2020ok  Directory of FREE Online Books and FREE eBooks

Free eBooks > Science > Mathematics > Pure Mathematics > Logic > Lectures on the Curry-Howard Isomorphism

Lectures on the Curry-Howard Isomorphism

by Morten Heine B. Sørenson


Download Book
(Respecting the intellectual property of others is utmost important to us, we make every effort to make sure we only link to legitimate sites, such as those sites owned by authors and publishers. If you have any questions about these links, please contact us.)


link 1
link 2



About Book

Book Description
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

Comments

SEND A COMMENT

PLEASE READ: All comments must be approved before appearing in the thread; time and space constraints prevent all comments from appearing. We will only approve comments that are directly related to the article, use appropriate language and are not attacking the comments of others.

Message (please, no HTML tags. Web addresses will be hyperlinked):

Related Free eBooks

Related Tags

DIGG This story   Save To Google   Save To Windows Live   Save To Del.icio.us   diigo it   Save To blinklist
Save To Furl   Save To Yahoo! My Web 2.0   Save To Blogmarks   Save To Shadows   Save To stumbleupon   Save To Reddit