How do you a apply a function to a cell and the cell below?

Question

I am trying to apply a function of two arguments to a cell and the cell below.

Eg. my function is

def foo(x,y):
    return f'{x} -> {y}'

# Input
s = pd.Series([1,2,3])

# Output
pd.Series(['1 -> 2', '2 -> 3', '3 -> nan'])

I'm not sure what command I could use to do this in pandas.

Notes:

1. If I were subtracting the values I could do s.diff(1)

2. If this were a vectorizable operation I could do foo(s, s.shift(-1))

3. I am looking for a functional style ideally (ie. avoiding an explicit loop) - just a style preference.

4. The function foo above is illustrative, I'm looking for something that works for any arbitrary function of two arguments (in my usecase I'm trying to compute text similarity using a function foo(text1:str, text2:str)->float)