# Lambda Calculus

The teacher from CS241E briefly covered this in his last lecture.

The professor from SE212 talked about this, and how they are related to SE212 talked about this, and how they are related to Turing Machines.

This is back-linked from Church-Turing Thesis.

Watch this by Computerphile: https://www.youtube.com/watch?v=eis11j_iGMs

Recommended by teacher: https://serokell.io/blog/untyped-lambda-calculus

An expression $e$ can be a variable $V$, a function $λv⋅e$, or a function call $ee$ (first $e$ is a function and second is an argument) $e→V∣λv⋅e∣ee$

- Function Calls require the function specified to be called
- $(λv⋅e_{1})e_{2}→e_{1}[e_{2}/v]$ - Beta Reduction
- Left-associative, so $eee$ is $(ee)e$
- $λv⋅ee$ is the same as $λv⋅(ee)$

- $(λv⋅vv)(abc)→λv⋅v$

https://www.ics.uci.edu/~lopes/teaching/inf212W12/readings/lambda-calculus-handout.pdf