[Haskell-cafe] unapplying function definitions?

[Thomas Davie]

On 4 May 2008, at 17:33, PR Stanley wrote:

> Hi
> What on earth is unapplying function definitions?
> The following is taken from chapter 13 of the Hutton book:
> "...when reasoning about programs, function definitions can be both  
> applied from left to right and unapplied from right to left."

Well, because of referential transparency, we can say that the left  
hand side of a function is exactly equal to the right hand side.   
Thus, we can instead of applying functions, and making progress  
towards a normal form, unapply them and get further away from a normal  
form... for example:

5 = head [5,6,7,8,9] = head ([5,6] ++ [7] ++ [8,9]) = head (([] ++ [5]  
++ [6]) ++ [7] ++ [8,9]) .......

There are of course an infinite number of ways of doing this, so it's  
usually only interesting, if we have some reason for applying a  
specific expansion.

Bob