To Dissect a Mockingbird:A Graphical Notation for the Lambda Calculus with Animated Reduction David C Keenan, 27-Aug-1996 last updated 10-May-200 The lambda calculus, and the closely related theory of combinators, are important in the foundations of mathematics, logic and computer science. This paper provides an informal and entertaining introduction by means of an animated graphical notation. Introduction In the 1930s and 40s, around the birth of the "automatic computer", mathematicians wanted to formalise what we mean when we say some result or some function is "effectively computable", whether by machine or human. A "computer", originally, was a person who performed arithmetic calculations. The "effectively" part is included to indicate that we are not concerned with the time any particular computer might take to produce the result, so long as it would get there eventually. They wanted to find the simplest possible system that could be said to compute.
With all that scope for reasonable disagreement, is there anything we can all agree on? How much of the hierarchy in the medal table is indisputable, and how much depends on your point of view? So we want to say that one country has done strictly better than another if the medal score of the latter can be transformed into the former by a sequence of medal additions and medal upgrades. A bit of thought shows that this is exactly equivalent to defining a partial order on triples of medals, in which a triple (G,S,B) is considered at least as good as another triple (g,s,b) if and only if it satisfies the three conditions * G ≥ g * G + S ≥ g + s * G + S + B ≥ g + s + b