/*
Throwing a coin with uncertainty on its fairness, from
J. Vennekens, S. Verbaeten, and M. Bruynooghe. Logic programs with annotated 
disjunctions. In International Conference on Logic Programming, 
volume 3131 of LNCS, pages 195-209. Springer, 2004.
*/
:- use_module(library(pita)).
:- use_module(library(cplint_r)).

:- if(current_predicate(use_rendering/1)).
:- use_rendering(graphviz).
:- use_rendering(table,[header(['Multivalued variable index','Rule index','Grounding substitution'])]).
:- endif.

:- pita.

:- begin_lpad.

heads(Coin): 1/2; tails(Coin) : 1/2:-toss(Coin),\+biased(Coin).
% if we toss a Coin that is not biased then it lands heads with probability 1/2
% and tails with probability 1/2
heads(Coin): 0.6 ; tails(Coin) : 0.4:-toss(Coin),biased(Coin).
% if we toss a Coin that is biased then it lands heads with probability 0.6
% % and tails with probability 0.4
fair(Coin):0.9 ; biased(Coin):0.1.
% a Coin is fair with probability 0.9 and biased with probability 0.1
toss(coin).
% coin is certainly tossed

:- end_lpad.

/** <examples>

?- prob(heads(coin),Prob).  % what is the probability that coin lands heads?
% expected result 0.51
?- prob(tails(coin),Prob).  % what is the probability that coin lands tails?
% expected result 0.49
?- prob(heads(coin),Prob),bar_r(Prob).  % what is the probability that coin lands heads?
% expected result 0.51
?- prob(tails(coin),Prob),bar_r(Prob).  % what is the probability that coin lands tails?
% expected result 0.49

?- prob(heads(coin),biased(coin),Prob).  
% what is the probability that coin lands heads given the coin is biased?
% expected result 0.6

?- bdd_dot_string(heads(coin),BDD,Var).  
% What is the BDD for query heads(coin)?
% A solid edge indicates a 1-child, a dashed edge indicates a 0-child and 
% a dotted 
% edge indicates a negated 0-child.
% The table Var contains the associations between the rule groundings and the
% multivalued variables.

*/