Prolog Day Three
Written on July 11, 2014
The final chapter on Prolog looks at constraint programming — namely, describing the rules for the Sudoku and Eight Queens puzzles and having Prolog solve them for you. I think these are the types of programming problems where Prolog would be the Right Tool for the Job™.
Input & output
Prolog has some input/output features as well. Find print predicates that print out variables.
I found the
write/1 predicate and gave it a test-drive.
| ?- write("Hello!"). [72,101,108,108,111,33] yes
Well that was weird! It gave me a list of integers. If I change the style of quotes I use however…
| ?- write('Hello!'). Hello! yes
… it works as expected. I’m not exactly sure why Prolog differentiates between the two, or what that would be useful for.
I found a paper by Vladimir Vacic and Christos Koufogiannakis that covers the rest of the I/O predicates.
Find a way to use the print predicates to print only successful solutions. How do they work?
I’m not sure if I’m understanding the question correctly, but I found that Prolog supports conditional statements with an arrow syntax. Here’s an example where I compare two numbers and print the result conditionally.
greater(X, Y) :- X > Y -> write('It’s greater.') ; write('Nope.').
This is essentially a one-liner, but I divided it up so the syntax is clearer. Prolog is not indent-sensitive.
Modify the Sudoku solver to work on 9×9 puzzles.
The book provides a Prolog script that solves 4×4 Sudoku puzzles. The script contains surprisingly little logic; the bulk of the code outlines structures to represent each row, column, and square in the game. Here’s the script, modified to work on 9×9 puzzles.
valid(). valid([Head|Tail]) :- fd_all_different(Head), valid(Tail). sudoku(Puzzle, Solution) :- Solution = Puzzle, Puzzle = [S11, S12, S13, S14, S15, S16, S17, S18, S19, S21, S22, S23, S24, S25, S26, S27, S28, S29, S31, S32, S33, S34, S35, S36, S37, S38, S39, S41, S42, S43, S44, S45, S46, S47, S48, S49, S51, S52, S53, S54, S55, S56, S57, S58, S59, S61, S62, S63, S64, S65, S66, S67, S68, S69, S71, S72, S73, S74, S75, S76, S77, S78, S79, S81, S82, S83, S84, S85, S86, S87, S88, S89, S91, S92, S93, S94, S95, S96, S97, S98, S99], fd_domain(Solution, 1, 9), Row1 = [S11, S12, S13, S14, S15, S16, S17, S18, S19], Row2 = [S21, S22, S23, S24, S25, S26, S27, S28, S29], Row3 = [S31, S32, S33, S34, S35, S36, S37, S38, S39], Row4 = [S41, S42, S43, S44, S45, S46, S47, S48, S49], Row5 = [S51, S52, S53, S54, S55, S56, S57, S58, S59], Row6 = [S61, S62, S63, S64, S65, S66, S67, S68, S69], Row7 = [S71, S72, S73, S74, S75, S76, S77, S78, S79], Row8 = [S81, S82, S83, S84, S85, S86, S87, S88, S89], Row9 = [S91, S92, S93, S94, S95, S96, S97, S98, S99], Col1 = [S11, S21, S31, S41, S51, S61, S71, S81, S91], Col2 = [S12, S22, S32, S42, S52, S62, S72, S82, S92], Col3 = [S13, S23, S33, S43, S53, S63, S73, S83, S93], Col4 = [S14, S24, S34, S44, S54, S64, S74, S84, S94], Col5 = [S15, S25, S35, S45, S55, S65, S75, S85, S95], Col6 = [S16, S26, S36, S46, S56, S66, S76, S86, S96], Col7 = [S17, S27, S37, S47, S57, S67, S77, S87, S97], Col8 = [S18, S28, S38, S48, S58, S68, S78, S88, S98], Col9 = [S19, S29, S39, S49, S59, S69, S79, S89, S99], Sqr1 = [S11, S12, S13, S21, S22, S23, S31, S32, S33], Sqr2 = [S14, S15, S16, S24, S25, S26, S34, S35, S36], Sqr3 = [S17, S18, S19, S27, S28, S29, S37, S38, S39], Sqr4 = [S41, S42, S43, S51, S52, S53, S61, S62, S63], Sqr5 = [S44, S45, S46, S54, S55, S56, S64, S65, S66], Sqr6 = [S47, S48, S49, S57, S58, S59, S67, S68, S69], Sqr7 = [S71, S72, S73, S81, S82, S83, S91, S92, S93], Sqr8 = [S74, S75, S76, S84, S85, S86, S94, S95, S96], Sqr9 = [S77, S78, S79, S87, S88, S89, S97, S98, S99], valid([Row1, Row2, Row3, Row4, Row5, Row6, Row7, Row8, Row9, Col1, Col2, Col3, Col4, Row5, Row6, Row7, Row8, Row9, Sqr1, Sqr2, Sqr3, Sqr4, Sqr5, Sqr6, Sqr7, Sqr8, Sqr9]).
This challenge wasn’t particularly exciting, as I really only extended the script I found in the book. I did however start searching for a way to not have to write out all of those lists manually, and after a couple of hours of chatting to a seasoned Prolog developer on IRC I was pointed towards a less verbose solution:
:- use_module(library(clpfd)). sudoku(Rows) :- length(Rows, 9), maplist(length_(9), Rows), append(Rows, Vs), Vs ins 1..9, maplist(all_distinct, Rows), transpose(Rows, Columns), maplist(all_distinct, Columns), Rows = [A,B,C,D,E,F,G,H,I], blocks(A, B, C), blocks(D, E, F), blocks(G, H, I). length_(L, Ls) :- length(Ls, L). blocks(, , ). blocks([A,B,C|Bs1], [D,E,F|Bs2], [G,H,I|Bs3]) :- all_distinct([A,B,C,D,E,F,G,H,I]), blocks(Bs1, Bs2, Bs3). problem(1, [[_,_,_,_,_,_,_,_,_], [_,_,_,_,_,3,_,8,5], [_,_,1,_,2,_,_,_,_], [_,_,_,5,_,7,_,_,_], [_,_,4,_,_,_,1,_,_], [_,9,_,_,_,_,_,_,_], [5,_,_,_,_,_,_,7,3], [_,_,2,_,1,_,_,_,_], [_,_,_,_,4,_,_,_,9]]).
I’m absolutely convinced that Prolog is a powerful tool and it’s worth coming back to. Since it has such little relation to the rest of the [imperative and functional] languages in Seven Languages in Seven Weeks, I don’t feel just a few chapters is enough to catalyse declarative thought. It’s certainly whet my appetite though.