[Haskell-cafe] "show" for functional types

[Christopher Brown]

>
> 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.
>


Another example:

In haskell the following is true:

f x + g x == g x + f x

Pure functions in Haskell do not have side effects, so for the same  
inputs they always give back the same output. This is referential  
transparency.
In a language such as C, which does not have referential  
transparency, the functions f and g may change x by a side effect and  
therefore:

f x + g x /= g x +  f x

In C (or a language with side effects).

Cheers,

Chris.

Christopher Brown
PhD Student, University of Kent.
http://www.cs.kent.ac.uk/people/rpg/cmb21/
cmb21 at kent.ac.uk