Finding all combinations of well-formed brackets

Question

This came up while talking to a friend and I thought I\'d ask here since it\'s an interesting problem and would like to see other people\'s solutions.

The task is to

Answer 1

def @memo brackets ( n )
    => [] if n == 0 else around( n ) ++ pre( n ) ++ post( n ) ++ [ "()" * n) ]

def @memo pre ( n )
    => map ( ( s ) => "()" ++ s, pre ( n - 1 ) ++ around ( n - 1 ) ) if n > 2 else []

def @memo post ( n )
    => map ( ( s ) => s ++ "()", post ( n - 1 ) ++ around ( n - 1 ) ) if n > 2 else []

def @memo around ( n )
    => map ( ( s ) => "(" ++ s ++ ")", brackets( n - 1 ) )

(kin, which is something like an actor model based linear python with traits. I haven't got round to implementing @memo but the above works without that optimisation)