Introduction to higher order categorical logic
Introduction to higher order categorical logic
A formulae-as-type notion of control
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The revised report on the syntactic theories of sequential control and state
Theoretical Computer Science
A Curry-Howard foundation for functional computation with control
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Lambda-My-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
On the Relation between the Lambda-Mu-Calculus and the Syntactic Theory of Sequential Control
LPAR '94 Proceedings of the 5th International Conference on Logic Programming and Automated Reasoning
A CPS-Translation of the Lambda-µ-Calculus
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
A semantic view of classical proofs: type-theoretic, categorical, and denotational characterizations
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Continuation models are universal for lambda-mu-calculus
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
The calculi of lambda-nu-cs conversion: a syntactic theory of control and state in imperative higher-order programming languages
Premonoidal categories and notions of computation
Mathematical Structures in Computer Science
Classical logic, continuation semantics and abstract machines
Journal of Functional Programming
An interpretation of λµ-calculus in λ-calculus
Information Processing Letters
Axioms for Recursion in Call-by-Value
Higher-Order and Symbolic Computation
Polarized proof-nets and λµ-calculus
Theoretical Computer Science
Axioms for Recursion in Call-by-Value
FoSSaCS '01 Proceedings of the 4th International Conference on Foundations of Software Science and Computation Structures
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
Strong Normalization of Second Order Symmetric lambda-Calculus
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
On the Computational Interpretation of Negation
Proceedings of the 14th Annual Conference of the EACSL on Computer Science Logic
A Proof Theoretical Account of Continuation Passing Style
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Duality between Call-by-Name Recursion and Call-by-Value Iteration
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Call-by-value is dual to call-by-name
ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
On the call-by-value CPS transform and its semantics
Information and Computation
Classical isomorphisms of types
Mathematical Structures in Computer Science
Syntax vs. semantics: a polarized approach
Theoretical Computer Science - Game theory meets theoretical computer science
Investigations on the Dual Calculus
Theoretical Computer Science
Call-by-push-value: Decomposing call-by-value and call-by-name
Higher-Order and Symbolic Computation
Game semantics and linear CPS interpretation
Theoretical Computer Science - Foundations of software science and computation structures
Categorical proof theory of classical propositional calculus
Theoretical Computer Science - Logic, language, information and computation
Parameterizations and Fixed-Point Operators on Control Categories
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
Relational Parametricity for Control Considered as a Computational Effect
Electronic Notes in Theoretical Computer Science (ENTCS)
A proof-theoretic foundation of abortive continuations
Higher-Order and Symbolic Computation
Focusing and higher-order abstract syntax
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
An approach to call-by-name delimited continuations
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proofs, tests and continuation passing style
ACM Transactions on Computational Logic (TOCL)
Refinement types and computational duality
Proceedings of the 3rd workshop on Programming languages meets program verification
Denotational Semantics of Call-by-name Normalization in Lambda-mu Calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
Dual Calculus with Inductive and Coinductive Types
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Theoretical Computer Science
Classical Natural Deduction for S4 Modal Logic
APLAS '09 Proceedings of the 7th Asian Symposium on Programming Languages and Systems
Asynchronous Games 3 An Innocent Model of Linear Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Continuation semantics for the Lambek--Grishin calculus
Information and Computation
Categorical semantics of control
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
A sound and complete CPS-translation for λµ-calculus
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
Parameterizations and fixed-point operators on control categories
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
Polarized proof nets with cycles and fixpoints semantics
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
Continuation semantics for symmetric categorial grammar
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
A substructural type system for delimited continuations
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
Call-by-name and call-by-value in normal modal logic
APLAS'07 Proceedings of the 5th Asian conference on Programming languages and systems
Call-by-value is dual to call-by-name, extended
APLAS'07 Proceedings of the 5th Asian conference on Programming languages and systems
What is the problem with proof nets for classical logic?
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Cartesian effect categories are Freyd-categories
Journal of Symbolic Computation
Negative translations and duality: toward a unified approach
Ludics, dialogue and interaction
Classical call-by-need and duality
TLCA'11 Proceedings of the 10th international conference on Typed lambda calculi and applications
Strong normalization of the dual classical sequent calculus
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Galois embedding from polymorphic types into existential types
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Call-by-value is dual to call-by-name: reloaded
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Call-by-value is dual to call-by-name: reloaded
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Game Semantics in String Diagrams
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Parameterizations and Fixed-Point Operators on Control Categories
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
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We give a categorical semantics to the call-by-name and call-by-value versions of Parigot's λμ-calculus with disjunction types. We introduce the class of control categories, which combine a cartesian-closed structure with a premonoidal structure in the sense of Power and Robinson. We prove, via a categorical structure theorem, that the categorical semantics is equivalent to a CPS semantics in the style of Hofmann and Streicher. We show that the call-by-name λμ-calculus forms an internal language for control categories, and that the call-by-value λμ-calculus forms an internal language for the dual co-control categories. As a corollary, we obtain a syntactic duality result: there exist syntactic translations between call-by-name and call-by-value that are mutually inverse and preserve the operational semantics. This answers a question of Streicher and Reus.