% An experiment - Prolog is good at searching, how about a binary search?
:-style_check(-singleton).

% Binary search.... 
%   Given: a monotonic increasing function f on a
%          finite set of integers lo..hi, 
%          and a value y in f(lo)..f(hi)
%   Goal: Find an x in lo..hi such that f(x)<=y<f(x+1).
%
%   Operations: Arithmetic on lo..hi

%   Note. in Prolog we think of f as a relation f(x,y) defined like
% the following example.
f(X,Y):- Y is X*X.

bsearch(X,Lo,Hi,Y):-Hi=:=Lo+1, X is Lo.
bsearch(X,Lo,Hi,Y):-Hi < Lo+1, fail.
bsearch(X,Lo,Hi,Y):-Hi>= Lo+1, Mid is (Lo+Hi)//2, 
		f(Mid, Val),
		( Val=<Y, bsearch(X,Mid,Hi,Y)
		; Val>Y,  bsearch(X,Lo,Mid,Y)
		).

go:-bsearch(X,1,100,49), nl,nl,print(X),nl.