Complete restrictions of the intersection type discipline
Theoretical Computer Science
Handbook of logic in computer science (vol. 2)
Lambda-calculus, types and models
Lambda-calculus, types and models
&lgr;&bgr;′—A &lgr;-calculus with a generalized &bgr;-reduction rule
Information Processing Letters
Perpetual reductions in &lgr;-calculus
Information and Computation
The Conservation Theorem revisited
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Behavioural inverse limit λ-models
Theoretical Computer Science - Logic, semantics and theory of programming
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We use the system of intersection types and the type assignment method to prove termination properties in λ-calculus. In the first part we deal with conservation properties. We give a type assignment proof of the classical conservation theorem for λI calculus and then we extend this method to the notion of the reduction βI and βS of de Groote [9]. We also give a direct type assignment proof of the extended conservation property according to which if a term is βI, βS-normalizable then it is β-strongly normalizable. We further extend the conservation theorem by introducing the notion of β*-normal form. In the second part we prove that if Ω is not a substring of a λ-term M then M can be typed in the Krivine's system D of intersection types. In that way we obtain a type assignment proof of the Sørensen's Ω-theorem.