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This handbook with exercises reveals in formalisms, hitherto mainly
used for hardware and software design and verification, unexpected
mathematical beauty. The lambda calculus forms a prototype
universal programming language, which in its untyped version is
related to Lisp, and was treated in the first author's classic The
Lambda Calculus (1984). The formalism has since been extended with
types and used in functional programming (Haskell, Clean) and proof
assistants (Coq, Isabelle, HOL), used in designing and verifying IT
products and mathematical proofs. In this book, the authors focus
on three classes of typing for lambda terms: simple types,
recursive types and intersection types. It is in these three
formalisms of terms and types that the unexpected mathematical
beauty is revealed. The treatment is authoritative and
comprehensive, complemented by an exhaustive bibliography, and
numerous exercises are provided to deepen the readers'
understanding and increase their confidence using types.
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