
The Deltacalculus: syntax and types
We present the Deltacalculus, an explicitly typed lambdacalculus with ...
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Sequence Types and Infinitary Semantics
We introduce a new representation of nonidempotent intersection types, ...
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Natural Deduction and Normalization Proofs for the Intersection Type Discipline
Refining and extending previous work by Retoré, we develop a systematic ...
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Intersection Types and (Positive) AlmostSure Termination
Randomized higherorder computation can be seen as being captured by a l...
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The Space of Interaction (long version)
The space complexity of functional programs is not well understood. In p...
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Intersection Type Distributors
Building on previous works, we present a general method to define proof ...
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Intersection Types for Unboundedness Problems
Intersection types have been originally developed as an extension of sim...
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Factoring Derivation Spaces via Intersection Types (Extended Version)
In typical nonidempotent intersection type systems, proof normalization is not confluent. In this paper we introduce a confluent nonidempotent intersection type system for the lambdacalculus. 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 lambdacalculus is established by simulation theorems. The machinery of nonidempotent 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 lambdaterm may be factorized using a variant of the Grothendieck construction for semilattices. This means, in particular, that any derivation in the lambdacalculus can be uniquely written as a garbagefree prefix followed by garbage.
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