A syntactic theory of sequential control
Theoretical Computer Science
Proofs and types
A formulae-as-type notion of control
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Games and full completeness for multiplicative linear logic
Journal of Symbolic Logic
A semantics of evidence for classical arithmetic
Journal of Symbolic Logic
Pi-calculus, dialogue games and full abstraction PCF
FPCA '95 Proceedings of the seventh international conference on Functional programming languages and computer architecture
Lambda-My-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Extracting Constructive Content from Classical Logic via Control-like Reductions
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
A Lambda-Calculus Structure Isomorphic to Gentzen-Style Sequent Calculus Structure
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
Program Extraction from Classical Proofs
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
A CPS-Translation of the Lambda-µ-Calculus
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
A Curry-Howard foundation for functional computation with control
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
CPS translating inductive and coinductive types
PEPM '02 Proceedings of the 2002 ACM SIGPLAN workshop on Partial evaluation and semantics-based program manipulation
An interpretation of λµ-calculus in λ-calculus
Information Processing Letters
Explicitly Typed lambda µ-Calculus for Polymorphism an Call-by-Value
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
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
Computational isomorphisms in classical logic
Theoretical Computer Science - Linear logic
Completeness of continuation models for λµ-calculus
Information and Computation - Special issue: LICS'97
Call-by-value is dual to call-by-name
ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
Sequentiality vs. concurrency in games and logic
Mathematical Structures in Computer Science
Control categories and duality: on the categorical semantics of the lambda-mu calculus
Mathematical Structures in Computer Science
Mathematical Structures in Computer Science
A confluent λ-calculus with a catch/throw mechanism
Journal of Functional Programming
An approach to call-by-name delimited continuations
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
On the Relations between the Syntactic Theories of λμ-Calculi
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Denotational Semantics of Call-by-name Normalization in Lambda-mu Calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
Game Semantics for Access Control
Electronic Notes in Theoretical Computer Science (ENTCS)
Categorical semantics of control
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
Typing streams in the Λμ-calculus
ACM Transactions on Computational Logic (TOCL)
A filter model for the λµ-calculus
TLCA'11 Proceedings of the 10th 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
Böhm theorem and Böhm trees for the Λμ-calculus
Theoretical Computer Science
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Classical logic is one of the best examples of a mathematical theory that is truly useful to computer science. Hardware and software engineers apply the theory routinely. Yet from a foundational standpoint, there are aspects of classical logic that are problematic. Unlike intuitionistic logic, classical logic is often held to be non-constructive, and so, is said to admit no proof semantics. To draw an analogy in the proofs- as-programs paradigm, it is as if we understand well the theory of manipulation between equivalent specifications (which we do), but have comparatively little foundational insight of the process of transforming one program to another that implements the same specification. This extended abstract outlines a {\em semantic} theory of classical proofs based on a variant of Parigot's $\lambda\mu$-calculus \cite{Par92}, but presented here as a type theory. After reviewing the conceptual problems in the area and the potential benefits of such a theory, we sketch the key steps of our approach in terms of the questions that we have sought to answer: - Syntax: How should one circumscribe a coherent system of classical proofs? Is there a satisfactory Curry-Howard style representation theory? - Categorical characterization: What is the ``boolean algebra'' of classical propositional proofs (as opposed to validity)? What manner of categories characterizes classical proofs the same way that cartesian closed categories capture intuitionistic propositional proofs? - Complete denotational models: Are there good intensional game models of classical logic canonical for the circumscribed proofs? We give an overview of an approach to understand classical propositional proofs based on a Curry-Howard style, type- theoretic presentation of a variant of Parigot's $\lambda\mu$-calculus. The intrinsic notion of equality between proofs is consistent, decidable, congruent, and compatible with cut. We give a categorical characterization of $\lambdamu$, and construct a game model that satisfies a completeness property.