% Risk Analysis for a system described in terms of and/or tree

% sample tree: 1 fails if both 2 and 3 happen, 2 happens when either, 4
% or 5 happens.   When can the system fail?
and(1, 2, 3).
or(2,4,5).

go:-risk(1,P), write(P), nl, fail.

% p  operates on a list of events representing the probabillty
% of ALL of them occuring. p([1,2,3]) is the probability of 1,2,and 3
% all happening at one time.

% risk(N, P) is true when event N has probabillity P
risk([],p([])):-!.
risk(A,p(PA)):-and(A,B,C),!,risk(C,p(PC)),risk(B,p(PB)),merge(PC,PB,PA).
risk(A,p(P)+p(Q)-p(R)):- or(A,B,C),!, risk(B, p(P)), risk(C, p(Q)),join(P,Q,R).
risk(A,p([A])).

merge(A,A,A):-!.
merge([],A,A):-!.
merge(A,[],A):-!.
merge([X|R],[X|S],[X|T]):-!,merge(R,S,T).
merge([X|R],[Y|S],[X|T]):-X<Y,!,merge(R,[Y|S],T).
merge([X|R],[Y|S],[Y|T]):-Y<X,!,merge([X|R],S,T).

join(A,A,A):-!.
join([],A,A):-!.
join(A,[],A):-!.
join([X|R],[X|S],[X|T]):-!,join(R,S,T).
join([X|R],[Y|S],T):-X<Y,!,join(R,[Y|S],T).
join([X|R],[Y|S],T):-Y<X,!,join([X|R],S,T).