Fixed points in graphic lambda calculus

Background: the page Graphic lambda calculus.

Let A be a graph in GRAPH with one input and one output. For any  graph B with one output, we denote by A(B) the graph obtained  by grafting the output of B to the input of A.

Problem:  Given A, find B such that A(B) \leftrightarrow B, where \leftrightarrow means any finite sequence of moves in graphic lambda calculus.

The solution is in principle the same as in usual lambda calculus, can you recognize it? Here is it. We start from the following:

fixpoint_1

That’s almost done. It suffices to do this:

fixpoint_3

to get a good graph B:

fixpoint_2

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s