For a web tutorial on graphic lambda calculus go here. There will be detailed explanations concerning the three main sectors of the graphic lambda calculus, for the moment here is a brief description of them.
A sector of the graphic lambda calculus is:
- a set of graphs, defined by a local or global condition,
- a set of moves from the list of all moves available.
The name “graphic lambda calculus” comes from the fact that there it has untyped lambda calculus as a sector. In fact, there are three important sectors of graphic lambda calculus:
- untyped lambda calculus sector, which contains all graphs in which are obtained from untyped lambda calculus terms by the algorithm described here. The moves of this sector are: graphic beta move, fan-out moves, pruning moves. The article arxiv:1207.0332 describes this sector in detail.
- emergent algebra sector, which contain all graphs in described in the article arxiv:1103.6007, via the emergent algebra crossing macros, and the following moves: dual graphic beta move (which forms with the graphic move the extended beta move), fan-out moves, pruning moves, emergent algebra moves.
- knot and tangle diagrams sector, defined by using crossings in lambda calculus macro and the Reidemeister moves as described in the post Generating set of Reidemeister moves for graphic lambda crossings, which are composite moves obtained from the graphic beta move and some local fan-out moves. The article arxiv:1211.1604 describes this sector in detail.