This book attempts to change the way we conceive, study, apply, and teach the lambda-calculus, or λ-calculus for short. Roughly speaking, the λ- calculus can be defined as an unambiguous logico-mathematical notation for functions understood as rules of correspondence or computation. However, in my opinion, there is much more involved in that standard definition of the λ-calculus than is usually thought. The main purpose of this book is to provide concrete and solid evidence of what the phrase “much more” truly means in this context. And part of the evidence is a new graphical notation for the λ-calculus and a new field of knowledge that arises from the research reported here.
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