#LAMBDA CALCULUS ARCHIVE#

moves one cell left or right on the tape.transitions to some some state (possibly the same it is already in), and.writes some symbol on the tape (possibly the same that was already there),.given a combination of current state and current symbol on the tape, always does an action consisting of three things:.

has some set of states it can be in, some of which are termed 'accepting' and one of which is the starting state and.

works on an infinite tape of cells from which a finite set of symbols can be read and written, and always points at one of these cells.

The Turing machine – that is, a machine that:.

At the end we will see a lambda calculus interpreter written in the lambda calculus, and realise that we're most of the way to Lisp.īut first, why care about lambda calculus? Consider four different systems: The goal is not to do maths with it, but rather to build up definitions within it so that we can express non-trivial algorithms easily. It is most useful if you want to get some intuition for the lambda calculus, or more generally for how simple axiomatisations of computation actually let you express anything.

#LAMBDA CALCULUS ARCHIVE#

This is a linkpost that I'm posting in response to a request to share more of the archive of my personal blog on LessWrong.

Lambda calculus