Imperative auto differentiation

imperative.py

class array(object) :
    """Simple Array object that support autodiff."""
    def __init__(self, value, name=None):
        self.value = value
        if name:
            self.grad = lambda g : {name : g}

    def __add__(self, other):
        assert isinstance(other, int)
        ret = array(self.value + other)
        ret.grad = lambda g : self.grad(g)
        return ret

    def __mul__(self, other):
        assert isinstance(other, array)
        ret = array(self.value * other.value)
        def grad(g):
            x = self.grad(g * other.value)
            x.update(other.grad(g * self.value))
            return x
        ret.grad = grad
        return ret

# some examples
a = array(1, 'a')
b = array(2, 'b')
c = b * a
d = c + 1
print d.value
print d.grad(1)
# Results
# 3
# {'a': 2, 'b': 1}