Lectures on the Curry-Howard Isomorphism

Elsevier (2007)
Abstract
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)   $178.73 used    Amazon page
Call number QA9.54.S67 2007
ISBN(s) 9780444520777   0444520775
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,360
External links
  •   Try with proxy.
  • Through your library Configure
    References found in this work BETA

    No references found.

    Citations of this work BETA
    Nir Fresco & Giuseppe Primiero (2013). Miscomputation. Philosophy and Technology 26 (3):253-272.
    Herman Geuvers, Robbert Krebbers & James McKinna (2013). The -Calculus. Annals of Pure and Applied Logic 164 (6):676-701.
    Similar books and articles
    Analytics

    Monthly downloads

    Added to index

    2009-01-28

    Total downloads

    19 ( #74,849 of 1,089,047 )

    Recent downloads (6 months)

    1 ( #69,722 of 1,089,047 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature


    Discussion
    Start a new thread
    Order:
    There  are no threads in this forum
    Nothing in this forum yet.