(There's a list with all the lambda notes here.)

Somewhat a test-post, for having not-dead lambda calculus within a post. If you're viewing this in a web browser and it runs the JavaScript and so on, it should be interactive.

(There’s also kind of a lambda playground over here.)

To try, put cursor on line below and do ctrl+enter couple of times:

If it works (if the ctrl+enter-business leads to a line that goes `foo bar`

), we can make a few numbers... (ctrl+enter each line).

The idea, or at least one way to look at it, is that the number five is the function that does something five times. So, if we want to `foo`

a `bar`

five times, then we can... (ctrl+r to replace `5`

with the lambdas from the definition we did above. Then ctrl+enter a couple of times.)

Which maybe evaluated to `foo (foo (foo (foo (foo bar))))`

. Five `foo`

s.

Okay. Addition is pretty numbery. Below is a function that takes arguments `a`

and `b`

, and gives back, uh, a `λf.λx.`

-function. This function applies `f`

to `x`

and it will do that “`b`

times.” And it will apply `f`

to the result of that “`a`

times.” Hopefully that amounts to `f`

being applied “`a`

+ `b`

times” to `x`

(ctrl+enter on line below)

If things seem fine so far, we can try to use it. ctrl+r on line below to replace the names of the things we’ve defined with their lambdas. Then ctrl+enter a bunch of times to evaluate. (Or ctrl+shift+enter one time.)

It’s maybe twelve! (Hopefully.)