Action Rules (AR)

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Action Rules (AR)

• Early Implementation methods
• Complex abstract machines (e.g., CHIP)
• Special purpose constructs
• Indexicals, delay constructs, attribute variables
• General purpose language (CHR)
• Motivation of AR
• A powerful , flexible, and efficient language for
  implementing propagation-based constraint solvers

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Suspension Domain Variables

• Suspension variables
• susp_attach_term(X,T)
• Attach term T to X
• susp_attached_term(X,T)
• The attached term to X is T
• Domain variables
• fd_var(V),fd_first(V,N),fd_last(V,N),fd_size(V,N)
  ,fd_true(V,E),fd_set_false(V,E),fd_next(V,E,NextE
  ),fd_prev(V,E,PrevE)

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Syntax and Semantics of AR

• Syntax

Agent, Condition, Event gt Action

• Operational semantics
• An agent (sub-goal) C will be suspended if
• C matches Agent,
• Condition is met, and
• Event is not empty
• C is activated whenever an event in Event is
  posted
• Action is executed when C is activated and
  Condition is met
• C is suspended again after Action is executed
• The next rule is tried if Condition fails
• C fails if Action fails

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Posting Events post(E)

• event(X,O)
• X suspension variable
• O event object
• Events for programming propagators
• ins(X) X is instantiated
• bound(X) The bound of the domain of X is
  updated
• dom(X,E) E is excluded from the domain of X

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Example 1An Echoing Agent
echo_agent(X), event(X,Message) gt
write(Message),nl.
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Example 2freeze(X,G)
freeze(X,G), var(X), ins(X) gt
true. freeze(X,G) gt call(G).
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Propagators for aXbYc

• Forward checking

'aXbYc_forward'(A,X,B,Y,C),var(X),var(Y), ins(
X),ins(Y) gt true. 'aXbYc_forward'(A,X,B,Y,
C),var(X) gt T is BYC,Ex is T//A,
AExT. 'aXbYc_forward'(A,X,B,Y,C) gt
T is AX-C, Ey is T//B, BEyT.
When either X or Y is instantiated, instantiate
the other variable.
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Propagators for aXbYc

• Interval consistency

'aX in bYc_interval'(A,X,B,Y,C),var(X),var(Y),
bound(Y) gt 'aX in
bYc_reduce_domain'(A,X,B,Y,C). 'aX in
bYc_interval'(A,X,B,Y,C) gt true.
Whenever the bound of Ys domain is
updated, reduce Xs domain to achieve interval
consistency.
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Propagators for aXbYc

• Arc consistency

'aX in bYc_arc'(A,X,B,Y,C),var(X),var(Y), dom(
Y,Ey) gt T is BEyC,
Ex is T//A, (AExT -gt
exclude(X,Ex)true). 'aX in
bYc_arc'(A,X,B,Y,C) gt true.
Whenever an element Ey is excluded from Ys
domain, exclude Eys counterpart Ex from Xs
domain.
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Propagator for A1X1...AnXnC 0
'A1X1...AnXnC0'(C,A1,A2,...,An,X1,X2,..,Xn)
, n_vars_gt(n,2), ins(X1),bound(X1),...,ins(Xn)
,bound(Xn) gt reduce domains of
X1,..,Xn to achieve ic. 'A1X1...AnXnC0'(
C,A1,A2,...,An,X1,X2,..,Xn) gt
nary_to_binary(NewC,B1,B2,Y1,Y2),
call_binary_propagator(NewC,B1,Y1,B2,Y2).
When the constraint has more than 2
variables, achieve interval consistency. When
the constraint is binary archive arc consistency.
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Performance EvaluationCLP(FD)
BP 6.4, Eclipse (EP) 5.5 46, Sicstus (SP) 3.10,
Gnu-Prolog (GP) 1.2.16)
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Performance EvaluationCLP(SET)
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Papers

• N.F. Zhou Programming Finite-Domain Constraint
  Propagators in Action Rules, submitted to TPLP,
  2004.
• N.F. Zhou Implementing Constraint Solvers in
  B-Prolog, IFIP World Congress, Intelligent
  Information Processing, pp.249-260, 2002.
• N.F. Zhou A High-Level Intermediate Language and
  the Algorithms for Compiling Finite-Domain
  Constraints, Proc. Joint International Conference
  and Symposium on Logic Programming, pp.70-84,
  1998.
• N.F. Zhou and J.Schimpf Implementation of
  Propagation Rules for Set Constraints Revisited,
  unpublished manuscript, 2002.