Lambda Multi-Variable Comparison

Normal Python (Def)

def add_ten(a):
    return a + 10

def multiply(a, b):
    return a * b

def sum_three(a, b, c):
    return a + b + c

Lambda Python (Shorthand)

x1 = lambda a : a + 10
print(x1(5))

x2 = lambda a, b : a * b
print(x2(5, 6))

x3 = lambda a, b, c : a + b + c
print(x3(5, 6, 2))

$\lambda$-Calculus Logic Breakdown

In pure $\lambda$-calculus, functions technically only take one input at a time. Python allows lambda a, b as a shortcut, but behind the scenes, it follows these rules:

Python Shorthand Pure $\lambda$ Logic What happens? (Application)
lambda a: a + 10 $\lambda a . (a + 10)$ Input 5 replaces a in the body.
lambda a, b: a * b $\lambda a . \lambda b . (a * b)$ Input 5 fills a, then input 6 fills b.
lambda a, b, c: ... $\lambda a . \lambda b . \lambda c . (\text{body})$ A chain of 3 applications occurs.

The Body (M): In your examples, the "Body" of the λ-term is the math operation (like a + b + c).
The Variable (V): The letters a, b, and c are the variables.
The Application (MM): When you write x(5, 6, 2), you are applying the function x to the values.