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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def to_dict(self, short_pred=True, properties=True):
 """ Encode the Mrs as a dictionary suitable for JSON serialization. """

        def _lnk(obj): return {'from': obj.cfrom, 'to': obj.cto}
        def _ep(ep, short_pred=True):
            p = ep.pred.short_form() if short_pred else ep.pred.string
            d = dict(label=ep.label, predicate=p, arguments=ep.args)
            if ep.lnk is not None: d['lnk'] = _lnk(ep)
            return d
        def _hcons(hc): return {'relation':hc[1], 'high':hc[0], 'low':hc[2]}
        def _icons(ic): return {'relation':ic[1], 'left':ic[0], 'right':ic[2]}
        def _var(v):
            d = {'type': var_sort(v)}
            if properties and self.properties(v):
                d['properties'] = self.properties(v)
            return d

        d = dict(
            relations=[_ep(ep, short_pred=short_pred) for ep in self.eps()],
            constraints=([_hcons(hc) for hc in self.hcons()] +
                         [_icons(ic) for ic in self.icons()]),
            variables={v: _var(v) for v in self.variables()}
        )
        if self.top is not None: d['top'] = self.top
        if self.index is not None: d['index'] = self.index
        # if self.xarg is not None: d['xarg'] = self.xarg
        # if self.lnk is not None: d['lnk'] = self.lnk
        # if self.surface is not None: d['surface'] = self.surface
        # if self.identifier is not None: d['identifier'] = self.identifier
        return d