From: Joachim Schimpf <jschimpf_at_coninfer.com>

Date: Mon, 08 Jul 2013 17:49:34 +0100

Date: Mon, 08 Jul 2013 17:49:34 +0100

This is a question from a few weeks ago, which I don't want to leave unanswered: On 23/06/2013 13:04, Claudio Cesar de Sá wrote: ... > 2. Really, the original idea is to formulate deterministics constraint like: > > ( X_var #= [1, 1, 0, 0] > OR > X_var #= [0, 1, 1, 0] > OR > X_var #= [0, 0, 1, 1] > ) > > As I could not find something to simulate this OR elegantly, > I used the member predicate, from a traditional logical programming. > > For a next time, how I can simulate a OR over an option list? There are several ways to do this. The most elegant is probably to use our magic library(propia), which can turn nondeterministic code into a deterministic constraint by simple annotation: :- lib(ic). :- lib(propia). dis1(Xs) :- ( Xs = [1, 1, 0, 0] ; Xs = [0, 1, 1, 0] ; Xs = [0, 0, 1, 1] ) infers ac. The 'ac' stands for 'arc consistency' and describes the resulting constraint propagation behaviour. For example: ?- dis1([X1, X2, X3, X4]). X1 = X1{[0, 1]} X2 = X2{[0, 1]} X3 = X3{[0, 1]} X4 = X4{[0, 1]} There are 4 delayed goals. Yes (0.00s cpu) ?- dis1([X1, X2, X3, X4]), X1 = 1. X1 = 1 X2 = 1 X3 = 0 X4 = 0 Yes (0.00s cpu) ?- dis1([X1, X2, X3, X4]), X1 = 0. X1 = 0 X2 = X2{[0, 1]} X3 = 1 X4 = X4{[0, 1]} There are 2 delayed goals. Yes (0.00s cpu) The way the library achieves this (in this case) is by rewriting the code into element/3 constraints -- as you can see by inspecting the delayed goals. Of course, you can do the same reformulation by hand. The idea is to introduce an index variable I to represent the 3 alternatives, resulting in: dis2([X1,X2,X3,X4]) :- element(I, [1,0,0], X1), element(I, [1,1,0], X2), element(I, [0,1,1], X3), element(I, [0,0,1], X4). This has the same behaviour as the code above. A third possible formulation is using reified constraints: dis3([X1,X2,X3,X4]) :- [X1,X2,X3,X4] :: 0..1, ( X1#=1 and X2#=1 and X3#=0 and X4#=0 or X1#=0 and X2#=1 and X3#=1 and X4#=0 or X1#=0 and X2#=0 and X3#=1 and X4#=1 ). but note that this has weaker constraint propagation behaviour, and does not achieve arc-consistency: ?- dis3([X1, X2, X3, X4]), X1 = 0. X1 = 0 X2 = X2{[0, 1]} X3 = X3{[0, 1]} X4 = X4{[0, 1]} There are 17 delayed goals. Yes (0.00s cpu) Cheers, JoachimReceived on Mon Jul 08 2013 - 16:49:46 CEST

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