viu.txt

Viu
http://www.janko.at/Raetsel/Nikoli/Viu.htm
Rules: Write numbers ≥ 0 into some cells of the diagram and blacken all other cells. All numbered cells must form a single orthogonally contiguous area. Same numbers must not be orthogonally adjacent. A number denotes how many black cells can be seen altogether looking north, south, east and west until a white cell or the edge of the diagram is reached.

Example puzzle
________
__12_2__
_1____2_
___43_1_
_1_02___
_4____1_
__4_10__
________
goes to
XXX32010
X212X2X2
313XX42X
XXX43X15
41202X2X
X4X2X21X
XX40102X
XXX302XX
Rules: 
A	Write numbers >= 0 into some cells of the diagram and blacken all other cells. 
B	All numbered cells must form a single orthogonally contiguous area. 
C	Same numbers must not be orthogonally adjacent. 
D	A number denotes how many black cells can be seen altogether looking north, south, east and west until a white cell or the edge of the diagram is reached.
	
condition A
Square = Square X Y Box
Box = Number N
	| Black
	
condition B
standard transitive closure of "adjacent and both members of some type"

condition C
matches(B = Board Qs) = 
	\forall Q = Square _ _ (Number N) \in Qs .
	  \not \exists P = Square _ _ (Number N) \in Qs .
	    adjacent(P,Q)
	
condition D
visible_count(Q,B = Board Qs) = 
	visible(north(Q),north) +
	visible(east(Q),east) +
	visible(south(Q),south) +
	visible(west(Q),west)
	
visible(S,f) =
	if black?(S)
	then 1 + visible(f(S),f)
	else 0
	
visibility(B = Board Qs) =
	\forall Q = Square _ _ (Number N) \in Qs .
	  visible_count(Q) == N
	  
all together
solution(B = Board) = 
	/\ matches(B)
	/\ solution(B)