FunctionalSequence.java

/*
 * Copyright (c) 2013, SRI International
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 * Licensed under the The BSD 3-Clause License;
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package com.sri.ai.util.functionalsequence;

import java.util.Iterator;

import com.google.common.annotations.Beta;

/**
 * <p>
 * Intuitively, a functional sequence is the sequence formed by an (optional)
 * initial arbitrary value, followed by the results of applying a function to a
 * set of arguments, when these arguments are updated, one at a time. Each
 * argument is updated from a specific sequence itself, and when that sequence
 * reaches its end, that argument is no longer updated. The main sequence stops
 * being generated when all arguments have no longer values to be updated with.
 * <p>
 * Here is a more precise definition: let f be a n-ary function from arguments
 * of type V to a set T and s_1, ..., s_n be n (possibly infinite) sequences,
 * with s_{i,j} the j-th element of the sequence s_i. Let k be a (possibly
 * infinite) sequence of index arrays (k_{1,1} ... k_{1,n}), ..., (k_{m,1}, ...,
 * k_{m, n}), ..., where k_{t,i} is an integer greater than 0, k_{1,i} = 1 for
 * all i, and each array k_t differs from k_{t+1} in exactly one element i(t),
 * and k_{t+1,i(t)} = k_{t,i(t)} + 1. Let f0 be an initial value in CoDomain.
 * Then the functional sequence fs(f, f0, s, k) is the sequence f0,
 * f(s_{1,k_{1,1}}, ..., s_{n,k_{1,n}}), ..., f(s_{1,k_{t,1}}, ...,
 * s_{n,k_{t,n}}), ...
 * <p>
 * 
 * @author braz
 * 
 * @param <CoDomain>
 *            the type of the co-domain.
 */
@Beta
public interface FunctionalSequence<CoDomain> extends Iterator<CoDomain> {

}