that the Haskell language is referentially transparent?
>  Many people state "haskell is RT" without backing up that claim.  I know
> that, in practice, I can't write any counter-examples but that's a bit
> handy-wavy.  Is there a formal proof that, for all possible haskell
> programs, we can replace coreferent expressions without changing the meaning
> of a program?
> (I was writing a blog post about the origins of the phrase 'referentially
> transparent' and it made me think about this)
> Andrew
> --
> - http://www.nobugs.org -
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