Lambda Calculus with Types -

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Résumé :
This handbook with exercises reveals the mathematical beauty of formalisms hitherto mostly used for software and hardware design and verification.

Biographie:
Henk Barendregt holds the chair on the Foundations of Mathematics and Computer Science at Radboud University, Nijmegen, The Netherlands.

Sommaire:
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....