# Some numbery functions

(2017-07-06. Index.)

This post is part of a list: Some lambda-notes
Next thing: How do the lambdas?

Somewhat a test-post, for to have not dead lambda calculus within post.

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

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

If it works (if the ctrl+enter-business leads to a line that goes foo bar), we can make like, a few numbers... (ctrl+enter each line).

(Oh by the way. Can do ctrl+l to insert a λ, and ctrl+d to insert a . Or can use \ instead of λ and := instead of .)

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 quite possibly evaluated to foo (foo (foo (foo (foo bar)))). Which is like five foos.

Okay. Addition is pretty numbery let’s that. Below is a function that takes arguments a and b. And gives back, uh, a λf.λx.-function. This function applies fb times” to x, and applies fa times” to the result of that again. Hopefully amounts to like, an a + b number of fs applied to x. (ctrl+enter on line below)

If things seem fine so far, we can try to use it to like, actually additioning. 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.)