Lawrence Bottorff borgauf at gmail.com
Tue Dec 22 05:59:57 UTC 2020

```Here's something from *Learn You... *

Lambdas are normally surrounded by parentheses unless we mean for them to
extend all the way to the right. Here's something interesting: due to the
way functions are curried by default, these two are equivalent:

addThree :: (Num a) => a -> a -> a -> a
addThree x y z = x + y + z

addThree :: (Num a) => a -> a -> a -> a
addThree = \x -> \y -> \z -> x + y + z

If we define a function like this, it's obvious why the type declaration is
what it is. There are three ->'s in both the type declaration and the
equation. But of course, the first way to write functions is far more
readable, the second one is pretty much a gimmick to illustrate currying.

So with the lambda version how exactly is the currying taking place? I
understand something like this

doubleDouble x = (\x -> x*2) (2 * x)

So with beta reduction we have (2*x)*2, then plug in the argument.

And with this

overwrite x = (\x -> (\x -> (\x -> x) 4) 3) 2

which gives (\x -> (\x -> 4) 3) 2
(\x -> 4) 2
4

But how is the beta reduction happening with addThree?

BTW, I flunked lambda calculus in Kindergarten.

LB
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