
== CSP ==

This is a Chicken Scheme egg which solves constraint satisfaction
problems.

A CSP is composed of a number of ''domain-variable''s that have a
domain, a set of bindings they can assume, along with a number of
constraints. This egg supports 5 kinds of constraints: ''efd'' (early
failure detection), ''fc'' (forward checking), ''vp'' (value
propagation), ''gfc'' (generalized forward checking) and ''ac'' (arc
consistency).

==== High-level ====

:(csp-solution domain-variables select)

Given a list of domain variables and a function to select which one to
try to bind next, one can simply pass in ''first'', this produces a
solution to the CSP.

:(create-domain-variable domain)

Create a domain variable whose domain is ''domain''.

:(assert-constraint! constraint domain-variables)

Assert a constraint, a function that returns a boolean, between a
number of domain variables. The kind of constraint is determined by
inspecting ''*strategy*''. Valid types are: ''efd'' (early failure
detection), ''fc'' (forward checking), ''vp'' (value propagation),
''gfc'' (generalized forward checking) and ''ac'' (arc
consistency). The default is ''ac''. For constraints of low arity, a
small number of domain variables, it will use an optimized version of
the constraint propagation code.

:(bound? domain-variable)
:(binding domain-variable)

Determine if the domain variable is bound and what its binding is.

==== Constraints ====

:(assert-unary-constraint-efd! constraint x)
:(assert-binary-constraint-efd! constraint x y)
:(assert-ternary-constraint-efd! constraint x y z)
:(assert-unary-constraint-fc! constraint x)
:(assert-binary-constraint-fc! constraint x y)
:(assert-ternary-constraint-fc! constraint x y z)
:(assert-unary-constraint-vp! constraint x)
:(assert-binary-constraint-vp! constraint x y)
:(assert-ternary-constraint-vp! constraint x y z)
:(assert-unary-constraint-gfc! constraint x)
:(assert-binary-constraint-gfc! constraint x y)
:(assert-ternary-constraint-gfc! constraint x y z)
:(assert-unary-constraint-ac! constraint x)
:(assert-binary-constraint-ac! constraint x y)
:(assert-ternary-constraint-ac! constraint x y z)

Assert each of the 5 kinds of constraints between domain-variables
''x'', ''y'' and ''z''. You can always use ''assert-constraint!''
instead and it will default to these functions if your constraint is
of low arity.

:(assert-constraint-efd! constraint ds)
:(assert-constraint-fc! constraint ds)
:(assert-constraint-vp! constraint ds)
:(assert-constraint-gfc! constraint ds)
:(assert-constraint-ac! constraint ds)

Assert each of the 5 kinds of constraints between the list of
domain-variables ds. You can always use ''assert-constraint!''
instead as it will pick an optimized version for each of the above if
the arity of the constraint is low.

==== Low-level ====

:(attach-before-demon! demon x)
:(attach-after-demon! demon x)
:(restrict-domain! x domain)

Only of interest to implementers.

=== Examples ===

This solves [[http://projecteuler.net/problem=43|Project Euler problem 43]].

  (use traversal nondeterminism csp)
  (let* ((ds (map-n (lambda _ (create-domain-variable (map-n identity 10))) 10))
  	(d3 (lambda (ns) (+ (* (first ns) 100) (* (second ns) 10) (third ns))))
  	(div (lambda (n) (lambda ns (= (modulo (d3 ns) n) 0))))
  	(nthd (lambda (a b) (sublist ds (- a 1) b))))
    (assert-constraint! (div 17) (nthd 8 10))
    (assert-constraint! (div 13) (nthd 7 9))
    (assert-constraint! (div 11) (nthd 6 8))
    (assert-constraint! (div 7) (nthd 5 7))
    (assert-constraint! (div 5) (nthd 4 6))
    (assert-constraint! (div 3) (nthd 3 5))
    (assert-constraint! (div 2) (nthd 2 4))
    (map-all-pairs (lambda l (assert-constraint! (lambda (a b) (not (= a b))) l)) ds)
    (foldl + 0
           (map (lambda (l) (foldl (lambda (a b) (+ (* a 10) b)) 0 l))
                (all-values (csp-solution ds last)))))

=== License ===

   Copyright 1993-1995 University of Toronto. All rights reserved.
   Copyright 1996 Technion. All rights reserved.
   Copyright 1996 and 1997 University of Vermont. All rights reserved.
   Copyright 1997-2001 NEC Research Institute, Inc. All rights reserved.
   Copyright 2002-2013 Purdue University. All rights reserved.

   Contact Andrei Barbu, andrei@0xab.com. Originally written by Jeff Siskind.

   This program is free software: you can redistribute it and/or modify
   it under the terms of the GNU Lesser General Public License as published by
   the Free Software Foundation, either version 3 of the License, or
   (at your option) any later version.
   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU Lesser General Public License for more details.
   You should have received a copy of the GNU Lesser General Public License
   along with this program.  If not, see http://www.gnu.org/licenses.
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