aspects of type theory relevant for the Curry-Howard isomorphism. Outline . (D IK U). Roughly one chapter was presented at each lecture, sometimes. CiteSeerX – Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The Curry-Howard isomorphism states an amazing correspondence between. Lectures on the. Curry-Howard Isomorphism. Morten Heine B. Sørensen. University of Copenhagen. Pawe l Urzyczyn. University of Warsaw.
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For instance,minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent Lectures on the Curry-Howard Isomorphism.
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: But there is more to the isomorphism than this.
For instance, it is an old ideadue to Brouwer, Kolmogorov, and Heytingthat a constructive proof of an implication is a lecutres 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.
Lectures on the Curry-Howard Isomorphism by Morten Heine B. Sørensen
This book give an introduction to curry-howatd 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: Chapter 2 Intuitionistic logic. Chapter 4 The Siomorphism isomorphism.
Lectures on the Curry-Howard Isomorphism
Chapter 5 Proofs as combinators. Chapter 6 Classical logic and control operators. Chapter 7 Sequent calculus. Chapter 8 Firstorder logic. Chapter 11 Secondorder logic and polymorphism.
Chapter 12 Secondorder arithmetic. Chapter 13 Dependent types.
Appendix A Mathematical background. Appendix B Solutions and hints to selected exercises. Chapter 9 Firstorder arithmetic.