Programming in Eclipse

Constraint ProgrammingIntroduction to Finite-DomainConstraint Logic ProgrammingAlan M. FrischArtificial Intelligence GroupDepartment of Computer ScienceUniversity of YorkUpdated 27 Nov 2008

Reversable Constraint Logic Program:Summing Elements of a ListProgramsumlist([],0).sumlist([H|T],Y) :- sumlist(T,X), Y #= H+X.Behaviour[eclipse 15]: sumlist([2,3],X).X = 5yes.[eclipse 16]: sumlist([2,X],5).X = 3yes.4

Reversable Constraint Logic Program:Summing Elements of a ListMore Behaviour[eclipse 17]: sumlist(X,Y).X = []Y = 0 More? (;)X = [H ]Y = H More? (;)X = [H , H ]Y = YDelayed goals: (This says Y #= H1 + H2)0 - H - H + Y #=0 More? (;)X = [H , H, H]Y = YDelayed goals: (This says X #= H1+H2, Y#= H3+X)0 - H - H + X #= 00 - X - H + Y #= 0 More? (;)5

How Logic Programs Operate• While the goal is not empty do– Use selection function to select a literal L in thegoal.– Non-deterministically chose a program clause,H :- B, such that H and L are unifiable. If there isno such clause, then Fail. Let θ be the mostgeneral unifier of H and L.– Modify the goal by replacing L with B and thenapplying θ to the goal• Succeed6

How Constraint Logic Programs Operate• Set the constraint store to empty• While goal is not empty do– Use selection function to select a literal L in thegoal.–If L is an ordinary logical literal then– Else add L to the constraint store– Simplify the constraint store (perhaps by GAC).If unsatisfiability is detected, then Fail• Succeedas before7

How Logic Programs Operate• While the goal is not empty do– Use selection function to select a literal L in thegoal.– Non-deterministically chose a program clausewhose head unifies with L. If there is no suchclause, then Fail. Let θ be the most generalunifier and B be the result of applying θ to thebody of the clause.– Modify the goal by replacing L with B• Succeed8

Example: Send More Money Problem (1):- lib(ic).sendmore1(Digits) :-Digits = [S,E,N,D,M,O,R,Y],Digits :: [0..9],alldifferent(Digits),S #\= 0,M #\= 0,1000*S + 100*E + 10*N + D+ 1000*M + 100*O + 10*R + E#= 10000*M + 1000*O + 100*N + 10*E + Y,labeling(Digits).9

Labeling• The predicate labeling is defined in ic library• Could easily be written aslabeling([]).labeling(H|T) :-indomain(H),labeling(T).• indomain is defined in the ic library.10

Example: Send More Money Problem (2)Idea: Use carries and set up a constraint foreach column.C1 C2 C3 C4S E N DM O R E________________________M O N E YWhat are the domains of the carry variables?11

Example: Send More Money Problem (2):- lib(ic).sendmore2(Digits) :-Digits = [S,E,N,D,M,O,R,Y],Digits :: [0..9],Carries = [C1,C2,C3,C4],Carries :: [0..1],alldifferent(Digits),S #\= 0, M #\= 0, C1 #= M,C2 + S + M #= O + 10*C1,C3 + E + O #= N + 10*C2,C4 + N + R #= E + 10*C3,D + E #= Y + 10*C4,labeling(Carries),labeling(Digits).What wouldhappen if thesewere swapped ?12

Example: N-Queens:- lib(ic).nqueens(N,Rows) :-length(Rows,N), % define N variablesRows::1..N, % give domains to varssafe(Rows), % impose constraintslabeling(Rows). % search13

Example: N-Queens (continued)/* ===== Set up the constraints ============ */safe(Rows) :-alldifferent(Rows),nondiagonal(Rows)./* no attacks on a diagonal */nondiagonal([]).nondiagonal([Column|Columns]) :-nonattack(Column,Columns,1),nondiagonal(Columns).nonattack(_,[],_).nonattack(Column1,[Column2|Columns],Offset) :-Column1 #\= Column2 + Offset,Column1 #\= Column2 - Offset,NewOffset is Offset + 1,nonattack(Column1, Columns, NewOffset).14

• In DepartmentEclipse System– Information (out of date) on Dept installation atwww.cs.york.ac.uk/support/linux/softcat.php?pkg=eclipse– Commands “eclipse” or “tkeclipse” or “jeclipe”starts version 6.0 #42• For your own computer– Download source and binaries for Linux, WindowsNT or other systems fromhttp://www.eclipse-clp.org15

Eclipse Documentation• Available at www.eclipse-clp.org• To get sarted, the most useful documents are– ECLIPSE: A Tutorial Introduction.– ECLIPSE Constraint Library Manual• Later use the on-line Reference Manual– Provides list of all libraries and a list of all built-inpredicate16

Introduction to Using Eclipse• To load the ic library for finite domains use either:-use_module(library(ic)).:-lib(ic).• To enter “input mode” use the command[user].and then exit with a control-d• To compile code in a file, use the command[filename].• To get history of command line:h.• To repeat a previous command:7.-1.17

Example: Magic Squares(from Joachim Schimpf):- lib(ic).magic(N) :-NN is N*N,% number of cellsSum is N*(NN+1)//2, % the magical sumprintf("Sum = %d%n", [Sum]),dim(Square, [N,N]), % make the variablesSquare[1..N,1..N] :: 1..NN,% set the domainsRows is Square[1..N,1..N],flatten(Rows, Vars),alldifferent(Vars), % cells are all different18

Example: Magic Squares (continued)( for(I,1,N),foreach(U,UpDiag),foreach(D,DownDiag),param(N,Square,Sum)doSum #= sum(Square[I,1..N]), % sum of row ISum #= sum(Square[1..N,I]), % sum of col IU is Square[I,I],D is Square[I,N+1-I]),Sum #= sum(UpDiag),% diagonal sumsSum #= sum(DownDiag),19

Example: Magic Squares (continued)Square[1,1] #< Square[1,N],Square[1,1] #< Square[N,N],Square[1,1] #< Square[N,1],Square[1,N] #< Square[N,1],mylabeling(Vars),print_square(Square).% symmetry removal% print resultprint_square(Square) :-dim(Square, [N,N]),( for(I,1,N), param(N,Square) do( for(J,1,N), param(I,Square) doField is Square[I,J],printf("%3d", Field)), nl), nl.20

Example: Magic Squares (continued)mylabeling(AllVars) :-( fromto(AllVars, Vars, Rest, []) dodelete(X,Vars,Rest,0,first_fail),indomain(X,min)).An alternative:mylabeling(AllVars,UpDiag,DownDiag) :-labeling(UpDiag),labeling(DownDiag),labeling(AllVars),21