David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Cambridge University Press (2000)
Mathematics is about proofs, that is the derivation of correct statements; and calculations, that is the production of results according to well-defined sets of rules. The two notions are intimately related. Proofs can involve calculations, and the algorithm underlying a calculation should be proved correct. The aim of the author is to explore this relationship. The book itself forms an introduction to simple type theory. Starting from the familiar propositional calculus the author develops the central idea of an applied lambda-calculus. This is illustrated by an account of Gödel's T, a system which codifies number-theoretic function hierarchies. Each of the book's 52 sections ends with a set of exercises, some 200 in total. These are designed to help the reader get to grips with the subject, and develop a further understanding. An appendix contains complete solutions of these exercises.
|Keywords||Proof theory Lambda calculus Type theory Curry-Howard isomorphism|
|Categories||categorize this paper)|
|Buy the book||$42.48 used (80% off) $60.00 new (72% off) $158.51 direct from Amazon (15% off) Amazon page|
|Call number||QA9.54.S55 2000|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Lucius T. Schoenbaum (2010). On the Syntax of Logic and Set Theory. Review of Symbolic Logic 3 (4):568-599.
Similar books and articles
William W. Tait (2006). Proof-Theoretic Semantics for Classical Mathematics. Synthese 148 (3):603 - 622.
Chris Hankin (1994). Lambda Calculi: A Guide for the Perplexed. Oxford University Press.
Simona Ronchi Della Rocca & Luca Roversi (1997). Lambda Calculus and Intuitionistic Linear Logic. Studia Logica 59 (3):417-448.
W. W. Tait (2003). The Completeness of Heyting First-Order Logic. Journal of Symbolic Logic 68 (3):751-763.
Sachio Hirokawa, Yuichi Komori & Misao Nagayama (2000). A Lambda Proof of the P-W Theorem. Journal of Symbolic Logic 65 (4):1841-1849.
David J. Pym (1995). A Note on the Proof Theory the λII-Calculus. Studia Logica 54 (2):199 - 230.
Added to index2009-01-28
Total downloads8 ( #381,178 of 1,792,270 )
Recent downloads (6 months)1 ( #464,764 of 1,792,270 )
How can I increase my downloads?