### queens.m

solns = layn(map show (queens 8))
queens 0 = [[]]
queens (n+1) = [q:b|b<-queens n;q<-[1..8];safe q b]
safe q b = and[~checks q b i|i<-index b]
checks q b i = q=b!i \/ abs(q-b!i)=i+1

This generates all solutions to the 8 queens problem -- say

solns

and it will print the solutions one per line - all 92 of them.
This is a good program for testing the garbage
collector. Say `/gc' to switch on garbage collector diagnostics.
Note that the function `queens n' returns a list of all solutions to
the n queens problem (placing queens in the first n columns of a chess
board, so that no queen gives check to another). A board with n
queens is represented as a list of n numbers, namely the positions of
the queens in each column

This example exhibits a basic technique of lazy functional
programming, which is to eliminate backtracking from a search problem
by working at the level of a list of all solutions, rather than a
single solution.