Characterisation of Approximation and (Head) Normalisation for λμ using Strict Intersection Types

Bakel, Steffen van

doi:10.4204/eptcs.242.4

Cited by 1 publication

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“…The results presented in sections 7, 8, and 9 are based on results presented in [9], although that paper dealt with a slightly different notion of type assignment. We will write n for the set {1, .…”

Section: Notementioning

confidence: 99%

Characterisation of Normalisation Properties for λμ using Strict Negated Intersection Types

Bakel

2018

ACM Trans. Comput. Logic

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We show characterisation results for normalisation, head-normalisation, and strong normalisation for λ μ using intersection types. We reach these results for a strict notion of type assignment for λ μ that is the natural restriction of the domain-based system of van Bakel et al. (2011) for λ μ by limiting the type inclusion relation to just intersection elimination. We show that this system respects β μ-equality, by showing both soundness and completeness results. We then define a notion of reduction on derivations that corresponds to cut-elimination, and show that this is strongly normalisable. We use this strong normalisation result to show an approximation result, and through that a characterisation of head-normalisation. Using the approximation result, we show that there is a very strong relation between the system of van Bakel et al. (2011) and ours. We then introduce a notion of type assignment that eliminates ω as an assignable type, and show, using the strong normalisation result for derivation reduction, that all terms typeable in this system are strongly normalisable as well, and show that all strongly normalisable terms are typeable. We conclude by adding type variables to our system, and show that system essentially is that of van Bakel (2010b).

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Section: Notementioning

confidence: 99%

Characterisation of Normalisation Properties for λμ using Strict Negated Intersection Types

Bakel

2018

ACM Trans. Comput. Logic

View full text Add to dashboard Cite

show abstract

Characterisation of Approximation and (Head) Normalisation for λμ using Strict Intersection Types

Cited by 1 publication

References 20 publications

Characterisation of Normalisation Properties for λμ using Strict Negated Intersection Types

Characterisation of Normalisation Properties for λμ using Strict Negated Intersection Types

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