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An Exposition of Facts
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:- use_module(library(clpfd)). % grab some matrix functions | |
% Herein we present facts about boards. | |
% Given these facts, the user can consult Prolog for interesting | |
% inferences based on these facts. | |
% Example consultation: | |
% | |
% › swipl facts.pl | |
% Welcome to SWI-Prolog (threaded, 64 bits, version 7.6.1) | |
% SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free s | |
% oftware. | |
% Please run ?- license. for legal details. | |
% | |
% For online help and background, visit http://www.swi-prolog. | |
% org | |
% For built-in help, use ?- help(Topic). or ?- apropos(Word). | |
% | |
% Upper case variables are uninstantiated. We ask of prolog, | |
% "What terms will cause X to satisfy the board predicate?" | |
% | |
% And so our board is returned. | |
% | |
% ?- board(X). | |
% X = [[mine, 0, 0, 0], [0, 0, 0, 0], [0, mine, 0, 0], [0, 0, | |
% 0, 0]]. | |
% | |
% | |
% We then ask, "given that X is a board, R is the result of shifting | |
% that X left. What is R?" | |
% | |
% ?- board(X), shift(X, left, R). | |
% X = [[mine, 0, 0, 0], [0, 0, 0, 0], [0, mine, 0, 0], [0, 0, | |
% 0, 0]], | |
% R = [[0, 0, 0, 0], [0, 0, 0, 0], [mine, 0, 0, 0], [0, 0, 0, | |
% 0]] | |
% | |
% | |
% And then... | |
% "X is a board, and R is the solved board. Do you know what | |
% R looks like, perchance?" | |
% | |
% ?- board(X), solveBoard(X, R). | |
% X = [[mine, 0, 0, 0], [0, 0, 0, 0], [0, mine, 0, 0], [0, 0, 0, 0]], | |
% R = [[mine, 1, 0, 0], [2, 2, 1, 0], [1, mine, 1, 0], [1, 1, 1, 0]] | |
% | |
board([[mine, 0, 0, 0] | |
,[ 0, 0, 0, 0] | |
,[ 0, mine, 0, 0] | |
,[ 0, 0, 0, 0]]). | |
fill(Z, [], Z). | |
fill(X, [_|T], Z) :- | |
fill([0|X], T, Z). | |
horizVert(right, down). | |
horizVert(left, up). | |
shift([H|Tail], up, R) :- | |
fill([], H, Z), | |
append(Tail, [Z], R). | |
shift(Xs, down, R) :- | |
reverse(Xs, T1), | |
shift(T1, up, T2), | |
reverse(T2, R). | |
shift(Xs, [A, B], R) :- | |
shift(Xs, A, T1), | |
shift(T1, B, R). | |
shift(Xs, Horiz, Ys) :- | |
transpose(Xs, T1), | |
horizVert(Horiz, Vert), | |
shift(T1, Vert, T2), | |
transpose(T2, Ys). | |
m_add(M1, M2, M3) :- | |
maplist(maplist(m_sum), M1, M2, M3). | |
mineToInt(mine, 1). | |
mineToInt(X, X). | |
m_sum(X,Y,Z) :- | |
mineToInt(X, X1), | |
mineToInt(Y, Y1), | |
Z is X1 + Y1. | |
solveBoard(X, R) :- | |
shift(X, up, T1), | |
shift(X, down, T2), | |
shift(X, left, T3), | |
shift(X, right, T4), | |
shift(X, [up, left], T5), | |
shift(X, [up, right], T6), | |
shift(X, [down, left], T7), | |
shift(X, [down, right], T8), | |
BoardPermutations = [T2, T3, T4, T5, T6, T7, T8], | |
foldl(m_add, BoardPermutations, T1, SolvedBoard), | |
mask(X, SolvedBoard, R). | |
mask([], _, []). | |
mask([H|T], [X|Xs], [R|Rtail]) :- | |
mask1d(H, X, R), | |
mask(T, Xs, Rtail). | |
mask1d([], [], []). | |
mask1d([mine|T], [_|T2] , [mine|Acc]) :- mask1d(T, T2, Acc). | |
mask1d([_|T], [AdjacentMines|T2], [AdjacentMines|Acc]) :- mask1d(T, T2, Acc). |
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