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Combinatorial logic notebook
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Posted by: Jason Cawley
Combinatorial Ornithology
Jaime Rangel-Mondragón
Abstract: This work is an exploration into the fascinating world of Combinatory Logic, inspired by the novel ornithological viewpoint introduced by Raymond Smullyan. The work begins with historical details and is followed by an introduction to the combinatorial properties of bracketed expressions; it continues to the computing of behaviours and genealogies, the solution of combinatorial equations and the development of propositional birds including an assortment of illustrative examples throughout. Finally, comments on the use of birds to algorithmic complexity are mentioned and a list of references is included. The author has developed and made repeated use of this work in his teachings on Functional Programming, Programming Paradigms and Automata and Formal Languages.
http://library.wolfram.com/infocenter/MathSource/4862/
Note that "birds" refers to particular combinator rules, whose deducible equivalents are traced like hereditary trees. This is quite an impressive notebook, packed with interesting results about combinator systems. The author developed it during a stay at Wolfram Research as a visiting scholar.
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