- library
- clp
- clpfd.pl -- CLP(FD): Constraint Logic Programming over Finite Domains
- in/2
- ins/2
- indomain/1
- label/1
- labeling/2
- all_different/1
- all_distinct/1
- sum/3
- scalar_product/4
- #>=/2
- #=</2
- #=/2
- #\=/2
- #>/2
- #</2
- #\/1
- #<==>/2
- #==>/2
- #<==/2
- #/\/2
- #\//2
- #\/2
- lex_chain/1
- tuples_in/2
- serialized/2
- element/3
- global_cardinality/2
- global_cardinality/3
- circuit/1
- cumulative/1
- cumulative/2
- disjoint2/1
- automaton/3
- automaton/8
- transpose/2
- zcompare/3
- chain/2
- fd_var/1
- fd_inf/2
- fd_sup/2
- fd_size/2
- fd_dom/2
- clpb.pl -- CLP(B): Constraint Logic Programming over Boolean Variables
- clpfd.pl -- CLP(FD): Constraint Logic Programming over Finite Domains
- clp
- automaton(+Sequence, ?Template, +Signature, +Nodes, +Arcs, +Counters, +Initials, ?Finals)
- Describes a list of finite domain variables with a finite
automaton. True iff the finite automaton induced by Nodes and Arcs
(extended with Counters) accepts Signature. Sequence is a list of
terms, all of the same shape. Additional constraints must link
Sequence to Signature, if necessary. Nodes is a list of
source(Node)andsink(Node)terms. Arcs is a list ofarc(Node,Integer,Node)andarc(Node,Integer,Node,Exprs)terms that denote the automaton's transitions. Each node is represented by an arbitrary term. Transitions that are not mentioned go to an implicit failure node. Exprs is a list of arithmetic expressions, of the same length as Counters. In each expression, variables occurring in Counters symbolically refer to previous counter values, and variables occurring in Template refer to the current element of Sequence. When a transition containing arithmetic expressions is taken, each counter is updated according to the result of the corresponding expression. When a transition without arithmetic expressions is taken, all counters remain unchanged. Counters is a list of variables. Initials is a list of finite domain variables or integers denoting, in the same order, the initial value of each counter. These values are related to Finals according to the arithmetic expressions of the taken transitions.The following example is taken from Beldiceanu, Carlsson, Debruyne and Petit: "Reformulation of Global Constraints Based on Constraints Checkers", Constraints 10(4), pp 339-362 (2005). It relates a sequence of integers and finite domain variables to its number of inflexions, which are switches between strictly ascending and strictly descending subsequences:
sequence_inflexions(Vs, N) :- variables_signature(Vs, Sigs), automaton(Sigs, _, Sigs, [source(s),sink(i),sink(j),sink(s)], [arc(s,0,s), arc(s,1,j), arc(s,2,i), arc(i,0,i), arc(i,1,j,[C+1]), arc(i,2,i), arc(j,0,j), arc(j,1,j), arc(j,2,i,[C+1])], [C], [0], [N]). variables_signature([], []). variables_signature([V|Vs], Sigs) :- variables_signature_(Vs, V, Sigs). variables_signature_([], _, []). variables_signature_([V|Vs], Prev, [S|Sigs]) :- V #= Prev #<==> S #= 0, Prev #< V #<==> S #= 1, Prev #> V #<==> S #= 2, variables_signature_(Vs, V, Sigs).Example queries:
?- sequence_inflexions([1,2,3,3,2,1,3,0], N). N = 3. ?- length(Ls, 5), Ls ins 0..1, sequence_inflexions(Ls, 3), label(Ls). Ls = [0, 1, 0, 1, 0] ; Ls = [1, 0, 1, 0, 1].