What is the logic used to break down multiple lambda variables in python?

Question

I am trying to reason through why the result of the following would be 8 but I’m a little stuck.

f = lambda x,y: lambda z: (x)(y)(z)
print((f)(lambda x: lambda y: x, lambda z: z*2)(3)(4))

I know that the next step would be to substitute f into the line as shown below, but this is where I get lost.

ans = (lambda x,y: lambda z: (x)(y)(z))(lambda x: lambda y: x, lambda z: z*2)(3)(4)

From my understanding, f requires three arguments in total, one in this (x,y) format and another one like (z).

(lambda x: lambda y: x, lambda z: z*2)(3)(4)

I think 3 should be the argument for lambda x and nothing should be inputted for lambda y. I think 4 would then be the argument for lambda z.

This leads me to think (3,8) is what is returned for (lambda x: lambda y: x, lambda z: z*2), but then I don’t have an input for lambda z in the original f.

I could use explanation of how this is processed to give a final answer of 8. Apologies for any formatting errors.

Asked By: moonmoon

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Source

Answer 1

Let’s give a name to some of those lambdas:

const = lambda x: (lambda y: x)
double = lambda z: (z*2)

And eta-reduct the lambda z:... inside f (that is lambda z: ( x(y) )(z) -> x(y)):

f = lambda x, y: x(y)

We can now rewrite that expression as ( ( f(const, double) )(3) )(4).

Reducing, we get:

f(const, double) -> const(double) -> lambda y: double
(lambda y: double)(3) -> double
double(4) -> 8

Answered By: Pignotto

What is the logic used to break down multiple lambda variables in python?

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