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name = 'prog_8puzzle/3'
slug = '8-puzzle-solving language with semantics'
description = '''\
<p>Write a DCG for solving 8-puzzles. The syntax for this language should be the same as in the previous exercise: the first symbol in every word is <code>[begin]</code>, followed by any sequence of "instruction" symbols from the set {<code>left</code>, <code>right</code>, <code>up</code>, <code>down</code>}, and finally <code>[end]</code>. The starting symbol should be named <code>prog_8puzzle</code>.</p>
<p>The meaning of a word (program) in this language has the form <code>In-->Out</code>, mapping from input to output states. Each state is a (permuted) list of numbers from 0 to 8, where 0 stands for the empty square and other numbers for the corresponding tiles. The first three numbers in the list correspond to the top row of the 8-puzzle, the next three numbers to the middle row, and the last three numbers to the last row. The meaning of instructions <code>left</code>, <code>right</code>, <code>up</code> and <code>down</code> is to move the blank tile in the given direction.</p>
<pre>
?- prog_8puzzle([0,1,2,3,4,5,6,7,8]-->Out, [begin,down,right,end], []).
Out = [3,1,2,4,0,5,6,7,8].
</pre>
<p>Helper predicates (already defined):<br />
<code>findblank(List,I)</code> returns the 1-based index <code>I</code> of the element 0 in <code>List</code><br />
<code>swap(List,I,J,NewList)</code> creates <code>NewList</code> by swapping elements <code>I</code> and <code>J</code> in <code>List</code></p>'''
hint = {}
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