A formulae-as-type notion of control
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Intersection and union types: syntax and semantics
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A symmetric lambda calculus for classical program extraction
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A Curry-Howard foundation for functional computation with control
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ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
Lambda terms for natural deduction, sequent calculus and cut elimination
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A calculus with polymorphic and polyvariant flow types
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From Polyvariant flow information to intersection and union types
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Minimal classical logic and control operators
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Structure of proofs and the complexity of cut elimination
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Intersection and Union Types in the λμμ~-calculus
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RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Strong normalization of the dual classical sequent calculus
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λµ-calculus and duality: call-by-name and call-by-value
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
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We investigate some fundamental properties of the reduction relation in the untyped term calculus derived from Curien and Herbelin's λμμ. The original λμμ has a system of simple types, based on sequent calculus, embodying a Curry-Howard correspondence with classical logic; the significance of the untyped calculus of raw terms is that it is a Turing-complete language for computation with explicit representation of control as well as code. We define a type assignment system for the raw terms satisfying: a term is typable if and only if it is strongly normalizing. The intrinsic symmetry in the λμμ calculus leads to an essential use of both intersection and union types; in contrast to other union-types systems in the literature, our system enjoys the Subject Reduction property.