Easy Syntax for Representing Trees
March 07, 2012

I’m working on a parser for Tree Adjoining Grammar (TAG) for this seminar I’m taking. TAG is an extension of context-free grammar (CFG) that’s more powerful while still being polynomially-parsable. Anyhow, TAG makes use of “tree production rules” instead of the “linear” production rules of CFG: instead of S -> NP VP, you’d have a small tree, the root of which being S, having NP and VP as its children. Of course these trees can be more than two-level deep, and they go all sorts of operations such as substitution and adjunction, but that’s for the parser.

So I needed a compact and (hopefully) readable way to express such trees in my code. At first I used lots of parenthesis, which was ugly and cumbersome, but then I devised this:

class NonTerminal(object):
    def __init__(self, name):
        self.name = name
    def __sub__(self, children):
        return Tree(self, children)
    def __pos__(self):
        return Foot(self)

class Foot(object):
    def __init__(self, nonterm):
        self.nonterm = nonterm

class Tree(object):
    def __init__(self, root, children):
        self.root = root
        self.children = children

And here’s how you use it:

S = NonTerminal("S")

t1 = S-["e"]
t2 = S-["a", S-["c", +S, "d"], "b"]

# Which represents the following two trees:
# t1:                t2:
#      S                  S
#      |                / | \
#      |               /  |  \
#      e              a   S   b
#                       / | \
#                      /  |  \
#                     c   S*  d

The peculiar +S is a way to mark that a leaf node is a foot, which is part of the semantics TAG (that’s where adjunction takes place). It’s represented in the diagram by the more conventional S*, but I had to resort to a unary operator in the code. Anyway, I’m not sure if it’s a recipe or just a nice trick, but I thought I’d share this.

By the way, you can use both __sub__ and __neg__ to achieve things like S-----X (i.e., more than a single - sign, to allow for better padding), but I tried to avoid too much ASCII art. I’d love to hear about other such ideas!