- Hardcover: 456 pages
- Publisher: Elsevier Science; 1 edition (Sep 14 2006)
- Language: English
- ISBN-10: 0444520775
- ISBN-13: 978-0444520777
- Product Dimensions: 2.3 x 1.6 x 0.2 cm
- Shipping Weight: 821 g
- Amazon Bestsellers Rank: #1,058,576 in Books (See Top 100 in Books)
- See Complete Table of Contents
|
||||||||||||||||||
|
||||||||||||||||||
|
||||||||||||||||||
Product Details |
Product Description
Product 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.
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
Inside This Book
(Learn More)
Front Cover | Copyright | Table of Contents | Excerpt | Index
Explore More
Concordance
Browse Sample PagesConcordance
Front Cover | Copyright | Table of Contents | Excerpt | Index
Tag this product(What's this?)Think of a tag as a keyword or label you consider is strongly related to this product.
Tags will help all customers organize and find favorite items. |
Customer Reviews
|
There are no customer reviews yet on Amazon.ca
|
||||||||||||||||||||
|
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
5.0 out of 5 stars (1 customer review)
2 of 2 people found the following review helpful
5.0 out of 5 stars
Curry-Howard and more!, Mar 21 2010
By symbolic - Published on Amazon.com
Amazon Verified Purchase(What's this?)
This review is from: Lectures on the Curry-Howard Isomorphism (Hardcover)
This is a superbly written, fascinating, greatly informative book.I have used it primarily as an introduction to lambda calculus and
intuitionistic logic in its BHK, natural deduction, and sequent calculus
forms, not to mention the comparative treatment of those with their
classical counterparts. In these regards, it is clear and concise while
nonetheless being thorough and presenting a full spectrum of interesting results,
i.e., all the highpoints and more. It also explains the history and motivation
and offers hundreds of useful references. It also has chapters on
second-order logic and polymorphism. I say all this having read
perhaps 1/15th of the material; I'm very happy I bought it.
And of course, it has a lot to say about their main topic, the Curry-Howard
isomorphism, which I am now finding I need to understand as well.
Good thing I have this book. These authors have just done a magnificent job.
Listmania!
Look for similar items by category
- Books > Computers & Internet > Computer Science > Information Theory
- Books > New & Used Textbooks > Computer Science & Information Systems
- Books > New & Used Textbooks > Sciences > Mathematics
- Books > Professional & Technical > Professional Science > Mathematics > Pure Mathematics
- Books > Science > Mathematics > Pure Mathematics > Logic
Look for similar items by subject
Feedback
Would you like to update product info or give feedback on images?
|
