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im seeing double, **four** new posts

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Shaun Kerr 2018-08-27 11:17:51 +12:00
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inprog/idiots-guide-lambda.md → posts/idiots-guide-lambda.md
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@ -1,6 +1,6 @@
---
title: An Idiot's Guide to Lambda Calculus
published: TBD
published: 2018-08-27
---
clarification: this is not a guide to lambda calculus for idiots, this is a guide to lambda calculus written by an idiot.
@ -21,7 +21,7 @@ what you would need is....
## a way to describe computability
and one way of doing that is with lambda calculus. to define lambda calculus we need just a few rules - variables, abstraction, application, reduction.
and one way of doing that is with lambda calculus. to define lambda calculus we need just a few rules - variables, abstraction, application.
these concepts aren't too difficult, so awayyyy we go.
@ -81,4 +81,50 @@ the identity function has `x` as its argument, so we take the application body,
so our abstraction body is `x`, and `x` is equal to our argument `y`, so therefore our function will return `y`, which is the identity.
a sligtly more interesting example is something like
a sligtly more interesting example is something like:
```
( (λx.xx) y )
```
here, our argument to our abstraction is `y`, which gets bound to `x` in the abstraction body, which is then fed into the `xx` to produce:
`yy`
and thats how we go.
as a spoiler for what the next lambda calc post will cover, heres a bit of an example, imagine we were using the same abstraction:
```
(λx.xx)
```
and instead of passing it `y`, we passed it **another abstraction**... say, itself?
```
( (λx.xx) (λx.xx) )
```
here, we bind the entire abstraction `(λx.xx)` to the variable `x` in the first abstraction.
when we do the substitution into the body `xx` we get left with...
```
( (λx.xx) (λx.xx) )
```
the same thing, which means this is an ***infinite loop***
fun stuff fun stuff imo
## further thoughts
theres a lot more to go before we get to a numbering system, and at this point it may seem like theres not much use to lambda calculus, but i am not joking when i say ***anything that can be done on a computer can be written in lambda calculus***.
it may be abstracted, it may be thousands of millions of pages long, but it is possible.
and thats what makes it so wonderful.
i'll write more in depth on this at some point in the near future when i'm feeling smarter, less lazy, and don't wanna write edgy armchair psych pieces instead.
peace out ny'all, if you're unlucky i'll talk about Nock after this.