The Language of Trees


A Tree is defined by the following (recursive) grammar.

       Tree ::= '(' String Tree+ ')'
              | String

where '(' and ')' are literals, and Tree+ means 
"one or more" sub-trees.


Examples
========

"(hello (cat dog) (apple pear orange))"

             hello
           /      \
          /        \
        cat       apple
         |        /   \
         |       /     \
        dog    pear   orange

"goodbye"

"(a b c d e f)"
                      a
                   / /|\ \
                  / / | \ \
                 b c  d  e  f

"(a)"  // wrong
"a"    // correct

"(a (b) (c))"  // wrong
"(a b c)"      // correct

         a
        / \
       /   \
      b     c


"3 + 4 * 5"  // infix notation

           +       Expression Tree  "(+ 3 (* 4 5))"  // prefix notation
          / \
         /   \
        3     *
             / \
            /   \
           4     5

"(3 + 4) * 5"  // infix notation

              *     Expression Tree   "(* (+ 3 4) 5)"  // prefix notation
             / \
            /   \
           +     5
          / \
         /   \
        3    4

"if (x == y) print(x) else print(y)"  // code

            if      Abstract Syntax Tree       "(if (== x y) (print x) (print y))"
          / |  \                                Lisp, Clojure, Scheme, Racket syntax
         /  |   \
        /   |    \
       /    |     \
     ==   print   print
    /  \     \        \
   /    \     \        \
  x      y     x        y