Call-by-value non-determinism in a linear logic type discipline

We consider the call-by-value lambda-calculus extended with a may-convergent non-deterministic choice and a must-convergent parallel composition. Inspired by recent works on the relational semantics of linear logic and non-idempotent intersection types, we endow this calculus with a type system based on the so-called Girard's second translation of intuitionistic logic into linear logic. We prove that a term is typable if and only if it is converging, and that its typing tree carries enough information to give a bound on the length of its lazy call-by-value reduction. Moreover, when the typing tree is minimal, such a bound becomes the exact length of the reduction.

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