[Haskell-cafe] "show" for functional types

[Greg Buchholz]

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