417 lines
14 KiB
Prolog
417 lines
14 KiB
Prolog
%%% -*- Mode: Prolog; -*-
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% $Date: 2011-11-28 14:41:26 +0100 (Mon, 28 Nov 2011) $
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% $Revision: 6764 $
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%
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% This file is part of ProbLog
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% http://dtai.cs.kuleuven.be/problog
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%
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% ProbLog was developed at Katholieke Universiteit Leuven
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%
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% Copyright 2009
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% Angelika Kimmig, Vitor Santos Costa, Bernd Gutmann
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%
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% Main authors of this file:
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% Bernd Gutmann
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% Artistic License 2.0
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Discrete probability distributions for ProbLog
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%
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% this file contains predicates to emulate discrete distributions in ProbLog
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%
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% uniform(I,N,ID)
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% emulates a uniform discrete distribution
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% P(I) = 1/N for I in {1,2,...,N}
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% If I is a variable, the predicate backtracks over all
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% possible values for I
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% ID has to be ground, it is an identifier which - if in the same proof -
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% reused, will always return the same value
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%
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% binomial(K,N,P,ID)
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% emulates a binomial distribution
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% P(K) = (N over K) x P^K x (1-P)^(N-K) for K in {0,1,...,N}
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% If K is a variable, the predicate backtracks over all
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% possible values for K
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% ID has to be ground, it is an identifier which - if in the same proof -
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% reused, will always return the same value
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%
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% poisson(K,Lambda,ID)
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% emulates a Poisson distribution
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% P(K) = Lamda^K / K! x exp(-Lambda) for K in {0,1,2, ....}
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% If K is a variable, the predicate backtracks over all
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% possible values for K
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% ID has to be ground, it is an identifier which - if in the same proof -
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% reused, will always return the same value
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%
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%
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% Author : Bernd Gutmann, bernd.gutmann@cs.kuleuven.be
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% Version : January 14, 2009
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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:- module(discrete, [uniform/3,binomial/4,poisson/3]).
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:- use_module('../problog').
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% A distribution over 1,2, ..., N
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% where P(I) := 1/N
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Prob::p_uniform(_I,_N,_ID,Prob).
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uniform(I,N,ID) :-
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integer(N),
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N>0,
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( var(I) ; integer(I), I>0, I=<N),
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uniform(1,I,true,N,ID).
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uniform(I,I,Old,N,ID) :-
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I=<N,
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FactProb is 1/(N-I+1),
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call(Old),
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p_uniform(I,N,ID,FactProb).
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uniform(I,I2,Old,N,ID) :-
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I<N,
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FactProb is 1/(N-I+1),
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NextI is I+1,
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uniform(NextI,I2,(problog_not(p_uniform(I,N,ID,FactProb)),Old),N,ID).
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Binomial Distribution
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% K in { 0,1,2,3, ... }
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% Lambda >= 0
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Prob::p_binomial(_K,_N,_P,_ID,Prob).
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binomial(K,N,P,ID) :-
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number(P),
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P >= 0,
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P =< 1,
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integer(N),
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N>=0,
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( var(K) ; integer(K),K>=0,K=<N),
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binomial(0,K,N,P,true,0.0,ID).
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binomial(K,KResult,N,P,Old,ProbAcc,ID) :-
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% KResult is a number, make sure, not to go over it
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% safes some time
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(
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number(KResult)
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->
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K=<KResult;
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true
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),
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binomial_coefficient(N,K,BinomCoeff),
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Prob is BinomCoeff * (P ** K) * ((1-P) ** (N-K)),
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FactProb is Prob / (1-ProbAcc),
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% this check stops the derivation, if the floating-point-based
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% rounding errors get too big
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FactProb > 0.0,
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FactProb =< 1.0,
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(
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(
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call(Old),
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p_binomial(K,N,P,ID,FactProb),
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KResult=K
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); (
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K<N,
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NextK is K+1,
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NextProbAcc is ProbAcc+Prob,
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binomial(NextK,KResult,N,P,(problog_not(p_binomial(K,N,P,ID,FactProb)),Old),NextProbAcc,ID)
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)
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).
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Poisson Distribution
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% K in { 0,1,2,3, ... } or var(K)
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% Lambda >= 0
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% ID has to be ground
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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P :: p_poisson(_K,_Lambda,_ID,P).
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poisson(K,Lambda,ID) :-
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( var(K); integer(K),K>=0 ),
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number(Lambda),
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Lambda>=0,
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ground(ID),
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poisson(0,K,true,Lambda,0.0,ID).
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poisson(K,K2,Old,Lambda,ProbAcc,ID) :-
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% KResult is a number, make sure, not to go over it
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% safes some time
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(
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integer(K2)
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->
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K=<K2;
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true
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),
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power_over_factorial(K,Lambda,Part1),
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% Prob is P(K) for a Poisson distribution with Lambda
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Prob is Part1 * exp(-Lambda),
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% now we have to determine the fact probability
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% conditioned on the aggregated probabilities so far
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FactProb is Prob/(1-ProbAcc),
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% this check stops the derivation, if the floating-point-based
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% rounding errors get too big
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FactProb > 0.0,
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FactProb =< 1.0,
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(
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(
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call(Old),
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p_poisson(K,Lambda,ID,FactProb),
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K2=K
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); (
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NextK is K+1,
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NextProbAcc is ProbAcc+Prob,
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poisson(NextK,K2,(problog_not(p_poisson(K,Lambda,ID,FactProb)),Old),Lambda,NextProbAcc,ID)
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)
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).
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% calculates (Lambda ** N) / N!
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power_over_factorial(N,Lambda,Result) :-
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integer(N),
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N>=0,
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power_over_factorial(N,Lambda,1.0,Result).
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power_over_factorial(N,Lambda,Old,Result) :-
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(
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N>0
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->
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(
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N2 is N-1,
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New is Old * Lambda/N,
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power_over_factorial(N2,Lambda,New,Result)
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); Result=Old
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).
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% calculates (N \over K) = N!/(K! * (N-K)!)
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binomial_coefficient(N,K,Result) :-
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integer(K),
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K >= 0,
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binomial_coefficient(K,N,1,Result).
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binomial_coefficient(I,N,Product,Result) :-
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(
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I=0
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->
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Result=Product;
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(
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I2 is I-1,
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Product2 is Product * (N+1-I)/I,
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binomial_coefficient(I2,N,Product2,Result)
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)
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). |