David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc. The isomorphism has many aspects, even at the syntactic level: formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc. But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transforms proofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq). This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic. Key features - The Curry-Howard Isomorphism treated as common theme - Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics - Thorough study of the connection between calculi and logics - Elaborate study of classical logics and control operators - Account of dialogue games for classical and intuitionistic logic - Theoretical foundations of computer-assisted reasoning · The Curry-Howard Isomorphism treated as the common theme. · Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics. · Elaborate study of classical logics and control operators. · Account of dialogue games for classical and intuitionistic logic. · Theoretical foundations of computer-assisted reasoning
|Keywords||Curry-Howard isomorphism Lambda calculus Proof theory|
|Categories||categorize this paper)|
|Buy the book||$124.30 new (27% off) $124.67 direct from Amazon (25% off) $159.89 used (6% off) Amazon page|
|Call number||QA9.54.S67 2007|
|Through your library||Configure|
Similar books and articles
Ken-etsu Fujita (1998). On Proof Terms and Embeddings of Classical Substructural Logics. Studia Logica 61 (2):199-221.
Harold Simmons (2000). Derivation and Computation: Taking the Curry-Howard Correspondence Seriously. Cambridge University Press.
Simona Ronchi Della Rocca & Luca Roversi (1997). Lambda Calculus and Intuitionistic Linear Logic. Studia Logica 59 (3):417-448.
Sachio Hirokawa, Yuichi Komori & Misao Nagayama (2000). A Lambda Proof of the P-W Theorem. Journal of Symbolic Logic 65 (4):1841-1849.
Simona Ronchi della Rocca & Luca Roversi (1997). Lambda Calculus and Intuitionistic Linear Logic. Studia Logica 59 (3):417-448.
G. E. Mint͡s (2000). A Short Introduction to Intuitionistic Logic. Kluwer Academic / Plenum Publishers.
Frank A. Bäuerle, David Albrecht, John N. Crossley & John S. Jeavons (1998). Curry-Howard Terms for Linear Logic. Studia Logica 61 (2):223-235.
H. B. Curry & R. Feys (1995). Basic Theory of Functionality. Analogies with Propositional Algebra. In Philippe De Groote (ed.), The Curry-Howard Isomorphism. Academia.
Added to index2009-01-28
Total downloads19 ( #73,391 of 1,004,651 )
Recent downloads (6 months)1 ( #64,617 of 1,004,651 )
How can I increase my downloads?