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- W2963404536 abstract "In typical non-idempotent intersection type systems, proof normalization is not confluent. In this paper we introduce a confluent non-idempotent intersection type system for the lambda-calculus. Typing derivations are presented using proof term syntax. The system enjoys good properties: subject reduction, strong normalization, and a very regular theory of residuals. A correspondence with the lambda-calculus is established by simulation theorems. The machinery of non-idempotent intersection types allows us to track the usage of resources required to obtain an answer. In particular, it induces a notion of garbage: a computation is garbage if it does not contribute to obtaining an answer. Using these notions, we show that the derivation space of a lambda-term may be factorized using a variant of the Grothendieck construction for semilattices. This means, in particular, that any derivation in the lambda-calculus can be uniquely written as a garbage-free prefix followed by garbage." @default.
- W2963404536 created "2019-07-30" @default.
- W2963404536 creator A5017542172 @default.
- W2963404536 creator A5038773699 @default.
- W2963404536 date "2019-07-20" @default.
- W2963404536 modified "2023-09-27" @default.
- W2963404536 title "Factoring Derivation Spaces via Intersection Types (Extended Version)." @default.
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- W2963404536 doi "https://doi.org/10.1007/978-3-030-02768-1\_2" @default.
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