Interpretation of a Monoid in Python

gistfile1.txt

from functools import reduce
from operator import add


def monoid(combine, create=lambda x:x):
    def wrapped(val):
        return Monoid(combine, create(val))
    return wrapped


class EmptyMonoid:
    def __add__(self, other):
        return other
    

class Monoid:
    empty_monoid=EmptyMonoid()  # singleton
    
    def __init__(self, combine, val):
        self.combine=combine
        self.val=val
        
    def __add__(self, other):
        if other is self.empty_monoid:
            return self
        return Monoid(self.combine, self.combine(self.val, other.val))
    
    def __repr__(self):
        return f"m:{self.val}"  # Python 3.6

    
def fold_tree(mono, tree):
    if not isinstance(tree, list):  # we got down to a leaf
        return mono(tree)
    return reduce(add, [fold_tree(mono, tree_part) for tree_part in tree], Monoid.empty_monoid)


tree=[[[1,2],[3,4]],[[5,6],[7,8],[9]]]   # trees are built and detected as lists

fold_tree(monoid(add), tree)