A syntactic theory of sequential control
Theoretical Computer Science
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
Lambda-calculus, types and models
Lambda-calculus, types and models
Free Deduction: An Analysis of "Computations" in Classical Logic
Proceedings of the First Russian Conference on Logic Programming
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 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
An environment machine for the λμ-calculus
Mathematical Structures in Computer Science
Separation with Streams in the ?µ-calculus
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
An approach to call-by-name delimited continuations
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A type-theoretic foundation of delimited continuations
Higher-Order and Symbolic Computation
Standardization and böhm trees for Λµ-calculus
FLOPS'10 Proceedings of the 10th international conference on Functional and Logic Programming
A hierarchy for delimited continuations in call-by-name
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
Böhm theorem and Böhm trees for the Λμ-calculus
Theoretical Computer Science
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Λμ-calculus is a Böhm-complete extension of Parigot's Λμ-calculus closely related with delimited control in functional programming. In this article, we investigate the meta-theory of untyped Λμ-calculus by proving confluence of the calculus and characterizing the basic observables for the Separation theorem, canonical normal forms. Then, we define Λs, a new type system for Λμ-calculus that contains a special type construction for streams, and prove that strong normalization and type preservation hold. Thanks to the new typing discipline of Λs, new computational behaviors can be observed, which were forbidden in previous type systems for λμ-calculi. Those new typed computational behaviors witness the stream interpretation of Λμ-calculus.