Generalizing the Curry-howard Isomorphism to Classical Logic PDF Download

Author: Luis Edmund Maldonado
Publisher:
ISBN:
Category :
Languages : en
Pages : 48

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Author: Morten Heine Sørensen
Publisher: Elsevier
ISBN: 0080478921
Category : Mathematics
Languages : en
Pages : 457

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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 transformsproofs 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

Author: Philippe De Groote
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 372

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Author: Iman Poernomo
Publisher: Springer Science & Business Media
ISBN: 0387281835
Category : Computers
Languages : en
Pages : 417

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This monograph details several important advances in the direction of a practical proofs-as-programs paradigm, which constitutes a set of approaches to developing programs from proofs in constructive logic with applications to industrial-scale, complex software engineering problems. One of the books central themes is a general, abstract framework for developing new systems of programs synthesis by adapting proofs-as-programs to new contexts.

Author: Morten Heine B. Sørensen
Publisher:
ISBN:
Category : Isomorphisms (Mathematics)
Languages : en
Pages : 261

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Author: Victor A. Carreno
Publisher: Springer Science & Business Media
ISBN: 3540440399
Category : Computers
Languages : en
Pages : 358

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Felty PuzzleTool:AnExampleofProgrammingComputationandDeduction . . 214 MichaelJ. C. Gordon AFormalApproachtoProbabilisticTermination. ... ... 230 JoeHurd UsingTheoremProvingforNumericalAnalysis. ... ... . 246 MicaelaMayero QuotientTypes:AModularApproach. ... ... ... 263 AlekseyNogin SequentSchemaforDerivedRules ... ... ... . 281 AlekseyNogin, JasonHickey AlgebraicStructuresandDependentRecords ... ... . 298 VirgilePrevosto, DamienDoligez, Thþ er` eseHardin ProvingtheEquivalenceofMicrostepandMacrostepSemantics. ... 314 KlausSchneider WeakestPreconditionforGeneralRecursiveProgramsFormalizedinCoq.

Author: Peter Selinger
Publisher:
ISBN: 9780359158850
Category : Science
Languages : en
Pages : 108

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This is a set of lecture notes that developed out of courses on the lambda calculus that the author taught at the University of Ottawa in 2001 and at Dalhousie University in 2007 and 2013. Topics covered in these notes include the untyped lambda calculus, the Church-Rosser theorem, combinatory algebras, the simply-typed lambda calculus, the Curry-Howard isomorphism, weak and strong normalization, polymorphism, type inference, denotational semantics, complete partial orders, and the language PCF.

Author: Claudia Casadio
Publisher: Springer Nature
ISBN: 3030665453
Category : Philosophy
Languages : en
Pages : 432

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Book Description
This book is dedicated to the life and work of the mathematician Joachim Lambek (1922–2014). The editors gather together noted experts to discuss the state of the art of various of Lambek’s works in logic, category theory, and linguistics and to celebrate his contributions to those areas over the course of his multifaceted career. After early work in combinatorics and elementary number theory, Lambek became a distinguished algebraist (notably in ring theory). In the 1960s, he began to work in category theory, categorical algebra, logic, proof theory, and foundations of computability. In a parallel development, beginning in the late 1950s and for the rest of his career, Lambek also worked extensively in mathematical linguistics and computational approaches to natural languages. He and his collaborators perfected production and type grammars for numerous natural languages. Lambek grammars form an early noncommutative precursor to Girard’s linear logic. In a surprising development (2000), he introduced a novel and deeper algebraic framework (which he called pregroup grammars) for analyzing natural language, along with algebraic, higher category, and proof-theoretic semantics. This book is of interest to mathematicians, logicians, linguists, and computer scientists.

Author: Samuel Mimram
Publisher:
ISBN:
Category :
Languages : en
Pages : 539

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Book Description
This course provides a first introduction to the Curry-Howard correspondence between programs and proofs, from a theoretical programmer's perspective: we want to understand the theory behind logic and programming languages, but also to write concrete programs (in OCaml) and proofs (in Agda). After an introduction to functional programming languages, we present propositional logic, λ-calculus, the Curry-Howard correspondence, first-order logic, Agda, dependent types and homotopy type theory.

Author: B. Jacobs
Publisher: Gulf Professional Publishing
ISBN: 9780444508539
Category : Computers
Languages : en
Pages : 784

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Book Description
This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.