%% Monotone Aggregation

% Schema
%-------
database({sure(Person:string),
	  friend(Person:string, Friend:string)}).

%Derivated predicates and rules
%------------------------------
% first, the primitive mcount
single(mcount, Y, 1).
multi(mcount, Y, Old, New) <-  New=Old+1.
ereturn(mcount, Y, Old, New) <- if(Old=nil then New = 1
					   else New = Old+1).

willcome(P)<-  sure(P).
willcome(P)<-  c_friends(P, K), K >= 3.
c_friends(P, mcount<F>) <-  willcome(F), friend(P, F).

export willcome(X).

% second, the more advanced kcount
single(kcount, (K,Y), 1).
multi(kcount, (K,Y), Old, New) <- Old<K, New=Old+1. 
ereturn(kcount, (K,Y), K1, 'yes') <- K1+1=K.

wllcm(F,yes) <- sure(F).
wllcm(X,kcount<(3,F)>) <- wllcm(F,_), friend(X,F).

export wllcm(X, Y).

% third, the even more advance zcount
single(zcount, (K,X), 1).
multi(zcount,  (K,X), Old, New) <- Old < K, New=Old+1.
ereturn(zcount, (K,X), K1) <- K1~=nil, K=K1+1.

wllcom(F) <- sure(F).
wllcom(X, zcount<(3,F)>) <- wllcom(F), friend(X, F).

export wllcom(X).