[Haskell-cafe] A law for MonadReader

[Benjamin Fox]

Here, as in general in the definitions of laws, the relevent question is
referential transparency, not Eq instances.

(You'll note that generally in the definitions of laws the symbol "=" is
used, not "==". Sometimes that's written as "≡", to be even clearer about
what it represents, as for instance the Monad Laws page
<https://wiki.haskell.org/Monad_laws> on the Haskell wiki does.)

For some laws, like the "fmap id = id" Functor law, this is obviously the
only possible interpretation, as both sides of that equation are
necessarily functions, and functions don't have an Eq instance.

So in this case, what the first law is asking for is that "ask >> ask" is
the same as "ask", in that any instance of "ask" in a program can be
replaced with "ask >> ask", or vice versa, without that changing the
program's semantics.


On Sun, Jun 3, 2018 at 9:47 AM Viktor Dukhovni <ietf-dane at dukhovni.org>
wrote:

>
>
> > On Jun 3, 2018, at 3:32 AM, Benjamin Fox <foxbenjaminfox at gmail.com>
> wrote:
> >
> > Here is the counterexample:
> >
> > instance MonadReader (IORef Int) IO where
> >     ask = newIORef 0
> >     local _ = id
> >
> > This obeys law (1): (newIORef 0 >> newIORef 0) == newIORef 0.
>
> Can you explain what you mean?
>
> Prelude> :m + Data.IORef
> Prelude Data.IORef> let z = 0 :: Int
> Prelude Data.IORef> a <- newIORef z
> Prelude Data.IORef> b <- newIORef z
> Prelude Data.IORef> let c = newIORef z
> Prelude Data.IORef> let d = newIORef z
> Prelude Data.IORef> a == b
> False
> Prelude Data.IORef> c == d
>
> <interactive>:8:1: error:
>     • No instance for (Eq (IO (IORef Int))) arising from a use of ‘==’
>     • In the expression: c == d
>       In an equation for ‘it’: it = c == d
>
> --
>         Viktor.
>
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