How to get predecessor of a church numeral

I'm practicing with SML and I'm doing a small assignment where we have to implement Church numerals defined as:

datatype 'a 开发者_如何学编程church = C of ('a -> 'a) * 'a  -> 'a

example val

ZERO = C(fn (f,x) => x)

I have already implemented the functions:

create: int -> 'a church  
churchToInt: 'a church -> int  

and SUC which returns the successor of a Church numeral.

Now I have to implement the function

PRED: 'a church -> 'a church * 'a church  

which returns the tuple of (predecessor, current numeral). I am not allowed to use churchToInt, I should directly work with Church numerals. Apparently this is solvable in one line by passing a specific argument.

I was thinking of just using SUC over and over until we hit the right number but there is no way for me to compare the 2 Church numerals. I am completely stuck on this.

suppose you want to construct the function that give you the pred of N. You have to use pairs on numbers like this (0,1) (1,2) ....(n,n+1) and construct the succPair function to go from (n-1,n) to (n,n+1) and then you apply succPair N times on (0,1) and last step you just apply snd on the last result I described and then boom! you get your pred of N look here to get the picture http://m2-info-upmc.blogspot.fr/2012/11/predecesseur-sur-les-entiers-de-church.html

You must have forced it to by an int in your subPred.