A syntactic theory of sequential control
Theoretical Computer Science
Abstract continuations: a mathematical semantics for handling full jumps
LFP '88 Proceedings of the 1988 ACM conference on LISP and functional programming
Parallel reductions in λ-calculus
Journal of Symbolic Computation
The theory and practice of first-class prompts
POPL '88 Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
LFP '90 Proceedings of the 1990 ACM conference on LISP and functional programming
A formulae-as-type notion of control
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A dynamic extent control operator for partial continuations
POPL '91 Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The revised report on the syntactic theories of sequential control and state
Theoretical Computer Science
POPL '94 Proceedings of the 21st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A generalization of exceptions and control in ML-like languages
FPCA '95 Proceedings of the seventh international conference on Functional programming languages and computer architecture
Intuitionistic and classical natural deduction systems with the catch and the throw rules
NSL '94 Proceedings of the first workshop on Non-standard logics and logical aspects of computer science
A Curry-Howard foundation for functional computation with control
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Strong normalizability of the non-deterministic catch/throw calculi
Theoretical Computer Science - Special issue on theories of types and proofs
Lambda-My-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
A Simple Calculus of Exception Handling
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
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Partial continuations are control operators in functional programming such that a function-like object is abstracted from a part of the rest of computation, rather than the whole rest of computation. Several different formulations of partial continuations have been proposed by Felleisen, Danvy&Filinski, Hieb et al, and others, but as far as we know, no one ever studied logic for partial continuations, nor proposed a typed calculus of partial continuations which corresponds to a logical system through the Curry-Howard isomorphism. This paper gives a simple type-theoretic formulation of a form of partial continuations (which we call delimited continuations), and study its properties. Our calculus does reflect the intended operational semantics, and enjoys nice properties such as subject reduction and confluence. By restricting the type of delimiters to be atomic, we obtain the normal form property. We also show a few examples.